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href="https://de.wikipedia.org/wiki/Linearer_Energietransfer" title="Linearer Energietransfer – German" lang="de" hreflang="de" data-title="Linearer Energietransfer" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Transferencia_lineal_de_energ%C3%ADa" title="Transferencia lineal de energía – Spanish" lang="es" hreflang="es" data-title="Transferencia lineal de energía" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Transfert_lin%C3%A9ique_d%27%C3%A9nergie" title="Transfert linéique d'énergie – French" lang="fr" hreflang="fr" data-title="Transfert linéique d'énergie" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Linear_energy_transfer" title="Linear energy transfer – Italian" lang="it" hreflang="it" data-title="Linear energy transfer" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Linear_energy_transfer" title="Linear energy transfer – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Linear energy transfer" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Liniowy_przekaz_energii" title="Liniowy przekaz energii – Polish" lang="pl" hreflang="pl" 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class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Measure for the energy lost by ions per traversed distance</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Cloud_chamber_ani_bionerd.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Cloud_chamber_ani_bionerd.gif/220px-Cloud_chamber_ani_bionerd.gif" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/7/73/Cloud_chamber_ani_bionerd.gif 1.5x" data-file-width="300" data-file-height="225" /></a><figcaption>Diffusion <a href="/wiki/Cloud_chamber" title="Cloud chamber">cloud chamber</a> with tracks of ionizing radiation (alpha particles) that are made visible as strings of droplets</figcaption></figure> <p>In <a href="/wiki/Dosimetry" title="Dosimetry">dosimetry</a>, <b>linear energy transfer (LET)</b> is the amount of energy that an ionizing particle transfers to the material traversed per unit distance. It describes the action of <a href="/wiki/Radiation" title="Radiation">radiation</a> into matter. </p><p>It is identical to the retarding <a href="/wiki/Force" title="Force">force</a> acting on a charged <a href="/wiki/Ionizing_radiation" title="Ionizing radiation">ionizing</a> particle travelling through the matter.<sup id="cite_ref-ICRU85a_1-0" class="reference"><a href="#cite_note-ICRU85a-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> By definition, LET is a positive quantity. LET depends on the nature of the radiation as well as on the material traversed. </p><p>A high LET will slow down the radiation more quickly, generally making shielding more effective and preventing deep penetration. On the other hand, the higher concentration of deposited energy can cause more severe damage to any microscopic structures near the particle track. If a microscopic defect can cause larger-scale failure, as is the case in <a href="/wiki/Biological_cell" class="mw-redirect" title="Biological cell">biological cells</a> and <a href="/wiki/Microelectronics" title="Microelectronics">microelectronics</a>, the LET helps explain why radiation damage is sometimes disproportionate to the <a href="/wiki/Absorbed_dose" title="Absorbed dose">absorbed dose</a>. <a href="/wiki/Dosimetry" title="Dosimetry">Dosimetry</a> attempts to factor in this effect with <a href="/wiki/Radiation_weighting_factor" class="mw-redirect" title="Radiation weighting factor">radiation weighting factors</a>. </p><p>Linear energy transfer is closely related to <a href="/wiki/Stopping_power_(particle_radiation)" title="Stopping power (particle radiation)">stopping power</a>, since both equal the retarding force. The unrestricted linear energy transfer is identical to linear electronic stopping power, as discussed below. But the stopping power and LET concepts are different in the respect that total stopping power has the nuclear stopping power component,<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> and this component does not cause electronic excitations. Hence nuclear stopping power is not contained in LET. </p><p>The appropriate SI unit for LET is the <a href="/wiki/Newton_(unit)" title="Newton (unit)">newton</a>, but it is most typically expressed in units of <a href="/wiki/Electronvolt" title="Electronvolt">kiloelectronvolts</a> per micrometre (keV/μm) or megaelectronvolts per centimetre (MeV/cm). While medical physicists and radiobiologists usually speak of <i>linear energy transfer</i>, most non-medical physicists talk about <i>stopping power</i>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Restricted_and_unrestricted_LET">Restricted and unrestricted LET</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Linear_energy_transfer&action=edit&section=1" title="Edit section: Restricted and unrestricted LET"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The secondary electrons produced during the process of <a href="/wiki/Ionization" title="Ionization">ionization</a> by the primary charged particle are conventionally called <a href="/wiki/Delta_ray" title="Delta ray">delta rays</a>, if their energy is large enough so that they themselves can ionize.