Decadimento alfa - Wikipedia

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vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Teoria_del_decadimento_alfa"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Teoria del decadimento alfa</span> </div> </a> <button aria-controls="toc-Teoria_del_decadimento_alfa-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Attiva/disattiva la sottosezione Teoria del decadimento alfa</span> </button> <ul id="toc-Teoria_del_decadimento_alfa-sublist" class="vector-toc-list"> <li id="toc-Equazione_di_Schrödinger" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Equazione_di_Schrödinger"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Equazione di Schrödinger</span> </div> </a> <ul id="toc-Equazione_di_Schrödinger-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Il_fattore_di_Gamow" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Il_fattore_di_Gamow"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Il fattore di Gamow</span> </div> </a> <ul id="toc-Il_fattore_di_Gamow-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Vita_media" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Vita_media"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Vita media</span> </div> </a> <ul id="toc-Vita_media-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Note" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Note"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Note</span> </div> </a> <ul id="toc-Note-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliografia" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliografia"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Bibliografia</span> </div> </a> <ul id="toc-Bibliografia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Voci_correlate" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Voci_correlate"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Voci correlate</span> </div> </a> <ul id="toc-Voci_correlate-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Altri_progetti" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Altri_progetti"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Altri progetti</span> </div> </a> <ul id="toc-Altri_progetti-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Collegamenti_esterni" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Collegamenti_esterni"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Collegamenti esterni</span> </div> </a> <ul id="toc-Collegamenti_esterni-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Indice" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Mostra/Nascondi l'indice" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Mostra/Nascondi l'indice</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Decadimento alfa</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Vai a una voce in un'altra lingua. Disponibile in 59 lingue" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-59" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">59 lingue</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Alfaverval" title="Alfaverval - afrikaans" lang="af" hreflang="af" data-title="Alfaverval" data-language-autonym="Afrikaans" data-language-local-name="afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A7%D8%B6%D9%85%D8%AD%D9%84%D8%A7%D9%84_%D8%A3%D9%84%D9%81%D8%A7" title="اضمحلال ألفا - arabo" lang="ar" hreflang="ar" data-title="اضمحلال ألفا" data-language-autonym="العربية" data-language-local-name="arabo" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Desintegraci%C3%B3n_alfa" title="Desintegración alfa - asturiano" lang="ast" hreflang="ast" data-title="Desintegración alfa" data-language-autonym="Asturianu" data-language-local-name="asturiano" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Alfa_da%C4%9F%C4%B1lmas%C4%B1" title="Alfa dağılması - azerbaigiano" lang="az" hreflang="az" data-title="Alfa dağılması" data-language-autonym="Azərbaycanca" data-language-local-name="azerbaigiano" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%90%D0%BB%D1%8C%D1%84%D0%B0-%D1%80%D0%B0%D1%81%D0%BF%D0%B0%D0%B4" title="Альфа-распад - bielorusso" lang="be" hreflang="be" data-title="Альфа-распад" data-language-autonym="Беларуская" data-language-local-name="bielorusso" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%90%D0%BB%D1%84%D0%B0-%D1%80%D0%B0%D0%B7%D0%BF%D0%B0%D0%B4" title="Алфа-разпад - bulgaro" lang="bg" hreflang="bg" data-title="Алфа-разпад" data-language-autonym="Български" data-language-local-name="bulgaro" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%86%E0%A6%B2%E0%A6%AB%E0%A6%BE_%E0%A6%95%E0%A7%8D%E0%A6%B7%E0%A6%AF%E0%A6%BC" title="আলফা ক্ষয় - bengalese" lang="bn" hreflang="bn" data-title="আলফা ক্ষয়" data-language-autonym="বাংলা" data-language-local-name="bengalese" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Desintegraci%C3%B3_%CE%B1" title="Desintegració α - catalano" lang="ca" hreflang="ca" data-title="Desintegració α" data-language-autonym="Català" data-language-local-name="catalano" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%90%D0%BB%D1%8C%D1%84%D0%B0-%D1%81%D0%B0%D0%BB%D0%B0%D0%BD%D1%83" title="Альфа-салану - ciuvascio" lang="cv" hreflang="cv" data-title="Альфа-салану" data-language-autonym="Чӑвашла" data-language-local-name="ciuvascio" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Alfahenfald" title="Alfahenfald - danese" lang="da" hreflang="da" data-title="Alfahenfald" data-language-autonym="Dansk" data-language-local-name="danese" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de badge-Q70894304 mw-list-item" title=""><a href="https://de.wikipedia.org/wiki/Alphazerfall" title="Alphazerfall - tedesco" lang="de" hreflang="de" data-title="Alphazerfall" data-language-autonym="Deutsch" data-language-local-name="tedesco" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%94%CE%B9%CE%AC%CF%83%CF%80%CE%B1%CF%83%CE%B7_%CE%AC%CE%BB%CF%86%CE%B1" title="Διάσπαση άλφα - greco" lang="el" hreflang="el" data-title="Διάσπαση άλφα" data-language-autonym="Ελληνικά" data-language-local-name="greco" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Alpha_decay" title="Alpha decay - inglese" lang="en" hreflang="en" data-title="Alpha decay" data-language-autonym="English" data-language-local-name="inglese" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Desintegraci%C3%B3n_alfa" title="Desintegración alfa - spagnolo" lang="es" hreflang="es" data-title="Desintegración alfa" data-language-autonym="Español" data-language-local-name="spagnolo" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Alfalagunemine" title="Alfalagunemine - estone" lang="et" hreflang="et" data-title="Alfalagunemine" data-language-autonym="Eesti" data-language-local-name="estone" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Alfa_desintegrazio" title="Alfa desintegrazio - basco" lang="eu" hreflang="eu" data-title="Alfa desintegrazio" data-language-autonym="Euskara" data-language-local-name="basco" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%88%D8%A7%D9%BE%D8%A7%D8%B4%DB%8C_%D8%A2%D9%84%D9%81%D8%A7" title="واپاشی آلفا - persiano" lang="fa" hreflang="fa" data-title="واپاشی آلفا" data-language-autonym="فارسی" data-language-local-name="persiano" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Alfahajoaminen" title="Alfahajoaminen - finlandese" lang="fi" hreflang="fi" data-title="Alfahajoaminen" data-language-autonym="Suomi" data-language-local-name="finlandese" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Radioactivit%C3%A9_%CE%B1" title="Radioactivité α - francese" lang="fr" hreflang="fr" data-title="Radioactivité α" data-language-autonym="Français" data-language-local-name="francese" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Alfa-mheath" title="Alfa-mheath - irlandese" lang="ga" hreflang="ga" data-title="Alfa-mheath" data-language-autonym="Gaeilge" data-language-local-name="irlandese" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A7%D7%A8%D7%99%D7%A0%D7%AA_%D7%90%D7%9C%D7%A4%D7%90" title="קרינת אלפא - ebraico" lang="he" hreflang="he" data-title="קרינת אלפא" data-language-autonym="עברית" data-language-local-name="ebraico" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%85%E0%A4%B2%E0%A5%8D%E0%A4%AB%E0%A4%BE_%E0%A4%95%E0%A5%8D%E0%A4%B7%E0%A4%AF" title="अल्फा क्षय - hindi" lang="hi" hreflang="hi" data-title="अल्फा क्षय" data-language-autonym="हिन्दी" data-language-local-name="hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr badge-Q17437796 badge-featuredarticle mw-list-item" title="voce in vetrina"><a href="https://hr.wikipedia.org/wiki/Alfa_raspad" title="Alfa raspad - croato" lang="hr" hreflang="hr" data-title="Alfa raspad" data-language-autonym="Hrvatski" data-language-local-name="croato" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Alfa-r%C3%A9szecske" title="Alfa-részecske - ungherese" lang="hu" hreflang="hu" data-title="Alfa-részecske" data-language-autonym="Magyar" data-language-local-name="ungherese" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B1%D5%AC%D6%86%D5%A1-%D5%BF%D6%80%D5%B8%D5%B0%D5%B8%D6%82%D5%B4" title="Ալֆա-տրոհում - armeno" lang="hy" hreflang="hy" data-title="Ալֆա-տրոհում" data-language-autonym="Հայերեն" data-language-local-name="armeno" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Peluruhan_alfa" title="Peluruhan alfa - indonesiano" lang="id" hreflang="id" data-title="Peluruhan alfa" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesiano" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Alfasundrun" title="Alfasundrun - islandese" lang="is" hreflang="is" data-title="Alfasundrun" data-language-autonym="Íslenska" data-language-local-name="islandese" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%82%A2%E3%83%AB%E3%83%95%E3%82%A1%E5%B4%A9%E5%A3%8A" title="アルファ崩壊 - giapponese" lang="ja" hreflang="ja" data-title="アルファ崩壊" data-language-autonym="日本語" data-language-local-name="giapponese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%90%E1%83%9A%E1%83%A4%E1%83%90-%E1%83%93%E1%83%90%E1%83%A8%E1%83%9A%E1%83%90" title="ალფა-დაშლა - georgiano" lang="ka" hreflang="ka" data-title="ალფა-დაშლა" data-language-autonym="ქართული" data-language-local-name="georgiano" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%90%D0%BB%D1%8C%D1%84%D0%B0-%D1%8B%D0%B4%D1%8B%D1%80%D0%B0%D1%83" title="Альфа-ыдырау - kazako" lang="kk" hreflang="kk" data-title="Альфа-ыдырау" data-language-autonym="Қазақша" data-language-local-name="kazako" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%95%8C%ED%8C%8C_%EB%B6%95%EA%B4%B4" title="알파 붕괴 - coreano" lang="ko" hreflang="ko" data-title="알파 붕괴" data-language-autonym="한국어" data-language-local-name="coreano" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Alfa_skilimas" title="Alfa skilimas - lituano" lang="lt" hreflang="lt" data-title="Alfa skilimas" data-language-autonym="Lietuvių" data-language-local-name="lituano" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Alfa_sabruk%C5%A1ana" title="Alfa sabrukšana - lettone" lang="lv" hreflang="lv" data-title="Alfa sabrukšana" data-language-autonym="Latviešu" data-language-local-name="lettone" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%90%D0%BB%D1%84%D0%B0-%D1%80%D0%B0%D1%81%D0%BF%D0%B0%D0%B4" title="Алфа-распад - macedone" lang="mk" hreflang="mk" data-title="Алфа-распад" data-language-autonym="Македонски" data-language-local-name="macedone" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%86%E0%B5%BD%E0%B4%AB%E0%B4%BE_%E0%B4%B6%E0%B5%8B%E0%B4%B7%E0%B4%A3%E0%B4%82" title="ആൽഫാ ശോഷണം - malayalam" lang="ml" hreflang="ml" data-title="ആൽഫാ ശോഷണം" data-language-autonym="മലയാളം" data-language-local-name="malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%90%D0%BB%D1%8C%D1%84%D0%B0_%D0%B7%D0%B0%D0%B4%D1%80%D0%B0%D0%BB" title="Альфа задрал - mongolo" lang="mn" hreflang="mn" data-title="Альфа задрал" data-language-autonym="Монгол" data-language-local-name="mongolo" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Pereputan_alfa" title="Pereputan alfa - malese" lang="ms" hreflang="ms" data-title="Pereputan alfa" data-language-autonym="Bahasa