<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> Many studies focus upon the energy transferred in the vicinity of the primary particle track and therefore exclude interactions that produce delta rays with energies larger than a certain value Δ.<sup id="cite_ref-ICRU85a_1-1" class="reference"><a href="#cite_note-ICRU85a-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> This energy limit is meant to exclude secondary electrons that carry energy far from the primary particle track, since a larger energy implies a larger <a href="/wiki/Range_(particle_radiation)" title="Range (particle radiation)">range</a>. This approximation neglects the directional distribution of secondary radiation and the non-linear path of delta rays, but simplifies analytic evaluation.<sup id="cite_ref-icru16_4-0" class="reference"><a href="#cite_note-icru16-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>In mathematical terms, <b>Restricted linear energy transfer</b> is defined by </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_{\Delta }={\frac {{\text{d}}E_{\Delta }}{{\text{d}}x}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>d</mtext> </mrow> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> </mrow> </msub> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>d</mtext> </mrow> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{\Delta }={\frac {{\text{d}}E_{\Delta }}{{\text{d}}x}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0954ce30c7bfae5d9511f34e9247a5cb8f693993" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:12.374ex; height:5.509ex;" alt="{\displaystyle L_{\Delta }={\frac {{\text{d}}E_{\Delta }}{{\text{d}}x}},}"></span></dd></dl> <p>where <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 {\text{d}}E_{\Delta }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>d</mtext> </mrow> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{d}}E_{\Delta }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/84135d660ebd7bd71857cc4e9b1c42af0afe8351" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.609ex; height:2.509ex;" alt="{\displaystyle {\text{d}}E_{\Delta }}"></span> is the energy loss of the charged particle due to electronic collisions while traversing a distance <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 {{\text{d}}x}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mtext>d</mtext> </mrow> <mi>x</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {{\text{d}}x}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e8348577e55970020663b1f2980c32197beb3da8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.622ex; height:2.176ex;" alt="{\displaystyle {{\text{d}}x}}"></span>, <i>excluding</i> all secondary electrons with kinetic energies larger than Δ. If Δ tends toward infinity, then there are no electrons with larger energy, and the linear energy transfer becomes the <b>unrestricted linear energy transfer</b> which is identical to the linear electronic <i><a href="/wiki/Stopping_power_(particle_radiation)" title="Stopping power (particle radiation)">stopping power</a></i>.<sup id="cite_ref-ICRU85a_1-2" class="reference"><a href="#cite_note-ICRU85a-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Here, the use of the term "infinity" is not to be taken literally; it simply means that no energy transfers, however large, are excluded. </p> <div class="mw-heading mw-heading2"><h2 id="Application_to_radiation_types">Application to radiation types</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Linear_energy_transfer&action=edit&section=2" title="Edit section: Application to radiation types"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>During his investigations of radioactivity, <a href="/wiki/Ernest_Rutherford" title="Ernest Rutherford">Ernest Rutherford</a> coined the terms <a href="/wiki/Alpha_rays" class="mw-redirect" title="Alpha rays">alpha rays</a>, <a href="/wiki/Beta_rays" class="mw-redirect" title="Beta rays">beta rays</a> and <a href="/wiki/Gamma_ray" title="Gamma ray">gamma rays</a> for the three types of emissions that occur during <a href="/wiki/Radioactive_decay" title="Radioactive decay">radioactive decay</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Alpha_particles_and_other_positive_ions">Alpha particles and other positive ions</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Linear_energy_transfer&action=edit&section=3" title="Edit section: Alpha particles and other positive ions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Bragg_Curve_for_Alphas_in_Air-PT-en.