Melayu" data-language-local-name="malese" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl badge-Q70894304 mw-list-item" title=""><a href="https://nl.wikipedia.org/wiki/Alfaverval" title="Alfaverval - olandese" lang="nl" hreflang="nl" data-title="Alfaverval" data-language-autonym="Nederlands" data-language-local-name="olandese" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Radioactivitat_%CE%B1" title="Radioactivitat α - occitano" lang="oc" hreflang="oc" data-title="Radioactivitat α" data-language-autonym="Occitan" data-language-local-name="occitano" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Rozpad_alfa" title="Rozpad alfa - polacco" lang="pl" hreflang="pl" data-title="Rozpad alfa" data-language-autonym="Polski" data-language-local-name="polacco" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Emiss%C3%A3o_alfa" title="Emissão alfa - portoghese" lang="pt" hreflang="pt" data-title="Emissão alfa" data-language-autonym="Português" data-language-local-name="portoghese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Dezintegrare_alfa" title="Dezintegrare alfa - rumeno" lang="ro" hreflang="ro" data-title="Dezintegrare alfa" data-language-autonym="Română" data-language-local-name="rumeno" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%90%D0%BB%D1%8C%D1%84%D0%B0-%D1%80%D0%B0%D1%81%D0%BF%D0%B0%D0%B4" title="Альфа-распад - russo" lang="ru" hreflang="ru" data-title="Альфа-распад" data-language-autonym="Русский" data-language-local-name="russo" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Alfa_raspad" title="Alfa raspad - serbo-croato" lang="sh" hreflang="sh" data-title="Alfa raspad" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbo-croato" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%87%E0%B6%BD%E0%B7%8A%E0%B7%86%E0%B7%8F_%E0%B6%9A%E0%B7%8A%E0%B7%82%E0%B6%BA%E0%B7%80%E0%B7%93%E0%B6%B8%E0%B7%8A" title="ඇල්ෆා ක්ෂයවීම් - singalese" lang="si" hreflang="si" data-title="ඇල්ෆා ක්ෂයවීම්" data-language-autonym="සිංහල" data-language-local-name="singalese" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Alfa_rozpad" title="Alfa rozpad - slovacco" lang="sk" hreflang="sk" data-title="Alfa rozpad" data-language-autonym="Slovenčina" data-language-local-name="slovacco" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Razpad_alfa" title="Razpad alfa - sloveno" lang="sl" hreflang="sl" data-title="Razpad alfa" data-language-autonym="Slovenščina" data-language-local-name="sloveno" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%90%D0%BB%D1%84%D0%B0_%D1%80%D0%B0%D1%81%D0%BF%D0%B0%D0%B4" title="Алфа распад - serbo" lang="sr" hreflang="sr" data-title="Алфа распад" data-language-autonym="Српски / srpski" data-language-local-name="serbo" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Alfas%C3%B6nderfall" title="Alfasönderfall - svedese" lang="sv" hreflang="sv" data-title="Alfasönderfall" data-language-autonym="Svenska" data-language-local-name="svedese" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%85%E0%AE%B2%E0%AF%8D%E0%AE%83%E0%AE%AA%E0%AE%BE_%E0%AE%9A%E0%AE%BF%E0%AE%A4%E0%AF%88%E0%AE%B5%E0%AF%81" title="அல்ஃபா சிதைவு - tamil" lang="ta" hreflang="ta" data-title="அல்ஃபா சிதைவு" data-language-autonym="தமிழ்" data-language-local-name="tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%AA%E0%B8%A5%E0%B8%B2%E0%B8%A2%E0%B9%83%E0%B8%AB%E0%B9%89%E0%B8%AD%E0%B8%99%E0%B8%B8%E0%B8%A0%E0%B8%B2%E0%B8%84%E0%B9%81%E0%B8%AD%E0%B8%A5%E0%B8%9F%E0%B8%B2" title="การสลายให้อนุภาคแอลฟา - thailandese" lang="th" hreflang="th" data-title="การสลายให้อนุภาคแอลฟา" data-language-autonym="ไทย" data-language-local-name="thailandese" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Alfa_bozunmas%C4%B1" title="Alfa bozunması - turco" lang="tr" hreflang="tr" data-title="Alfa bozunması" data-language-autonym="Türkçe" data-language-local-name="turco" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%90%D0%BB%D1%8C%D1%84%D0%B0-%D1%82%D0%B0%D1%80%D0%BA%D0%B0%D0%BB%D1%8B%D1%88" title="Альфа-таркалыш - tataro" lang="tt" hreflang="tt" data-title="Альфа-таркалыш" data-language-autonym="Татарча / tatarça" data-language-local-name="tataro" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%90%D0%BB%D1%8C%D1%84%D0%B0-%D1%80%D0%BE%D0%B7%D0%BF%D0%B0%D0%B4" title="Альфа-розпад - ucraino" lang="uk" hreflang="uk" data-title="Альфа-розпад" data-language-autonym="Українська" data-language-local-name="ucraino" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Alfa-parchalanish" title="Alfa-parchalanish - uzbeco" lang="uz" hreflang="uz" data-title="Alfa-parchalanish" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbeco" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Ph%C3%A2n_r%C3%A3_alpha" title="Phân rã alpha - vietnamita" lang="vi" hreflang="vi" data-title="Phân rã alpha" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamita" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%CE%91%E8%A1%B0%E5%8F%98" title="Α衰变 - cinese" lang="zh" hreflang="zh" data-title="Α衰变" data-language-autonym="中文" data-language-local-name="cinese" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Alpha_soe-pi%C3%A0n" title="Alpha soe-piàn - min nan" lang="nan" hreflang="nan" data-title="Alpha soe-piàn" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="min nan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link 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class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Strumenti</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">sposta nella barra laterale</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">nascondi</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Altre opzioni" > <div 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class="vector-menu-heading"> Generale </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Speciale:PuntanoQui/Decadimento_alfa" title="Elenco di tutte le pagine che sono collegate a questa [j]" accesskey="j"><span>Puntano qui</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Speciale:ModificheCorrelate/Decadimento_alfa" rel="nofollow" title="Elenco delle ultime modifiche alle pagine collegate a questa [k]" accesskey="k"><span>Modifiche correlate</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Speciale:PagineSpeciali" title="Elenco di tutte le pagine speciali [q]" accesskey="q"><span>Pagine speciali</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Decadimento_alfa&oldid=139111622" title="Collegamento permanente a questa versione di questa pagina"><span>Link permanente</span></a></li><li id="t-info" 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hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q179856" title="Collegamento all'elemento connesso dell'archivio dati [g]" accesskey="g"><span>Elemento Wikidata</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Strumenti pagine"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Aspetto"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Aspetto</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">sposta nella barra laterale</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">nascondi</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Da Wikipedia, l'enciclopedia libera.</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="it" dir="ltr"><p>In <a href="/wiki/Fisica_nucleare" title="Fisica nucleare">fisica nucleare</a> il <b>decadimento alfa</b> è quel tipo di <a href="/wiki/Decadimento_radioattivo" class="mw-redirect" title="Decadimento radioattivo">decadimento radioattivo</a> per cui un <a href="/wiki/Nucleo_atomico" title="Nucleo atomico">nucleo atomico</a> instabile (<a href="/wiki/Radionuclide" title="Radionuclide">radionuclide</a>) di un dato <a href="/wiki/Elemento_chimico" title="Elemento chimico">elemento chimico</a> decade emettendo una <a href="/wiki/Particella_%CE%B1" title="Particella α">particella α</a>, ossia un nucleo di <sup>4</sup><a href="/wiki/Elio" title="Elio">He</a>, <a href="/wiki/Trasmutazione" title="Trasmutazione">trasmutandosi</a> in un nucleo di un altro elemento. In tal modo il <a href="/wiki/Numero_di_massa" title="Numero di massa">numero di massa</a> del radionuclide viene ridotto di 4 unità e il suo <a href="/wiki/Numero_atomico" title="Numero atomico">numero atomico</a> di 2 unità; il <a href="/wiki/Nuclide" title="Nuclide">nuclide</a> così prodotto può essere stabile così, o essere ancora <a href="/wiki/Radioattivit%C3%A0" title="Radioattività">radioattivo</a> e decadere a sua volta. Il decadimento alfa è tipico dei radionuclidi che presentano un eccesso di <a href="/wiki/Protoni" class="mw-redirect" title="Protoni">protoni</a> rispetto ai neutroni<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>. </p><p>Il decadimento alfa è un <a href="/wiki/Fenomeno_fisico" class="mw-redirect" title="Fenomeno fisico">fenomeno fisico</a> che si basa sull'<a href="/wiki/Effetto_tunnel" title="Effetto tunnel">effetto tunnel</a>, e quindi non spiegabile dalla <a href="/wiki/Meccanica_classica" title="Meccanica classica">meccanica classica</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Descrizione">Descrizione</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Decadimento_alfa&veaction=edit&section=1" title="Modifica la sezione Descrizione" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Decadimento_alfa&action=edit&section=1" title="Edit section's source code: Descrizione"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Il <b>decadimento alfa</b> avviene in accordo con la <a href="/wiki/E%3Dmc%5E2" class="mw-redirect" title="E=mc^2">legge di conservazione della massa/energia</a> con l'emissione di una particella, detta appunto <a href="/wiki/Particella_%CE%B1" title="Particella α">particella α</a>, composta da due <a href="/wiki/Protone" title="Protone">protoni</a> e due <a href="/wiki/Neutrone" title="Neutrone">neutroni</a>, da un <a href="/wiki/Isotopo" title="Isotopo">isotopo</a> radioattivo di un elemento con elevato numero atomico (Z>83). In generale si può dire che il decadimento alfa è un processo probabilistico che trasforma un nucleo con <a href="/wiki/Numero_di_massa" title="Numero di massa">numero di massa</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> (avente <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1cc6b75e09a8aa3f04d8584b11db534f88fb56bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.68ex; height:2.176ex;" alt="{\displaystyle Z}"></span> protoni e <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}"></span> neutroni) in un nucleo con numero di massa <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A-4}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>−</mo> <mn>4</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A-4}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb144e9d68d66eed5f0b18388dabce78268ecfd0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.746ex; height:2.343ex;" alt="{\displaystyle A-4}"></span> tramite l'emissione di un nucleo di <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ^{4}{\hbox{He}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>He</mtext> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ^{4}{\hbox{He}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c1483bddf437b184a1e660623d4ebed2e2cfe3d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.83ex; height:2.676ex;" alt="{\displaystyle ^{4}{\hbox{He}}}"></span> secondo lo schema di reazione<sup id="cite_ref-giorgio_bendiscioli_springer_pagina_113_2-0" class="reference"><a href="#cite_note-giorgio_bendiscioli_springer_pagina_113-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A_{1}(Z,N)\;\to \;A_{2}(Z-2,N-2)+\alpha .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>Z</mi> <mo>,</mo> <mi>N</mi> <mo stretchy="false">)</mo> <mspace width="thickmathspace" /> <mo stretchy="false">→</mo> <mspace width="thickmathspace" /> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>Z</mi> <mo>−</mo> <mn>2</mn> <mo>,</mo> <mi>N</mi> <mo>−</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>+</mo> <mi>α</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A_{1}(Z,N)\;\to \;A_{2}(Z-2,N-2)+\alpha .