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Bragg_Curve_for_Alphas_in_Air-PT-en.svg/300px-Bragg_Curve_for_Alphas_in_Air-PT-en.svg.png" decoding="async" width="300" height="199" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Bragg_Curve_for_Alphas_in_Air-PT-en.svg/450px-Bragg_Curve_for_Alphas_in_Air-PT-en.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Bragg_Curve_for_Alphas_in_Air-PT-en.svg/600px-Bragg_Curve_for_Alphas_in_Air-PT-en.svg.png 2x" data-file-width="719" data-file-height="478" /></a><figcaption>Bragg curve of 5.49 MeV <a href="/wiki/Alpha_particle" title="Alpha particle">alpha particles</a> in air. This radiation is produced by the decay of <a href="/wiki/Radon" title="Radon">radon</a> (<sup>222</sup>Rn); its range is 4.14 cm. Stopping power (which is essentially identical to LET) is plotted here versus path length; its peak is the "<a href="/wiki/Bragg_peak" title="Bragg peak">Bragg peak</a>"</figcaption></figure> <p>Linear energy transfer is best defined for monoenergetic ions, i.e. <a href="/wiki/Proton" title="Proton">protons</a>, <a href="/wiki/Alpha_radiation" class="mw-redirect" title="Alpha radiation">alpha particles</a>, and the heavier nuclei called <a href="/wiki/HZE_ions" class="mw-redirect" title="HZE ions">HZE ions</a> found in <a href="/wiki/Cosmic_ray" title="Cosmic ray">cosmic rays</a> or produced by <a href="/wiki/Particle_accelerator" title="Particle accelerator">particle accelerators</a>. These particles cause frequent direct ionizations within a narrow diameter around a relatively straight track, thus approximating continuous deceleration. As they slow down, the changing <a href="/wiki/Particle_cross_section" class="mw-redirect" title="Particle cross section">particle cross section</a> modifies their LET, generally increasing it to a <a href="/wiki/Bragg_peak" title="Bragg peak">Bragg peak</a> just before achieving thermal equilibrium with the absorber, i.e., before the end of <a href="/wiki/Stopping_power_(particle_radiation)" title="Stopping power (particle radiation)">range</a>. At equilibrium, the incident particle essentially comes to rest or is absorbed, at which point LET is undefined. </p><p>Since the LET varies over the particle track, an average value is often used to represent the spread. Averages weighted by track length or weighted by absorbed dose are present in the literature, with the latter being more common in dosimetry. These averages are not widely separated for heavy particles with high LET, but the difference becomes more important in the other type of radiations discussed below.<sup id="cite_ref-icru16_4-1" class="reference"><a href="#cite_note-icru16-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>Often overlooked for alpha particles is the recoil-nucleus of the alpha emitter, which has significant ionization energy of roughly 5% of the alpha particle, but because of its high electric charge and large mass, has an ultra-short range of only a few <a href="/wiki/Angstrom" title="Angstrom">Angstroms</a>. This can skew results significantly if one is examining the <a href="/wiki/Relative_Biological_Effectiveness" class="mw-redirect" title="Relative Biological Effectiveness">Relative Biological Effectiveness</a> of the alpha particle in the cytoplasm, while ignoring the recoil nucleus contribution, which alpha-parent being one of numerous <a href="/wiki/Heavy_metals" class="mw-redirect" title="Heavy metals">heavy metals</a>, is typically adhered to chromatic material such as <a href="/wiki/Chromosome" title="Chromosome">chromosomes</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Beta_particles">Beta particles</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Linear_energy_transfer&action=edit&section=4" title="Edit section: Beta particles"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Electrons produced in nuclear decay are called <a href="/wiki/Beta_particle" title="Beta particle">beta particles</a>. Because of their low mass relative to atoms, they are strongly scattered by nuclei (Coulomb or <a href="/wiki/Rutherford_scattering" class="mw-redirect" title="Rutherford scattering">Rutherford scattering</a>), much more so than heavier particles. Beta particle tracks are therefore crooked. In addition to producing <a href="/wiki/Secondary_electrons" title="Secondary electrons">secondary electrons</a> (delta rays) while ionizing atoms, they also produce <a href="/wiki/Bremsstrahlung" title="Bremsstrahlung">bremsstrahlung</a> photons. A maximum range of beta radiation can be defined experimentally<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> which