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eb4a215359f525dec243c2052f545f86c4575245" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:36.654ex; height:2.843ex;" alt="{\displaystyle A_{1}(Z,N)\;\to \;A_{2}(Z-2,N-2)+\alpha .}"></span></dd></dl> <p>Il <a href="/wiki/Numero_atomico" title="Numero atomico">numero dei protoni</a> passa da da <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1cc6b75e09a8aa3f04d8584b11db534f88fb56bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.68ex; height:2.176ex;" alt="{\displaystyle Z}"></span> a <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z-2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Z</mi> <mo>−</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z-2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d99f8c1ffad92958ca9a6a82811d93988efdb89" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.683ex; height:2.343ex;" alt="{\displaystyle Z-2}"></span> e il <a href="/wiki/Numero_neutronico" title="Numero neutronico">numero dei neutroni</a> passa da <i><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e3890c981ae85503089652feb48b191b57aae3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle N}"></span></i> a <i><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N-2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo>−</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N-2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9cdfb930783ca4ca0062df54535c6e35d555dd0c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:6.066ex; height:2.343ex;" alt="{\displaystyle N-2}"></span></i>. Perdendo due protoni, l'elemento indietreggia di due posizioni nella <a href="/wiki/Tavola_periodica" class="mw-redirect" title="Tavola periodica">tavola periodica</a> degli elementi.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>La stabilità dei nuclei atomici degli <a href="/wiki/Elemento_transuranico" class="mw-redirect" title="Elemento transuranico">elementi transuranici</a> è uno dei campi di ricerca più attivi della <a href="/wiki/Fisica_nucleare" title="Fisica nucleare">fisica nucleare</a>. Il decadimento alfa è tipico di nuclei con <a href="/wiki/Numero_di_massa" title="Numero di massa">numero di massa</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A>210}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>></mo> <mn>210</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A>210}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3fc7d590d323fde62029a60e98b802b46f94acc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.329ex; height:2.176ex;" alt="{\displaystyle A>210}"></span>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Dall'esame delle energie di decadimento alfa di svariati nuclidi (Q<sub>α</sub>) è possibile determinare una casistica in base al valore che assume <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> :<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <ul><li>per valori di <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A<140}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo><</mo> <mn>140</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A<140}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/76cde36d8b6518a8049c29a0dda85e638ffc7f77" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.329ex; height:2.176ex;" alt="{\displaystyle A<140}"></span> Q<sub>α</sub> è quasi sempre negativa, quindi il decadimento generalmente non avviene, anche se esistono due eccezioni per i nuclei del <a href="/wiki/Berillio" title="Berillio">berillio</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ^{8}{Be}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mn>8</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> <mi>e</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ^{8}{Be}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/325c97ae4707cbc1217a3ccf76984a70fd0762d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.902ex; height:2.676ex;" alt="{\displaystyle ^{8}{Be}}"></span>) e del <a href="/wiki/Boro" title="Boro">boro</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ^{9}{B}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mn>9</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ^{9}{B}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/df1a63a08cad18606789bbfcd853c201f82349cb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.818ex; height:2.676ex;" alt="{\displaystyle ^{9}{B}}"></span>);</li> <li>per <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 140<A<210}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>140</mn> <mo><</mo> <mi>A</mi> <mo><</mo> <mn>210</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 140<A<210}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4f3c94db793683d0a04b802450e9ece0a8df94b1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:14.915ex; height:2.176ex;" alt="{\displaystyle 140<A<210}"></span> Q<sub>α</sub> è positiva, ma molto piccola (< 3 MeV); ciò comporta una bassa probabilità di decadimento e conseguente difficoltà di rivelazione. Tuttavia, è noto il decadimento α dei due nuclei del <a href="/wiki/Gadolinio" title="Gadolinio">gadolinio</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ^{162}{Gd}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mn>162</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mi>G</mi> <mi>d</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ^{162}{Gd}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/13b6adcf6a1eb26f1720a042ac7382fd1401b92e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.741ex; height:2.676ex;" alt="{\displaystyle ^{162}{Gd}}"></span>) e dell'<a href="/wiki/Afnio" title="Afnio">afnio</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ^{174}{Hf}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi></mi> <mrow class="MJX-TeXAtom-ORD"> <mn>174</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> <mi>f</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ^{174}{Hf}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7f6af4878f1789e3821a4541e497c37b2e5cfdf0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.04ex; height:3.009ex;" alt="{\displaystyle ^{174}{Hf}}"></span>), con <a href="/wiki/Tempo_di_dimezzamento" class="mw-redirect" title="Tempo di dimezzamento">tempi di dimezzamento</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t_{1/2}>10^{14}a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msub> <mo>></mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>14</mn> </mrow> </msup> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t_{1/2}>10^{14}a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e560f749d2c135b2883016083a89cd198b42f003" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:12.067ex; height:3.509ex;" alt="{\displaystyle t_{1/2}>10^{14}a}"></span>;</li></ul> <ul><li>per <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A>210}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>></mo> <mn>210</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A>210}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3fc7d590d323fde62029a60e98b802b46f94acc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.329ex; height:2.176ex;" alt="{\displaystyle A>210}"></span> Q<sub>α</sub> è positiva e grande (sopra i 3 M<a href="/wiki/Elettronvolt" title="Elettronvolt">eV</a>).</li></ul> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Alpha_Decay.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Alpha_Decay.svg/220px-Alpha_Decay.svg.png" decoding="async" width="220" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Alpha_Decay.svg/330px-Alpha_Decay.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/79/Alpha_Decay.svg/440px-Alpha_Decay.svg.png 2x" data-file-width="250" data-file-height="170" /></a><figcaption>Decadimento alfa</figcaption></figure> <p>Come molti processi <a href="/wiki/Meccanica_quantistica" title="Meccanica quantistica">quantistici</a>, anche il decadimento alfa è descritto da <a href="/wiki/Fisica_statistica" title="Fisica statistica">leggi statistiche</a>: la percentuale di <a href="/wiki/Atomo" title="Atomo">atomi</a> che, in un certo intervallo di tempo, subisce il <a href="/wiki/Decadimento_radioattivo" class="mw-redirect" title="Decadimento radioattivo">decadimento</a>, è una costante. Per dare un'unità di misura standard, si indica solitamente il tempo in cui metà degli atomi di un <a href="/wiki/Isotopo" title="Isotopo">isotopo</a> radioattivo decadono. Tale periodo prende il nome di <b><a href="/wiki/Emivita_(fisica)" title="Emivita (fisica)">emivita</a></b> dell'isotopo. Caratteristica del decadimento alfa è quella di avere emivite con un campo di variabilità molto ampio, da poche frazioni di <a href="/wiki/Secondo" title="Secondo">secondo</a> a migliaia di anni: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 10^{-7}s<t_{1/2}<10^{10}a,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>7</mn> </mrow> </msup> <mi>s</mi> <mo><</mo> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msub> <mo><</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msup> <mi>a</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 10^{-7}s<t_{1/2}<10^{10}a,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6ea5623a446bc57b34a9dfa99eb8edf6c70f8e2e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:21.561ex; height:3.509ex;" alt="{\displaystyle 10^{-7}s<t_{1/2}<10^{10}a,}"></span></dd></dl> <p>contrapposto a un ristretto campo di variabilità di energia liberata: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 4MeV<Q_{\alpha }<9MeV.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>4</mn> <mi>M</mi> <mi>e</mi> <mi>V</mi> <mo><</mo> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> <mo><</mo> <mn>9</mn> <mi>M</mi> <mi>e</mi> <mi>V</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 4MeV<Q_{\alpha }<9MeV.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1c3fa0f2534604497caec4a699efcd506239923a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:22.917ex; height:2.509ex;" alt="{\displaystyle 4MeV<Q_{\alpha }<9MeV.}"></span><sup id="cite_ref-giorgio_bendiscioli_springer_pagina_113_2-1" class="reference"><a href="#cite_note-giorgio_bendiscioli_springer_pagina_113-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup></dd></dl> <p>Nella maggior parte dei casi, gli isotopi instabili subiscono decadimenti di vario tipo in successione, e pertanto si parla di <b><a href="/wiki/Catena_di_decadimento" title="Catena di decadimento">catena di decadimento</a></b> di un isotopo, intendendo la sequenza di decadimenti che tale atomo percorre. Quasi tutte le catene di decadimento finiscono con un <a href="/wiki/Isotopo_stabile" title="Isotopo stabile">isotopo stabile</a> del <a href="/wiki/Piombo" title="Piombo">piombo</a>. </p><p>La <a href="/wiki/Vita_media" title="Vita media">vita media</a> di un elemento soggetto a questo tipo di decadimento è varia: si passa, infatti dagli oltre 10<sup>10</sup> <a href="/wiki/Anno" title="Anno">anni</a> del <a href="/wiki/Torio" title="Torio">torio</a>, alle frazioni di <a href="/wiki/Secondo" title="Secondo">secondo</a> del <a href="/wiki/Polonio" title="Polonio">polonio</a> 214 pari a 1,6 x 10<sup>−4</sup> s. Il decadimento più noto è però quello dell'<a href="/wiki/Uranio" title="Uranio">uranio</a>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {}_{92}^{238}{\hbox{U}}\;\to \;{}_{90}^{234}{\hbox{Th}}\;+\alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>92</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>238</mn> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>U</mtext> </mstyle> </mrow> <mspace width="thickmathspace" /> <mo stretchy="false">→</mo> <mspace width="thickmathspace" /> <msubsup> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>90</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>234</mn> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Th</mtext> </mstyle> </mrow> <mspace width="thickmathspace" /> <mo>+</mo> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {}_{92}^{238}{\hbox{U}}\;\to \;{}_{90}^{234}{\hbox{Th}}\;+\alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7146219c60d0b57032e705131693408d71dfa925" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:19.988ex; height:3.176ex;" alt="{\displaystyle {}_{92}^{238}{\hbox{U}}\;\to \;{}_{90}^{234}{\hbox{Th}}\;+\alpha }"></span></dd></dl> <p>dove <i>α</i> indica la <a href="/wiki/Particella_%CE%B1" title="Particella α">particella α</a> prodotta. </p><p>Il decadimento alfa è tipico degli isotopi radioattivi contenuti nelle <a href="/wiki/Scorie_nucleari" class="mw-redirect" title="Scorie nucleari">scorie nucleari</a> prodotte nella reazione di <a href="/wiki/Fissione_nucleare" title="Fissione nucleare">fissione nucleare</a> che avvengono nei <a href="/wiki/Reattore_nucleare_a_fissione" title="Reattore nucleare a fissione">reattori a fissione</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Teoria_del_decadimento_alfa">Teoria del decadimento alfa</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Decadimento_alfa&veaction=edit&section=2" title="Modifica la sezione Teoria del decadimento alfa" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Decadimento_alfa&action=edit&section=2" title="Edit section's source code: Teoria del decadimento alfa"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Barriera_coulombiana.