is smaller than the range that would be measured along the particle path. </p> <div class="mw-heading mw-heading3"><h3 id="Gamma_rays">Gamma rays</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Linear_energy_transfer&action=edit&section=5" title="Edit section: Gamma rays"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Gamma_ray" title="Gamma ray">Gamma rays</a> are photons, whose absorption cannot be described by LET. When a gamma <a href="/wiki/Quantum" title="Quantum">quantum</a> passes through matter, it may be absorbed in a single process (<a href="/wiki/Photoelectric_effect" title="Photoelectric effect">photoelectric effect</a>, <a href="/wiki/Compton_scattering" title="Compton scattering">Compton effect</a> or <a href="/wiki/Pair_production" title="Pair production">pair production</a>), or it continues unchanged on its path. (Only in the case of the Compton effect, another gamma quantum of lower energy proceeds). Gamma ray absorption therefore obeys an <a href="/wiki/Exponential_decay" title="Exponential decay">exponential</a> law (see <a href="/wiki/Gamma_ray" title="Gamma ray">Gamma rays</a>); the absorption is described by the absorption coefficient or by the <a href="/wiki/Half-value_thickness" class="mw-redirect" title="Half-value thickness">half-value thickness</a>. </p><p>LET has therefore no meaning when applied to photons. However, many authors speak of "gamma LET" anyway,<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> where they are actually referring to the LET of the <a href="/wiki/Secondary_electrons" title="Secondary electrons">secondary electrons</a>, i.e., mainly Compton electrons, produced by the gamma radiation.<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> The <a href="/wiki/Secondary_electron" class="mw-redirect" title="Secondary electron">secondary electrons</a> will ionize far more atoms than the primary photon. This gamma LET has little relation to the attenuation rate of the beam, but it may have some correlation to the microscopic defects produced in the absorber. Even a monoenergetic gamma beam will produce a spectrum of electrons, and each secondary electron will have a variable LET as it slows down, as discussed above. The "gamma LET" is therefore an average. </p><p>The transfer of energy from an uncharged primary particle to charged secondary particles can also be described by using the <i>mass energy-transfer coefficient</i>.<sup id="cite_ref-ICRU85a_1-3" class="reference"><a href="#cite_note-ICRU85a-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Biological_effects">Biological effects</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Linear_energy_transfer&action=edit&section=6" title="Edit section: Biological effects"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:QF_vs_LET.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/QF_vs_LET.jpg/220px-QF_vs_LET.jpg" decoding="async" width="220" height="142" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6f/QF_vs_LET.jpg/330px-QF_vs_LET.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6f/QF_vs_LET.jpg/440px-QF_vs_LET.jpg 2x" data-file-width="785" data-file-height="507" /></a><figcaption>The <a href="/wiki/ICRP" class="mw-redirect" title="ICRP">ICRP</a> used to recommend <a href="/wiki/Radiation_weighting_factor" class="mw-redirect" title="Radiation weighting factor">quality factors</a> as a generalized approximation of RBE based on LET.</figcaption></figure> <p>Many studies have attempted to relate linear energy transfer to the <a href="/wiki/Relative_biological_effectiveness" title="Relative biological effectiveness">relative biological effectiveness</a> (RBE) of radiation, with inconsistent results. The relationship varies widely depending on the nature of the biological material, and the choice of endpoint to define effectiveness. Even when these are held constant, different radiation spectra that shared the same LET have significantly different RBE.<sup id="cite_ref-icru16_4-2" class="reference"><a href="#cite_note-icru16-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>Despite these variations, some overall trends are commonly seen. The RBE is generally independent of LET for any LET less than 10 keV/μm, so a low LET is normally chosen as the reference condition where RBE is set to unity. Above 10 keV/μm, some systems show a decline in RBE with increasing LET, while others show an initial increase to a peak before declining. Mammalian cells usually experience a peak RBE for LET's around 100 keV/μm.<sup id="cite_ref-icru16_4-3" class="reference"><a href="#cite_note-icru16-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> These are very rough numbers; for example, one set of experiments found a peak at 30 keV/μm. </p><p>The International Commission on Radiation Protection (<a href="/wiki/ICRP" class="mw-redirect" title="ICRP">ICRP</a>) proposed a simplified model of RBE-LET relationships for use in <a href="/wiki/Dosimetry" title="Dosimetry">dosimetry</a>. They defined a <i>quality factor</i> of radiation as a function of dose-averaged unrestricted LET in water, and intended it as a highly uncertain, but generally conservative, approximation of RBE. Different iterations of their model are shown in the graph to the right. The 1966 model was integrated into their 1977 recommendations for radiation protection in ICRP 26. This model was largely replaced in the 1991 recommendations of ICRP 60 by <a href="/wiki/Radiation_weighting_factor" class="mw-redirect" title="Radiation weighting factor">radiation weighting factors</a> that were tied to the particle type and independent of LET. ICRP 60 revised the quality factor function and reserved it for use with unusual radiation types that did not have radiation weighting factors assigned to them.<sup id="cite_ref-icrp92_8-0" class="reference"><a href="#cite_note-icrp92-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Application_fields">Application fields</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Linear_energy_transfer&action=edit&section=7" title="Edit section: Application fields"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>When used to describe the <i><a href="/wiki/Dosimetry" title="Dosimetry">dosimetry</a></i> of ionizing radiation in the biological or biomedical setting, the LET (like <a href="/wiki/Stopping_power_(particle_radiation)" title="Stopping power (particle radiation)">linear stopping power</a>) is usually expressed in units of k<a href="/wiki/Electron_volts" class="mw-redirect" title="Electron volts">eV</a>/<a href="/wiki/Micrometre" title="Micrometre">μm</a>. </p><p>In <i><a href="/wiki/Outer_space" title="Outer space">space</a> applications</i>, <a href="/wiki/Electronic_device" class="mw-redirect" title="Electronic device">electronic devices</a> can be disturbed by the passage of energetic electrons, protons or heavier ions that may alter the state of a <a href="/wiki/Electronic_circuit" title="Electronic circuit">circuit</a>, producing "<a href="/wiki/Single_event_upset" class="mw-redirect" title="Single event upset">single event effects</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> The effect of the radiation is described by the LET (which is here taken as synonymous with stopping power), typically expressed in units of MeV·cm<sup>2</sup>/mg of material, the units used for mass stopping power (the material in question is usually Si for MOS devices). The units of measurement arise from a combination of the energy lost by the particle to the material per unit path length (MeV/cm) divided by the density of the material (mg/cm<sup>3</sup>).<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><p>"Soft errors" of electronic devices due to <a href="/wiki/Cosmic_rays" class="mw-redirect" title="Cosmic rays">cosmic rays</a> on earth are, however, mostly due to <a href="/wiki/Neutron" title="Neutron">neutrons</a> which do not directly interact with the material and whose passage can therefore not be described by LET. Rather, one measures their effect in terms of neutrons per cm<sup>2</sup> per hour, see <a href="/wiki/Soft_error" title="Soft error">Soft error</a>. </p> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Linear_energy_transfer&action=edit&section=8" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-ICRU85a-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-ICRU85a_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-ICRU85a_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-ICRU85a_1-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-ICRU85a_1-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFInternational_Commission_on_Radiation_Units_and_Measurements2011" class="citation journal cs1">International Commission on Radiation Units and Measurements (October 2011). Seltzer, Stephen M. (ed.). "Report 85: Fundamental Quantities and Units for Ionizing Radiation". <i>Journal of the International Commission on Radiation Units and Measurements</i>. <b>11</b> (1) (Revised ed.): 1–31. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fjicru%2Fndr012">10.1093/jicru/ndr012</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/24174259">24174259</a>. ICRU report 85a.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+the+International+Commission+on+Radiation+Units+and+Measurements&rft.atitle=Report+85%3A+Fundamental+Quantities+and+Units+for+Ionizing+Radiation&rft.volume=11&rft.issue=1&rft.pages=1-31&rft.date=2011-10&rft_id=info%3Adoi%2F10.1093%2Fjicru%2Fndr012&rft_id=info%3Apmid%2F24174259&rft.au=International+Commission+on+Radiation+Units+and+Measurements&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALinear+energy+transfer" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSmith1997" class="citation book cs1">Smith, Roger (1997). <i>Atomic & ion collisions in solids and at surfaces: theory, simulation and applications</i>. Cambridge, UK: Cambridge University Press.