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/89/Barriera_coulombiana.jpg/220px-Barriera_coulombiana.jpg" decoding="async" width="220" height="140" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/89/Barriera_coulombiana.jpg/330px-Barriera_coulombiana.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/89/Barriera_coulombiana.jpg/440px-Barriera_coulombiana.jpg 2x" data-file-width="733" data-file-height="468" /></a><figcaption>La barriera coulombiana</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Barriera_coulombiana_(alfa).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/97/Barriera_coulombiana_%28alfa%29.jpg/220px-Barriera_coulombiana_%28alfa%29.jpg" decoding="async" width="220" height="240" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/97/Barriera_coulombiana_%28alfa%29.jpg/330px-Barriera_coulombiana_%28alfa%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/9/97/Barriera_coulombiana_%28alfa%29.jpg 2x" data-file-width="423" data-file-height="461" /></a><figcaption>La barriera coulombiana (in verde l'energia cinetica della particella <i>α</i>)</figcaption></figure> <p>La teoria che sta alla base di tale decadimento è stata sviluppata dal <a href="/wiki/Fisico" title="Fisico">fisico</a> <a href="/wiki/Ucraina" title="Ucraina">ucraino</a> <a href="/wiki/George_Gamow" title="George Gamow">George Gamow</a> e si basa sull'<a href="/wiki/Effetto_tunnel" title="Effetto tunnel">effetto tunnel</a><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup>. </p><p>Si può prendere, come esempio di decadimento, quello del <a href="/wiki/Radio_(elemento_chimico)" title="Radio (elemento chimico)">radio</a>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {}_{88}^{226}{\hbox{Ra}}\;\to \;{}_{86}^{222}{\hbox{Rn}}\;+\alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>88</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>226</mn> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Ra</mtext> </mstyle> </mrow> <mspace width="thickmathspace" /> <mo stretchy="false">→</mo> <mspace width="thickmathspace" /> <msubsup> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>86</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>222</mn> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Rn</mtext> </mstyle> </mrow> <mspace width="thickmathspace" /> <mo>+</mo> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {}_{88}^{226}{\hbox{Ra}}\;\to \;{}_{86}^{222}{\hbox{Rn}}\;+\alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/29b8a08752a9acfc1aa5be11117cb77c0e215734" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:21.15ex; height:3.176ex;" alt="{\displaystyle {}_{88}^{226}{\hbox{Ra}}\;\to \;{}_{86}^{222}{\hbox{Rn}}\;+\alpha }"></span></dd></dl> <p>dove <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Rn}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Rn}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/677bbbc8b3a9f79df35a592eafb67fd6aec3b4c1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.159ex; height:2.176ex;" alt="{\displaystyle Rn}"></span> è il <a href="/wiki/Radon" title="Radon">radon</a>, il <a href="/wiki/Gas_nobile" class="mw-redirect" title="Gas nobile">gas nobile</a> successivo allo <a href="/wiki/Xeno" title="Xeno">xenon</a>. </p><p>Prima di scendere nel dettaglio, si supponga di unire <a href="/wiki/Due" class="mw-redirect" title="Due">due</a> <a href="/wiki/Nucleo_atomico" title="Nucleo atomico">nuclei</a> di <a href="/wiki/Deuterio" title="Deuterio">deuterio</a>: si otterrà una particella <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span>: ogni reazione di questo tipo dà un'energia di circa 10 <a href="/wiki/MeV" class="mw-redirect" title="MeV">MeV</a>. I due atomi, per unirsi, devono però superare la cosiddetta <a href="/wiki/Barriera_coulombiana" class="mw-redirect" title="Barriera coulombiana">barriera coulombiana</a>, che è anche la barriera che deve superare la particella <i>α</i> per poter uscire dal nucleo <i>decadente</i>. Ora, chiamando con <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{P}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{P}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b58bf73434769ef9bf999f369ec52a874358848" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.507ex; height:2.009ex;" alt="{\displaystyle m_{P}}"></span> la <a href="/wiki/Massa_(fisica)" title="Massa (fisica)">massa</a> del radio e con <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{D}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{D}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b38761ea3904a313a4086bfd223524736d8cd438" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.633ex; height:2.009ex;" alt="{\displaystyle m_{D}}"></span> quella del radon, si possono scrivere alcune relazioni energetiche<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{tot}^{i}=m_{p}c^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mi>o</mi> <mi>t</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msubsup> <mo>=</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{tot}^{i}=m_{p}c^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ecfd05011aecca1b5b8e42b88de1886ccea78cba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:12.191ex; height:3.343ex;" alt="{\displaystyle E_{tot}^{i}=m_{p}c^{2}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{tot}^{f}=m_{\alpha }c^{2}+m_{D}c^{2}+T_{\alpha }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mi>o</mi> <mi>t</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msubsup> <mo>=</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> </msub> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{tot}^{f}=m_{\alpha }c^{2}+m_{D}c^{2}+T_{\alpha }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65932b2aa9c7d24e7788d82c71963a10e6483e08" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:26.433ex; height:3.509ex;" alt="{\displaystyle E_{tot}^{f}=m_{\alpha }c^{2}+m_{D}c^{2}+T_{\alpha }}"></span></dd></dl> <p>e per la <a href="/wiki/Conservazione_dell%27energia" class="mw-redirect" title="Conservazione dell'energia">conservazione dell'energia</a> (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{tot}^{i}=E_{tot}^{f}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mi>o</mi> <mi>t</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> <mi>o</mi> <mi>t</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{tot}^{i}=E_{tot}^{f}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d29afdb112ff7c3f3056ad05815cb0b3780c016" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:10.963ex; height:3.509ex;" alt="{\displaystyle E_{tot}^{i}=E_{tot}^{f}}"></span>): </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{\alpha }=((m_{P}\left)-(m_{\alpha }+m_{D}\right))c^{2}>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> </mrow> </msub> <mrow> <mo>)</mo> <mrow> <mo>−</mo> <mo stretchy="false">(</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo stretchy="false">)</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{\alpha }=((m_{P}\left)-(m_{\alpha }+m_{D}\right))c^{2}>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/36b0a073ed0ec6e8fa81288d408370d86f4fd6ca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:32.99ex; height:3.176ex;" alt="{\displaystyle T_{\alpha }=((m_{P}\left)-(m_{\alpha }+m_{D}\right))c^{2}>0}"></span></dd></dl> <p>e quindi il decadimento avviene solo quando la massa del nucleo che decade (massa iniziale) è maggiore della somma delle masse dei nuclei prodotti. </p> <div class="mw-heading mw-heading3"><h3 id="Equazione_di_Schrödinger"><span id="Equazione_di_Schr.C3.B6dinger"></span>Equazione di Schrödinger</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Decadimento_alfa&veaction=edit&section=3" title="Modifica la sezione Equazione di Schrödinger" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Decadimento_alfa&action=edit&section=3" title="Edit section's source code: Equazione di Schrödinger"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Per studiare il decadimento, quindi, si fa intervenire l'<a href="/wiki/Equazione_di_Schr%C3%B6dinger" title="Equazione di Schrödinger">equazione di Schrödinger</a><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(H_{0}+V_{C}\right)\psi =E\psi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mi>ψ</mi> <mo>=</mo> <mi>E</mi> <mi>ψ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(H_{0}+V_{C}\right)\psi =E\psi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72ad5b482b8c19c2db7f941a4681f5bab332612c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.759ex; height:2.843ex;" alt="{\displaystyle \left(H_{0}+V_{C}\right)\psi =E\psi }"></span></dd></dl> <p>dove <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43910602a221b7a4c373791f94793e3008622070" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.985ex; height:2.509ex;" alt="{\displaystyle H_{0}}"></span> è l'<a href="/wiki/Operatore_hamiltoniano" title="Operatore hamiltoniano">hamiltoniana</a> che descrive l'<a href="/wiki/Energia_cinetica" title="Energia cinetica">energia cinetica</a> di due particelle, con masse <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{\alpha }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{\alpha }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/46cbcede3b6470d7e97fb926da5a426ac307f16d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.325ex; height:2.009ex;" alt="{\displaystyle m_{\alpha }}"></span> ed <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{D}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{D}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b38761ea3904a313a4086bfd223524736d8cd438" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.633ex; height:2.009ex;" alt="{\displaystyle m_{D}}"></span>. </p><p>Questo <a href="/wiki/Problema_dei_due_corpi" title="Problema dei due corpi">problema a due corpi</a> può essere semplicemente descritto come un problema ad un corpo solo separando la parte del moto relativo da quella del <a href="/wiki/Centro_di_massa" title="Centro di massa">centro di massa</a>, che non è interessante ai fini dell'interazione studiata. L'<a href="/wiki/Equazione" title="Equazione">equazione</a> diventa pertanto: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {p^{2}}{2\mu }}+V_{C}\right)\psi =E\psi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>2</mn> <mi>μ</mi> </mrow> </mfrac> </mrow> <mo>+</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mi>ψ</mi> <mo>=</mo> <mi>E</mi> <mi>ψ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {p^{2}}{2\mu }}+V_{C}\right)\psi =E\psi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cda83ae00efe854e62760e84c7b257b5e143656f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:20.786ex; height:6.343ex;" alt="{\displaystyle \left({\frac {p^{2}}{2\mu }}+V_{C}\right)\psi =E\psi }"></span></dd></dl> <p>dove: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}{\frac {1}{\mu }}&={\frac {1}{m_{\alpha }}}+{\frac {1}{m_{D}}}\\{\vec {p}}&={\frac {m_{D}{\vec {p}}_{\alpha }-m_{\alpha }{\vec {p}}_{D}}{m_{D}+m_{\alpha }}}\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>μ</mi> </mfrac> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> </msub> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> </msub> </mrow> <mrow> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}{\frac {1}{\mu }}&={\frac {1}{m_{\alpha }}}+{\frac {1}{m_{D}}}\\{\vec {p}}&={\frac {m_{D}{\vec {p}}_{\alpha }-m_{\alpha }{\vec {p}}_{D}}{m_{D}+m_{\alpha }}}\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b81686138cc0ae9554a1e9797f02884410f6b8e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.338ex; width:22.25ex; height:11.843ex;" alt="{\displaystyle {\begin{aligned}{\frac {1}{\mu }}&={\frac {1}{m_{\alpha }}}+{\frac {1}{m_{D}}}\\{\vec {p}}&={\frac {m_{D}{\vec {p}}_{\alpha }-m_{\alpha }{\vec {p}}_{D}}{m_{D}+m_{\alpha }}}\end{aligned}}}"></span></dd></dl> <p>(nelle quali abbiamo indicato con <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fd47b2a39f7a7856952afec1f1db72c67af6161" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.402ex; height:2.176ex;" alt="{\displaystyle \mu }"></span> la <a href="/wiki/Massa_ridotta" title="Massa ridotta">massa ridotta</a> e con <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {p}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {p}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/84fee53c81592db54e0fe6c6f9eba002bb1dc74b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.415ex; height:2.676ex;" alt="{\displaystyle {\vec {p}}}"></span> la <a href="/wiki/Quantit%C3%A0_di_moto" title="Quantità di moto">quantità di moto</a>), </p><p>e nella notazione ad operatori di <a href="/wiki/Schr%C3%B6dinger" class="mw-redirect" title="Schrödinger">Schrödinger</a> si ottiene: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(-{\frac {\hbar ^{2}}{2\mu }}\nabla ^{2}+V_{C}\right)\psi =E\psi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>2</mn> <mi>μ</mi> </mrow> </mfrac> </mrow> <msup> <mi mathvariant="normal">∇</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mi>ψ</mi> <mo>=</mo> <mi>E</mi> <mi>ψ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(-{\frac {\hbar ^{2}}{2\mu }}\nabla ^{2}+V_{C}\right)\psi =E\psi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b7747b704c33402a6e3ddb81e58d2b165e571acb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:25.584ex; height:6.343ex;" alt="{\displaystyle \left(-{\frac {\hbar ^{2}}{2\mu }}\nabla ^{2}+V_{C}\right)\psi =E\psi }"></span></dd></dl> <p>che può essere scritta in <a href="/wiki/Coordinate_sferiche" class="mw-redirect" title="Coordinate sferiche">coordinate sferiche</a>, poiché anche lo stesso potenziale dipende solo da <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left[-{\frac {\hbar ^{2}}{2\mu }}{\frac {1}{r^{2}}}\left({\frac {\partial }{\partial r}}r^{2}{\frac {\partial }{\partial r}}\right)+{\frac {L^{2}}{2\mu r^{2}}}+V_{C}\right]\psi (r,\theta ,\varphi )=E\psi (r,\theta ,\varphi )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>[</mo> <mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>2</mn> <mi>μ</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂</mi> <mrow> <mi mathvariant="normal">∂</mi> <mi>r</mi> </mrow> </mfrac> </mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂</mi> <mrow> <mi mathvariant="normal">∂</mi> <mi>r</mi> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>2</mn> <mi>μ</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> </mrow> <mo>]</mo> </mrow> <mi>ψ</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo>,</mo> <mi>θ</mi> <mo>,</mo> <mi>φ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>E</mi> <mi>ψ</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo>,</mo> <mi>θ</mi> <mo>,</mo> <mi>φ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left[-{\frac {\hbar ^{2}}{2\mu }}{\frac {1}{r^{2}}}\left({\frac {\partial }{\partial r}}r^{2}{\frac {\partial }{\partial r}}\right)+{\frac {L^{2}}{2\mu r^{2}}}+V_{C}\right]\psi (r,\theta ,\varphi )=E\psi (r,\theta ,\varphi )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/00ae3ae4dd25382dd397e412fdb70acc8fcc12c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:60.3ex; height:6.343ex;" alt="{\displaystyle \left[-{\frac {\hbar ^{2}}{2\mu }}{\frac {1}{r^{2}}}\left({\frac {\partial }{\partial r}}r^{2}{\frac {\partial }{\partial r}}\right)+{\frac {L^{2}}{2\mu r^{2}}}+V_{C}\right]\psi (r,\theta ,\varphi )=E\psi (r,\theta ,\varphi )}"></span></dd></dl> <p>La <a href="/wiki/Funzione_d%27onda" title="Funzione d'onda">funzione d'onda</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \psi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ψ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45e5789e5d9c8f7c79744f43ecaaf8ba42a8553a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.513ex; height:2.509ex;" alt="{\displaystyle \psi }"></span>, soluzione dell'equazione, può essere scritta come il prodotto di una funzione <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3e6bb763d22c20916ed4f0bb6bd49d7470cffd8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle u}"></span> della sola posizione per una <a href="/wiki/Armonica_sferica" class="mw-redirect" title="Armonica sferica">armonica sferica</a>, ovvero un'<a href="/wiki/Autofunzioni_del_momento_angolare" title="Autofunzioni del momento angolare">autofunzione</a> dell'<a href="/wiki/Operatore_momento_angolare" title="Operatore momento angolare">operatore momento angolare</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba162c66ca85776c83557af5088cc6f8584d1912" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.637ex; height:2.676ex;" alt="{\displaystyle L^{2}}"></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L^{2}Y_{l}^{m}(\theta ,\varphi )=\hbar ^{2}l(l+1)Y_{l}^{m}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msubsup> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msubsup> <mo stretchy="false">(</mo> <mi>θ</mi> <mo>,</mo> <mi>φ</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>l</mi> <mo stretchy="false">(</mo> <mi>l</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <msubsup> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L^{2}Y_{l}^{m}(\theta ,\varphi )=\hbar ^{2}l(l+1)Y_{l}^{m}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef96837d780c598d13bb7794f7387d041a407e72" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:27.915ex; height:3.343ex;" alt="{\displaystyle L^{2}Y_{l}^{m}(\theta ,\varphi )=\hbar ^{2}l(l+1)Y_{l}^{m}}"></span></dd></dl> <p>e quindi l'equazione di Schrödinger diventa: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left[-{\frac {\hbar ^{2}}{2\mu }}{\frac {1}{r^{2}}}\left({\frac {\partial }{\partial r}}r^{2}{\frac {\partial }{\partial r}}\right)+{\frac {\hbar ^{2}l(l+1)}{2\mu r^{2}}}+V_{C}\right]u(r)=Eu(r)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>[</mo> <mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>2</mn> <mi>μ</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂</mi> <mrow> <mi mathvariant="normal">∂</mi> <mi>r</mi> </mrow> </mfrac> </mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂</mi> <mrow> <mi mathvariant="normal">∂</mi> <mi>r</mi> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>l</mi> <mo stretchy="false">(</mo> <mi>l</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> <mrow> <mn>2</mn> <mi>μ</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> </mrow> <mo>]</mo> </mrow> <mi>u</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>E</mi> <mi>u</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left[-{\frac {\hbar ^{2}}{2\mu }}{\frac {1}{r^{2}}}\left({\frac {\partial }{\partial r}}r^{2}{\frac {\partial }{\partial r}}\right)+{\frac {\hbar ^{2}l(l+1)}{2\mu r^{2}}}+V_{C}\right]u(r)=Eu(r)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c0e8e3c932d3f874472130af445b68b5f6b1081b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:55.739ex; height:7.509ex;" alt="{\displaystyle \left[-{\frac {\hbar ^{2}}{2\mu }}{\frac {1}{r^{2}}}\left({\frac {\partial }{\partial r}}r^{2}{\frac {\partial }{\partial r}}\right)+{\frac {\hbar ^{2}l(l+1)}{2\mu r^{2}}}+V_{C}\right]u(r)=Eu(r)}"></span></dd></dl> <p>che può essere ulteriormente semplificata introducendo la funzione <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \chi (r)=r\cdot u(r)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>χ</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>r</mi> <mo>⋅</mo> <mi>u</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \chi (r)=r\cdot u(r)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/44c5cefaf23135461311c2dc5cbe6fcfbcec50ad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.327ex; height:2.843ex;" alt="{\displaystyle \chi (r)=r\cdot u(r)}"></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left[-{\frac {\hbar ^{2}}{2\mu }}{\frac {\partial ^{2}}{\partial r^{2}}}+{\frac {\hbar ^{2}}{2\mu r^{2}}}l(l+1)+V_{C}\right]\chi (r)=E\chi (r)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>[</mo> <mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>2</mn> <mi>μ</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mn>2</mn> <mi>μ</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mi>l</mi> <mo stretchy="false">(</mo> <mi>l</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>+</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> </mrow> <mo>]</mo> </mrow> <mi>χ</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>E</mi> <mi>χ</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left[-{\frac {\hbar ^{2}}{2\mu }}{\frac {\partial ^{2}}{\partial r^{2}}}+{\frac {\hbar ^{2}}{2\mu r^{2}}}l(l+1)+V_{C}\right]\chi (r)=E\chi (r)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/82505cb8bd053ba2e4d977c35ff369773645bc42" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:47.027ex; height:6.343ex;" alt="{\displaystyle \left[-{\frac {\hbar ^{2}}{2\mu }}{\frac {\partial ^{2}}{\partial r^{2}}}+{\frac {\hbar ^{2}}{2\mu r^{2}}}l(l+1)+V_{C}\right]\chi (r)=E\chi (r)}"></span></dd></dl> <p>In <b>onda S</b> (<a href="/wiki/Onda_sferica" title="Onda sferica">onda sferica</a>, con <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle l}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>l</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle l}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/829091f745070b9eb97a80244129025440a1cfac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.693ex; height:2.176ex;" alt="{\displaystyle l}"></span>=<a href="/wiki/Zero" class="mw-redirect" title="Zero">0</a>), trovare le <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \chi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>χ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \chi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/656111758322ace96d80a9371771aa6d3de25437" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.455ex; height:2.009ex;" alt="{\displaystyle \chi }"></span> soluzioni si riduce a risolvere la seguente <a href="/wiki/Equazione_differenziale" title="Equazione differenziale">equazione differenziale</a><sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\partial ^{2}}{\partial r^{2}}}\chi (r)-K^{2}(r)\chi (r)=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mi>χ</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mo>−</mo> <msup> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mi>χ</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\partial ^{2}}{\partial r^{2}}}\chi (r)-K^{2}(r)\chi (r)=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b81ec60684bb17349b6a7edbb58f1868ab56f8f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:25.991ex; height:6.009ex;" alt="{\displaystyle {\frac {\partial ^{2}}{\partial r^{2}}}\chi (r)-K^{2}(r)\chi (r)=0}"></span></dd></dl> <p>con </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K^{2}(r)={\frac {2\mu }{\hbar ^{2}}}\left(V(r)-E\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>μ</mi> </mrow> <msup> <mi class="MJX-variant">ℏ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mi>V</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>E</mi> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K^{2}(r)={\frac {2\mu }{\hbar ^{2}}}\left(V(r)-E\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa0d552b432f14601d2e0c3bdf13cf9fab5e974f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:23.962ex; height:5.676ex;" alt="{\displaystyle K^{2}(r)={\frac {2\mu }{\hbar ^{2}}}\left(V(r)-E\right)}"></span></dd></dl> <p>Se <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K(r)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>K</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K(r)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d949aa869b18dc50d5c1c356567904a3e1943f63" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.924ex; height:2.843ex;" alt="{\displaystyle K(r)}"></span> non fosse una <a href="/wiki/Funzione_(matematica)" title="Funzione (matematica)">funzione</a> della posizione, la soluzione sarebbe semplicemente del tipo: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \chi (r)=A\operatorname {e} ^{-k\cdot r}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>χ</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>A</mi> <msup> <mi mathvariant="normal">e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi>k</mi> <mo>⋅</mo> <mi>r</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \chi (r)=A\operatorname {e} ^{-k\cdot r}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72f27b8d3d28cc877391a9bbc5b4ed6f80700f9a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.14ex; height:3.176ex;" alt="{\displaystyle \chi (r)=A\operatorname {e} ^{-k\cdot r}}"></span></dd></dl> <p>ma in questo caso anche la fase sarà una funzione di <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \chi (r)=A\operatorname {e} ^{f(r)}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>χ</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>A</mi> <msup> <mi mathvariant="normal">e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \chi (r)=A\operatorname {e} ^{f(r)}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a6b1c9913d03936cf9ec776b027097bbc3ccbe80" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.731ex; height:3.343ex;" alt="{\displaystyle \chi (r)=A\operatorname {e} ^{f(r)}}"></span></dd></dl> <p>ottenendo un'equazione differenziale per <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -{\frac {\operatorname {d} ^{2}f}{\operatorname {d} r^{2}}}+\left({\frac {\operatorname {d} f}{\operatorname {d} r}}\right)^{2}-k^{2}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">d</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>⁡</mo> <mi>f</mi> </mrow> <mrow> <mi mathvariant="normal">d</mi> <mo>⁡</mo> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">d</mi> <mo>⁡</mo> <mi>f</mi> </mrow> <mrow> <mi mathvariant="normal">d</mi> <mo>⁡</mo> <mi>r</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -{\frac {\operatorname {d} ^{2}f}{\operatorname {d} r^{2}}}+\left({\frac {\operatorname {d} f}{\operatorname {d} r}}\right)^{2}-k^{2}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86dd7ecfaae7a30c1791daca9592fbe0bab776bf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:27.134ex; height:6.509ex;" alt="{\displaystyle -{\frac {\operatorname {d} ^{2}f}{\operatorname {d} r^{2}}}+\left({\frac {\operatorname {d} f}{\operatorname {d} r}}\right)^{2}-k^{2}=0}"></span></dd></dl> <p>Risolvere in maniera esatta questa <a href="/wiki/Equazione" title="Equazione">equazione</a> è molto difficile (per non dire impossibile): esistono però alcuni metodi di approssimazione, come il <a href="/wiki/Approssimazione_WKB" title="Approssimazione WKB">WKB</a><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> o, più semplicemente, trascurando la derivata seconda di <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></span> rispetto ad <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span> (essa è certamente più piccola rispetto al quadrato della derivata prima). In questo caso è semplice verificare che </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(r)=\int k(r')\operatorname {d} r'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>∫</mo> <mi>k</mi> <mo stretchy="false">(</mo> <msup> <mi>r</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mi mathvariant="normal">d</mi> <mo>⁡</mo> <msup> <mi>r</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(r)=\int k(r')\operatorname {d} r'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db61c39a87f021cc6d274dac1c5f1b556cbaea31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:18.37ex; height:5.676ex;" alt="{\displaystyle f(r)=\int k(r')\operatorname {d} r'}"></span></dd></dl> <p>è soluzione. </p><p>Ora, poiché l'armonica sferica di ordine 0 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y_{0}^{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y_{0}^{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/49b460145ebe1dce8e44d623255b7c8c5f16b193" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.954ex; height:3.176ex;" alt="{\displaystyle Y_{0}^{0}}"></span> è<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y_{0}^{0}={\frac {1}{\sqrt {4\pi }}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>4</mn> <mi>π</mi> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y_{0}^{0}={\frac {1}{\sqrt {4\pi }}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d72d528ea4d5251fcd90258c07d74cc4af88e95" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:11.319ex; height:6.176ex;" alt="{\displaystyle Y_{0}^{0}={\frac {1}{\sqrt {4\pi }}}}"></span></dd></dl> <p>sostituendo la <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></span> nella <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \chi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>χ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \chi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/656111758322ace96d80a9371771aa6d3de25437" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.455ex; height:2.009ex;" alt="{\displaystyle \chi }"></span> e quest'ultima nella <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3e6bb763d22c20916ed4f0bb6bd49d7470cffd8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle u}"></span> e quindi il tutto nella <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \psi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ψ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45e5789e5d9c8f7c79744f43ecaaf8ba42a8553a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.513ex; height:2.509ex;" alt="{\displaystyle \psi }"></span>, si può finalmente scrivere la soluzione dell'equazione di Schrödinger di partenza: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \psi (r)={\frac {1}{\sqrt {4\pi }}}{\frac {A}{r}}\operatorname {e} ^{-\int K(r')\operatorname {d} r'}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ψ</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mn>4</mn> <mi>π</mi> </msqrt> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>A</mi> <mi>r</mi> </mfrac> </mrow> <msup> <mi mathvariant="normal">e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mo>∫</mo> <mi>K</mi> <mo stretchy="false">(</mo> <msup> <mi>r</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mi mathvariant="normal">d</mi> <mo>⁡</mo> <msup> <mi>r</mi> <mo>′</mo> </msup> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi (r)={\frac {1}{\sqrt {4\pi }}}{\frac {A}{r}}\operatorname {e} ^{-\int K(r')\operatorname {d} r'}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2618979d1622358f09d51d940324deb8334fe90" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:26.997ex; height:6.343ex;" alt="{\displaystyle \psi (r)={\frac {1}{\sqrt {4\pi }}}{\frac {A}{r}}\operatorname {e} ^{-\int K(r')\operatorname {d} r'}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Il_fattore_di_Gamow">Il fattore di Gamow</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Decadimento_alfa&veaction=edit&section=4" title="Modifica la sezione Il fattore di Gamow" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Decadimento_alfa&action=edit&section=4" title="Edit section's source code: Il fattore di Gamow"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>È proprio grazie alla funzione d'onda trovata che si riesce a scrivere il cosiddetto <b>fattore di Gamow</b>: della dinamica del decadimento, infatti, siamo interessati solo alla fase iniziale (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r=R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r=R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a088bb7b6b4be9ff6b0fdb33fc1dd53af91e356" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.911ex; height:2.176ex;" alt="{\displaystyle r=R}"></span> - quando inizia il decadimento) e a quella finale (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r=r_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> <mo>=</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r=r_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b0adf8ec52d4c2c453d5d69553375b80d4db4311" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.25ex; height:2.009ex;" alt="{\displaystyle r=r_{0}}"></span> - la fine del tunnel); e quindi<sup id="cite_ref-giorgio_bendiscioli_springer_pagina_128_14-0" class="reference"><a href="#cite_note-giorgio_bendiscioli_springer_pagina_128-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\psi (r=r_{0})}{\psi (r=R)}}={\frac {R}{r_{0}}}\operatorname {e} ^{-\int _{R}^{r_{0}}K(r)\operatorname {d} r}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>ψ</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo>=</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>ψ</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo>=</mo> <mi>R</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>R</mi> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <msup> <mi mathvariant="normal">e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </msubsup> <mi>K</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mi mathvariant="normal">d</mi> <mo>⁡</mo> <mi>r</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\psi (r=r_{0})}{\psi (r=R)}}={\frac {R}{r_{0}}}\operatorname {e} ^{-\int _{R}^{r_{0}}K(r)\operatorname {d} r}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41b9546fd1a90d62f7d6ab1475264c4e19643bf6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:28.7ex; height:6.509ex;" alt="{\displaystyle {\frac {\psi (r=r_{0})}{\psi (r=R)}}={\frac {R}{r_{0}}}\operatorname {e} ^{-\int _{R}^{r_{0}}K(r)\operatorname {d} r}}"></span></dd></dl> <p>Il fattore di Gamow è legato al <b>coefficiente di trasmissione</b> o <b>penetrazione</b>, in quanto quest'ultimo è definito come il quadrato del primo: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T={\frac {\left|\psi (r_{0})\right|^{2}}{\left|\psi (R)\right|^{2}}}={\frac {R^{2}}{r_{0}^{2}}}\operatorname {e} ^{-2\int _{R}^{r_{0}}K(r)\operatorname {d} r}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow> <mo>|</mo> <mrow> <mi>ψ</mi> <mo stretchy="false">(</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> <mo>|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msup> <mrow> <mo>|</mo> <mrow> <mi>ψ</mi> <mo stretchy="false">(</mo> <mi>R</mi> <mo stretchy="false">)</mo> </mrow> <mo>|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msubsup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mfrac> </mrow> <msup> <mi mathvariant="normal">e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </msubsup> <mi>K</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mi mathvariant="normal">d</mi> <mo>⁡</mo> <mi>r</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T={\frac {\left|\psi (r_{0})\right|^{2}}{\left|\psi (R)\right|^{2}}}={\frac {R^{2}}{r_{0}^{2}}}\operatorname {e} ^{-2\int _{R}^{r_{0}}K(r)\operatorname {d} r}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c4a5163f780c61d8485dcf32f91b804766981300" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:33.172ex; height:7.343ex;" alt="{\displaystyle T={\frac {\left|\psi (r_{0})\right|^{2}}{\left|\psi (R)\right|^{2}}}={\frac {R^{2}}{r_{0}^{2}}}\operatorname {e} ^{-2\int _{R}^{r_{0}}K(r)\operatorname {d} r}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Vita_media">Vita