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Atomic+%26+ion+collisions+in+solids+and+at+surfaces%3A+theory%2C+simulation+and+applications&rft.place=Cambridge%2C+UK&rft.pub=Cambridge+University+Press&rft.date=1997&rft.aulast=Smith&rft.aufirst=Roger&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALinear+energy+transfer" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.britannica.com/EBchecked/topic/156866/delta-ray">"Delta ray" in Encyclopedia britannica online, retrieved 22 Dec. 2012</a></span> </li> <li id="cite_note-icru16-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-icru16_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-icru16_4-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-icru16_4-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-icru16_4-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFInternational_Commission_on_Radiation_Units_and_Measurements1970" class="citation book cs1">International Commission on Radiation Units and Measurements (1970). <i>Linear Energy Transfer</i>. Washington D.C. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fjicru%2Fos9.1.Report16">10.1093/jicru/os9.1.Report16</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0913394090" title="Special:BookSources/978-0913394090"><bdi>978-0913394090</bdi></a>. ICRU report 16.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Linear+Energy+Transfer&rft.place=Washington+D.C.&rft.date=1970&rft_id=info%3Adoi%2F10.1093%2Fjicru%2Fos9.1.Report16&rft.isbn=978-0913394090&rft.au=International+Commission+on+Radiation+Units+and+Measurements&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALinear+energy+transfer" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: location missing publisher (<a href="/wiki/Category:CS1_maint:_location_missing_publisher" title="Category:CS1 maint: location missing publisher">link</a>)</span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">G. Knop and W. Paul: <i>Interaction of electrons</i> in <i>Alpha- Beta- and Gamma-Ray Spectroscopy</i> edited by K. Siegbahn, North-Holland, Amsterdam, 1966</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text">ICRP (International Commission on Radiation Protection) publication 103, ICRP 37 (2-4) (2007): "(116) Photons, electrons, and muons are radiations with LET values of less than 10 keV/microm."</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChabot" class="citation web cs1">Chabot, George. <a rel="nofollow" class="external text" href="http://www.hps.org/publicinformation/ate/q10010.html">"Radiation Basics — Radiation Quantities and Units"</a>. <i>Ask the Experts FAQ</i>. Health Physics Society<span class="reference-accessdate">. Retrieved <span class="nowrap">12 December</span> 2012</span>. <q>When the term "stopping power" is used in reference to photons, as seems to be the case for the example you give, it is not really being used for the photons themselves, but for the electrons set free by the photon interactions.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Ask+the+Experts+FAQ&rft.atitle=Radiation+Basics+%E2%80%94+Radiation+Quantities+and+Units&rft.aulast=Chabot&rft.aufirst=George&rft_id=http%3A%2F%2Fwww.hps.org%2Fpublicinformation%2Fate%2Fq10010.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALinear+energy+transfer" class="Z3988"></span></span> </li> <li id="cite_note-icrp92-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-icrp92_8-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSinclair2003" class="citation journal cs1">Sinclair, Dr. W. K.; et al. (January 2003). <a rel="nofollow" class="external text" href="http://www.elsevier.ca/ISBN/9780080443119/ICRP-Publication-92-Relative-Biological-Effectiveness-RBE-Quality-Factor-Q-and-Radiation-Weighting-Factor-wR">"Relative biological effectiveness (RBE), quality factor (Q) and radiation weighting factor (Wr)"</a>. <i>Annals of the ICRP</i>. <b>33</b> (4). <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-08-044311-9" title="Special:BookSources/978-0-08-044311-9"><bdi>978-0-08-044311-9</bdi></a>. ICRP Publication 92.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annals+of+the+ICRP&rft.atitle=Relative+biological+effectiveness+%28RBE%29%2C+quality+factor+%28Q%29+and+radiation+weighting+factor+%28Wr%29&rft.volume=33&rft.issue=4&rft.date=2003-01&rft.isbn=978-0-08-044311-9&rft.aulast=Sinclair&rft.aufirst=Dr.+W.+K.