media</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Decadimento_alfa&veaction=edit&section=5" title="Modifica la sezione Vita media" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Decadimento_alfa&action=edit&section=5" title="Edit section's source code: Vita media"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Esso è a sua volta legato alla <a href="/wiki/Vita_media" title="Vita media">vita media</a> del decadimento attraverso la rapidità<sup id="cite_ref-giorgio_bendiscioli_springer_pagina_128_14-1" class="reference"><a href="#cite_note-giorgio_bendiscioli_springer_pagina_128-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Gamma ={\frac {T}{\tau _{n}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Γ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>T</mi> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Gamma ={\frac {T}{\tau _{n}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e1ceb7569f343662992c228d19480b4f15564d79" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:7.622ex; height:5.509ex;" alt="{\displaystyle \Gamma ={\frac {T}{\tau _{n}}}}"></span></dd></dl> <p>dove </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{\tau _{n}}}={\frac {\hbar }{R^{2}m_{p}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>τ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi class="MJX-variant">ℏ</mi> <mrow> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{\tau _{n}}}={\frac {\hbar }{R^{2}m_{p}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3167f777218f6a01e6be76e5ba92f684ab17ee46" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:12.923ex; height:6.176ex;" alt="{\displaystyle {\frac {1}{\tau _{n}}}={\frac {\hbar }{R^{2}m_{p}}}}"></span></dd></dl> <p>che è la <a href="/wiki/Frequenza" title="Frequenza">frequenza</a> con la quale la particella <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span> va contro la parete del potenziale. </p><p>Quindi, per stimare la vita media <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tau }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>τ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tau }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38a7dcde9730ef0853809fefc18d88771f95206c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.202ex; height:1.676ex;" alt="{\displaystyle \tau }"></span> del decadimento bisogna calcolare la rapidità dello stesso<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Gamma ={\frac {1}{\tau }}={\frac {\hbar }{r_{0}^{2}m_{p}}}\operatorname {e} ^{-2{\frac {\sqrt {8m}}{\hbar }}\int _{R}^{r_{0}}{\sqrt {V(R)-E}}\operatorname {d} r}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Γ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>τ</mi> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi class="MJX-variant">ℏ</mi> <mrow> <msubsup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <msup> <mi mathvariant="normal">e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msqrt> <mn>8</mn> <mi>m</mi> </msqrt> <mi class="MJX-variant">ℏ</mi> </mfrac> </mrow> <msubsup> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>V</mi> <mo stretchy="false">(</mo> <mi>R</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>E</mi> </msqrt> </mrow> <mi mathvariant="normal">d</mi> <mo>⁡</mo> <mi>r</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Gamma ={\frac {1}{\tau }}={\frac {\hbar }{r_{0}^{2}m_{p}}}\operatorname {e} ^{-2{\frac {\sqrt {8m}}{\hbar }}\int _{R}^{r_{0}}{\sqrt {V(R)-E}}\operatorname {d} r}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/54a2384cd2989b5647b8a3af90cf763b865fe3c0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:37.074ex; height:6.843ex;" alt="{\displaystyle \Gamma ={\frac {1}{\tau }}={\frac {\hbar }{r_{0}^{2}m_{p}}}\operatorname {e} ^{-2{\frac {\sqrt {8m}}{\hbar }}\int _{R}^{r_{0}}{\sqrt {V(R)-E}}\operatorname {d} r}}"></span></dd></dl> <p>dove al posto della massa ridotta <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9fd47b2a39f7a7856952afec1f1db72c67af6161" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.402ex; height:2.176ex;" alt="{\displaystyle \mu }"></span> si è sostituito 4 volte <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"></span>, <a href="/wiki/Massa_(fisica)" title="Massa (fisica)">massa</a> del <a href="/wiki/Nucleone" title="Nucleone">nucleone</a>, poiché generalmente, per masse <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m_{D}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m_{D}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b38761ea3904a313a4086bfd223524736d8cd438" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.633ex; height:2.009ex;" alt="{\displaystyle m_{D}}"></span> molto grandi (come spesso avviene) la massa ridotta è circa quella della particella <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span>. </p><p>Questa vita media, in generale, varierà in dipendenza del tipo di nuclei che decadono e della quantità iniziale di energia cinetica posseduta dal nucleo di elio prodotto. Da studi fatti, sono peraltro emerse delle correlazioni tra vita media, energia cinetica delle particelle <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span> emesse, numero di massa e numero atomico<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup>: </p> <ul><li>per una famiglia di isotopi (cioè con numero atomico <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1cc6b75e09a8aa3f04d8584b11db534f88fb56bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.68ex; height:2.176ex;" alt="{\displaystyle Z}"></span> fissato), si ha che all'aumentare del <a href="/wiki/Numero_di_massa" title="Numero di massa">numero di massa</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> l'energia cinetica <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{\alpha }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{\alpha }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f309d00b1d4b7827a958df7d8e4334831886a6d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.642ex; height:2.509ex;" alt="{\displaystyle T_{\alpha }}"></span> delle particelle <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span> emesse decresce e la vita media aumenta</li> <li>per una famiglia di <a href="/wiki/Isobaro" title="Isobaro">isobari</a> (cioè con <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> costante), si ha che all'aumentare di <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1cc6b75e09a8aa3f04d8584b11db534f88fb56bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.68ex; height:2.176ex;" alt="{\displaystyle Z}"></span> l'energia cinetica delle particelle <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span> risulta crescente e la vita media risulta invece decrescente</li> <li>la vita media diminuisce quando aumenta l'energia cinetica <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{\alpha }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>α</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{\alpha }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f309d00b1d4b7827a958df7d8e4334831886a6d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.642ex; height:2.509ex;" alt="{\displaystyle T_{\alpha }}"></span>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Note">Note</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Decadimento_alfa&veaction=edit&section=6" title="Modifica la sezione Note" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Decadimento_alfa&action=edit&section=6" title="Edit section's source code: Note"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><a href="#cite_ref-1"><b>^</b></a> <span class="reference-text"><cite class="citation libro" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) Michael G Stabin, <span style="font-style:italic;">Radiation Protection and Dosimetry</span>, Springer, 2008, p. 21, <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/Speciale:RicercaISBN/978-0-387-49982-6" title="Speciale:RicercaISBN/978-0-387-49982-6">978-0-387-49982-6</a>.</cite></span> </li> <li id="cite_note-giorgio_bendiscioli_springer_pagina_113-2"><span class="mw-cite-backlink"><b>^</b> <sup><i><a href="#cite_ref-giorgio_bendiscioli_springer_pagina_113_2-0">a</a></i></sup> <sup><i><a href="#cite_ref-giorgio_bendiscioli_springer_pagina_113_2-1">b</a></i></sup></span> <span class="reference-text"><cite class="citation cita" style="font-style:normal"><a href="#CITEREFG._Bendiscioli">G. Bendiscioli</a></cite> p.113</span> </li> <li id="cite_note-3"><a href="#cite_ref-3"><b>^</b></a> <span class="reference-text"><cite class="citation web" style="font-style:normal"> G.Valitutti, M.Falasca, A.Tifi, A.Gentile, <a rel="nofollow" class="external text" href="http://ebook.scuola.zanichelli.it/concettimodelli/parte-b/le-particelle-dell-atomo/i-tipi-di-decadimento-radioattivo-e-la-legge-del-decadimento#141"><span style="font-style:italic;">Chimica: concetti e modelli</span></a>, su <span style="font-style:italic;">ebook.scuola.zanichelli.it</span>. <small>URL consultato il 9 dicembre 2016</small>.</cite></span> </li> <li id="cite_note-4"><a href="#cite_ref-4"><b>^</b></a> <span class="reference-text"><cite class="citation cita" style="font-style:normal"><a href="#CITEREFG._Bendiscioli">G. Bendiscioli</a></cite> p.1</span> </li> <li id="cite_note-5"><a href="#cite_ref-5"><b>^</b></a> <span class="reference-text"><cite class="citation cita" style="font-style:normal"><a href="#CITEREFG._Bendiscioli">G. Bendiscioli</a></cite> p.115</span> </li> <li id="cite_note-6"><a href="#cite_ref-6"><b>^</b></a> <span class="reference-text"><cite class="citation pubblicazione" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="tedesco">DE</abbr></span>) G. Gamow, <a rel="nofollow" class="external text" href="https://link.springer.com/article/10.1007/BF01343196"><span style="font-style:italic;">Zur Quantentheorie des Atomkernes</span></a>, in <span style="font-style:italic;">Zeitschrift für Physik</span>, vol. 51, n. 3-4, pp. 204–212, <a href="/wiki/Digital_object_identifier" title="Digital object identifier">DOI</a>:<a rel="nofollow" class="external text" href="https://dx.doi.org/10.1007%2FBF01343196">10.1007/BF01343196</a>. <small>URL consultato il 9 dicembre 2016</small>.</cite></span> </li> <li id="cite_note-7"><a href="#cite_ref-7"><b>^</b></a> <span class="reference-text"><cite class="citation web" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) <a rel="nofollow" class="external text" href="http://web.ihep.su/dbserv/compas/src/gamow28/eng.pdf"><span style="font-style:italic;">Quantum Theory of the Atomic Nucleus</span></a> (<span style="font-weight: bolder; font-size:80%"><abbr title="documento in formato PDF">PDF</abbr></span>), su <span style="font-style:italic;">web.ihep.su</span>.</cite></span> </li> <li id="cite_note-8"><a href="#cite_ref-8"><b>^</b></a> <span class="reference-text"><cite class="citation cita" style="font-style:normal"><a href="#CITEREFG._Bendiscioli">G. Bendiscioli</a></cite> pp.114/121-122</span> </li> <li id="cite_note-9"><a href="#cite_ref-9"><b>^</b></a> <span class="reference-text"><cite class="citation cita" style="font-style:normal"><a href="#CITEREFN._Manini">N. Manini</a></cite> p.2</span> </li> <li id="cite_note-10"><a href="#cite_ref-10"><b>^</b></a> <span class="reference-text"><cite class="citation cita" style="font-style:normal"><a href="#CITEREFN._Manini">N. Manini</a></cite> pp.12-13</span> </li> <li id="cite_note-11"><a href="#cite_ref-11"><b>^</b></a> <span class="reference-text"><cite class="citation cita" style="font-style:normal"><a href="#CITEREFG._Bendiscioli">G. Bendiscioli</a></cite> p.127</span> </li> <li id="cite_note-12"><a href="#cite_ref-12"><b>^</b></a> <span class="reference-text"><cite class="citation libro" style="font-style:normal"> David J. Griffiths, <span style="font-style:italic;">Introduzione alla meccanica quantistica</span>, Casa Editrice Ambrosiana, 2005, <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/Speciale:RicercaISBN/978-88-08-08747-8" title="Speciale:RicercaISBN/978-88-08-08747-8">978-88-08-08747-8</a>.</cite> p.320</span> </li> <li id="cite_note-13"><a href="#cite_ref-13"><b>^</b></a> <span class="reference-text"><cite class="citation cita" style="font-style:normal"><a href="#CITEREFN._Manini">N. Manini</a></cite> p.18</span> </li> <li id="cite_note-giorgio_bendiscioli_springer_pagina_128-14"><span class="mw-cite-backlink"><b>^</b> <sup><i><a href="#cite_ref-giorgio_bendiscioli_springer_pagina_128_14-0">a</a></i></sup> <sup><i><a href="#cite_ref-giorgio_bendiscioli_springer_pagina_128_14-1">b</a></i></sup></span> <span class="reference-text"><cite class="citation cita" style="font-style:normal"><a href="#CITEREFG._Bendiscioli">G. Bendiscioli</a></cite> p.128</span> </li> <li id="cite_note-15"><a href="#cite_ref-15"><b>^</b></a> <span class="reference-text"><cite class="citation cita" style="font-style:normal"><a href="#CITEREFG._Bendiscioli">G. Bendiscioli</a></cite> p.129</span> </li> <li id="cite_note-16"><a href="#cite_ref-16"><b>^</b></a> <span class="reference-text"><cite class="citation cita" style="font-style:normal"><a href="#CITEREFG._Bendiscioli">G. Bendiscioli</a></cite> p.119</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Bibliografia">Bibliografia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Decadimento_alfa&veaction=edit&section=7" title="Modifica la sezione Bibliografia" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Decadimento_alfa&action=edit&section=7" title="Edit section's source code: Bibliografia"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite id="CITEREFG._Bendiscioli" class="citation libro" style="font-style:normal"> Giorgio Bendiscioli, <span style="font-style:italic;">Fenomeni Radioattivi</span>, Springer, 2013, <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/Speciale:RicercaISBN/978-88-470-0803-8" title="Speciale:RicercaISBN/978-88-470-0803-8">978-88-470-0803-8</a>.</cite></li> <li><cite id="CITEREFN._Manini" class="citation libro" style="font-style:normal"> Nicola Manini, <span style="font-style:italic;">Introduction to the Physics of Matter</span>, Springer, 2014, <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/Speciale:RicercaISBN/978-3-319-14381-1" title="Speciale:RicercaISBN/978-3-319-14381-1">978-3-319-14381-1</a>.</cite></li></ul> <div class="mw-heading mw-heading2"><h2 id="Voci_correlate">Voci correlate</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Decadimento_alfa&veaction=edit&section=8" title="Modifica la sezione Voci correlate" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Decadimento_alfa&action=edit&section=8" title="Edit section's source code: Voci correlate"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Radioattivit%C3%A0" title="Radioattività">Radioattività</a></li> <li><a href="/wiki/Decadimento_beta" title="Decadimento beta">Decadimento beta</a></li> <li><a href="/wiki/Decadimento_gamma" class="mw-redirect" title="Decadimento gamma">Decadimento gamma</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Altri_progetti">Altri progetti</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Decadimento_alfa&veaction=edit&section=9" title="Modifica la sezione Altri progetti" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Decadimento_alfa&action=edit&section=9" title="Edit section's source code: Altri progetti"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <div id="interProject" class="toccolours" style="display: none; clear: both; margin-top: 2em"><p id="sisterProjects" style="background-color: #efefef; color: black; font-weight: bold; margin: 0"><span>Altri progetti</span></p><ul title="Collegamenti verso gli altri progetti Wikimedia"> <li class="" title=""><span class="plainlinks" title="commons:Category:Alpha decay"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Alpha_decay?uselang=it">Wikimedia Commons</a></span></li></ul></div> <ul><li><span typeof="mw:File"><a href="https://commons.wikimedia.org/wiki/?uselang=it" title="Collabora a Wikimedia Commons"><img alt="Collabora a Wikimedia Commons" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png" decoding="async" width="18" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/27px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/36px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> <span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/?uselang=it">Wikimedia Commons</a></span> contiene immagini o altri file su <b><span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Alpha_decay?uselang=it">decadimento alfa</a></span></b></li></ul> <div class="mw-heading mw-heading2"><h2 id="Collegamenti_esterni">Collegamenti esterni</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Decadimento_alfa&veaction=edit&section=10" title="Modifica la sezione Collegamenti esterni" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Decadimento_alfa&action=edit&section=10" title="Edit section's source code: Collegamenti esterni"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li class="mw-empty-elt"></li> <li><cite id="CITEREFBritannica.com" class="citation web" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) <a rel="nofollow" class="external text" href="https://www.britannica.com/science/alpha-decay"><span style="font-style:italic;">alpha decay</span></a>, su <span style="font-style:italic;"><a href="/wiki/Enciclopedia_Britannica" title="Enciclopedia Britannica">Enciclopedia Britannica</a></span>, Encyclopædia Britannica, Inc.</cite> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q179856#P1417" title="Modifica su Wikidata"><img alt="Modifica su Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/10px-Blue_pencil.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/15px-Blue_pencil.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/20px-Blue_pencil.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></li></ul> <style data-mw-deduplicate="TemplateStyles:r141815314">.mw-parser-output .navbox{border:1px solid #aaa;clear:both;margin:auto;padding:2px;width:100%}.mw-parser-output .navbox th{padding-left:1em;padding-right:1em;text-align:center}.mw-parser-output .navbox>tbody>tr:first-child>th{background:#ccf;font-size:90%;width:100%;color:var(--color-base,black)}.mw-parser-output .navbox_navbar{float:left;margin:0;padding:0 10px 0 0;text-align:left;width:6em}.mw-parser-output .navbox_title{font-size:110%}.mw-parser-output .navbox_abovebelow{background:#ddf;font-size:90%;font-weight:normal}.mw-parser-output .navbox_group{background:#ddf;font-size:90%;padding:0 10px;white-space:nowrap}.mw-parser-output .navbox_list{font-size:90%;width:100%}.mw-parser-output .navbox_list a{white-space:nowrap}html:not(.vector-feature-night-mode-enabled) .mw-parser-output .navbox_odd{background:#fdfdfd;color:var(--color-base,black)}html:not(.vector-feature-night-mode-enabled) .mw-parser-output .navbox_even{background:#f7f7f7;color:var(--color-base,black)}.mw-parser-output .navbox a.mw-selflink{color:var(--color-base,black)}.mw-parser-output .navbox_center{text-align:center}.mw-parser-output .navbox .navbox_image{padding-left:7px;vertical-align:middle;width:0}.mw-parser-output .navbox+.navbox{margin-top:-1px}.mw-parser-output .navbox .mw-collapsible-toggle{font-weight:normal;text-align:right;width:7em}body.skin--responsive .mw-parser-output .navbox_image img{max-width:none!important}.mw-parser-output .subnavbox{margin:-3px;width:100%}.mw-parser-output .subnavbox_group{background:#e6e6ff;padding:0 10px}@media screen{html.skin-theme-clientpref-night .mw-parser-output .navbox>tbody>tr:first-child>th{background:var(--background-color-interactive)!important}html.skin-theme-clientpref-night .mw-parser-output .navbox th{color:var(--color-base)!important}html.skin-theme-clientpref-night .mw-parser-output .navbox_abovebelow,html.skin-theme-clientpref-night .mw-parser-output .navbox_group{background:var(--background-color-interactive-subtle)!important}html.skin-theme-clientpref-night .mw-parser-output .subnavbox_group{background:var(--background-color-neutral-subtle)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbox>tbody>tr:first-child>th{background:var(--background-color-interactive)!important}html.skin-theme-clientpref-os .mw-parser-output .navbox th{color:var(--color-base)!important}html.skin-theme-clientpref-os .mw-parser-output .navbox_abovebelow,html.skin-theme-clientpref-os .mw-parser-output .navbox_group{background:var(--background-color-interactive-subtle)!important}html.skin-theme-clientpref-os .mw-parser-output .subnavbox_group{background:var(--background-color-neutral-subtle)!important}}</style><table class="navbox mw-collapsible autocollapse noprint metadata" id="navbox-Processinucleari"><tbody><tr><th colspan="2"><div class="navbox_navbar"><div class="noprint plainlinks" style="background-color:transparent; padding:0; font-size:xx-small; color:var(--color-base, #000000); white-space:nowrap;"><a href="/wiki/Template:Processinucleari" title="Template:Processinucleari"><span title="Vai alla pagina del template">V</span></a> · <a href="/w/index.php?title=Discussioni_template:Processinucleari&action=edit&redlink=1" class="new" title="Discussioni template:Processinucleari (la pagina non esiste)"><span title="Discuti del template">D</span></a> · <a class="external text" href="https://it.wikipedia.org/w/index.php?title=Template:Processinucleari&action=edit"><span title="Modifica il template. 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font-size:80%"><abbr title="tedesco">DE</abbr></span>) <a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4142015-9">4142015-9</a></span></td></tr></tbody></table> <div class="noprint" style="width:100%; padding: 3px 0; display: flex; flex-wrap: wrap; row-gap: 4px; column-gap: 8px; box-sizing: border-box;"><div style="flex-basis: calc( 100% / 2 - 8px / 2 );"><style data-mw-deduplicate="TemplateStyles:r140555418">.mw-parser-output .itwiki-template-occhiello{width:100%;line-height:25px;border:1px solid #CCF;background-color:#F0EEFF;box-sizing:border-box}.mw-parser-output .itwiki-template-occhiello-progetto{background-color:#FAFAFA}@media screen{html.skin-theme-clientpref-night .mw-parser-output .itwiki-template-occhiello{background-color:#202122;border-color:#54595D}html.skin-theme-clientpref-night .mw-parser-output .itwiki-template-occhiello-progetto{background-color:#282929}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .itwiki-template-occhiello{background-color:#202122;border-color:#54595D}html.skin-theme-clientpref-os .mw-parser-output .itwiki-template-occhiello-progetto{background-color:#282929}}</style><div class="itwiki-template-occhiello"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.png" class="mw-file-description" title="Energia nucleare"><img alt=" " src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.png/22px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.png" decoding="async" width="22" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.png/33px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1f/Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.png/44px-Stylised_atom_with_three_Bohr_model_orbits_and_stylised_nucleus.png 2x" data-file-width="260" data-file-height="296" /></a></span> <b><a href="/wiki/Portale:Energia_nucleare" title="Portale:Energia nucleare">Portale Energia nucleare</a></b></div></div><div style="flex-basis: calc( 100% / 2 - 8px / 2 );"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r140555418"><div class="itwiki-template-occhiello"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Nuvola_apps_katomic.svg" class="mw-file-description" title="Fisica"><img alt=" " src="//upload.wikimedia.org/wikipedia/commons/thumb/5/55/Nuvola_apps_katomic.svg/25px-Nuvola_apps_katomic.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/55/Nuvola_apps_katomic.svg/38px-Nuvola_apps_katomic.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/55/Nuvola_apps_katomic.svg/50px-Nuvola_apps_katomic.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span> <b><a href="/wiki/Portale:Fisica" title="Portale:Fisica">Portale Fisica</a></b></div></div></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; 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Decadimento alfa - Wikipedia