&rft_id=http%3A%2F%2Fwww.elsevier.ca%2FISBN%2F9780080443119%2FICRP-Publication-92-Relative-Biological-Effectiveness-RBE-Quality-Factor-Q-and-Radiation-Weighting-Factor-wR&rfr_id=info%3Asid%2Fen.wikipedia.org%3ALinear+energy+transfer" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text">V. Zajic and P. Thieberger, "Heavy Ion Linear Energy Transfer Measurements during Single Event Upset Testing of Electronic Devices," IEEE Transactions on Nuclear Science 46, pp. 59-69, (1999)</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://radhome.gsfc.nasa.gov/top.htm">Radiation Effects & Analysis Home Page of NASA</a></span> </li> </ol></div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl 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fusion</a></li> <li><a href="/wiki/Nuclear_reactor" title="Nuclear reactor">Nuclear reactors</a></li> <li><a href="/wiki/Nuclear_weapon" title="Nuclear weapon">Nuclear weapons</a></li> <li><a href="/wiki/Particle_accelerator" title="Particle accelerator">Particle accelerators</a></li> <li><a href="/wiki/Radionuclide" title="Radionuclide">Radioactive materials</a></li> <li><a href="/wiki/X-ray" title="X-ray">X-ray</a></li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Earth%27s_energy_budget" title="Earth's energy budget">Earth's energy budget</a></li> <li><a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">Electromagnetic radiation</a></li> <li><a href="/wiki/Synchrotron_radiation" title="Synchrotron radiation">Synchrotron radiation</a></li> <li><a href="/wiki/Thermal_radiation" title="Thermal radiation">Thermal radiation</a></li> <li><a href="/wiki/Black-body_radiation" title="Black-body radiation">Black-body radiation</a></li> <li><a href="/wiki/Particle_radiation" title="Particle radiation">Particle radiation</a></li> <li><a href="/wiki/Gravitational_radiation" class="mw-redirect" title="Gravitational radiation">Gravitational radiation</a></li> <li><a href="/wiki/Cosmic_background_radiation" title="Cosmic background radiation">Cosmic background radiation</a></li> <li><a href="/wiki/Cherenkov_radiation" title="Cherenkov radiation">Cherenkov radiation</a></li> <li><a href="/wiki/Askaryan_radiation" title="Askaryan radiation">Askaryan radiation</a></li> <li><a href="/wiki/Bremsstrahlung" title="Bremsstrahlung">Bremsstrahlung</a></li> <li><a href="/wiki/Unruh_radiation" class="mw-redirect" title="Unruh radiation">Unruh radiation</a></li> <li><a href="/wiki/Dark_radiation" title="Dark radiation">Dark radiation</a></li> <li><a href="/wiki/Radiation_exposure" title="Radiation exposure">Radiation exposure</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Radiation <br />and health</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>Radiation syndrome <ul><li><a href="/wiki/Acute_radiation_syndrome" title="Acute radiation syndrome">acute</a></li> <li><a href="/wiki/Chronic_radiation_syndrome" title="Chronic radiation syndrome">chronic</a></li></ul></li> <li><a href="/wiki/Health_physics" title="Health physics">Health physics</a></li> <li><a href="/wiki/Dosimetry" title="Dosimetry">Dosimetry</a></li> <li><a href="/wiki/Electromagnetic_radiation_and_health" title="Electromagnetic radiation and health">Electromagnetic radiation and health</a></li> <li><a href="/wiki/Laser_safety" title="Laser safety">Laser safety</a></li> <li><a href="/wiki/Lasers_and_aviation_safety" title="Lasers and aviation safety">Lasers and aviation safety</a></li> <li><a href="/wiki/Medical_radiography" class="mw-redirect" title="Medical radiography">Medical radiography</a></li> <li><a href="/wiki/Radiation_protection" title="Radiation protection">Radiation protection</a></li> <li><a href="/wiki/Radiation_therapy" title="Radiation therapy">Radiation therapy</a></li> <li><a href="/wiki/Radiation_damage" title="Radiation damage">Radiation damage</a></li> <li><a href="/wiki/Radioactivity_in_the_life_sciences" title="Radioactivity in the life sciences">Radioactivity in the life sciences</a></li> <li><a href="/wiki/Radioactive_contamination" title="Radioactive contamination">Radioactive contamination</a></li> <li><a href="/wiki/Radiobiology" title="Radiobiology">Radiobiology</a></li> <li><a href="/wiki/Sievert" title="Sievert">Biological dose units and quantities</a></li> <li><a href="/wiki/Wireless_device_radiation_and_health" title="Wireless device radiation and health">Wireless device radiation and health</a></li> <li><a href="/wiki/Wireless_electronic_devices_and_health" class="mw-redirect" title="Wireless electronic devices and health">Wireless electronic devices and health</a></li> <li><a href="/wiki/Heat_transfer" title="Heat transfer">Radiation heat-transfer</a></li> <li><a class="mw-selflink selflink">Linear energy transfer</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Radiation incidents</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_civilian_radiation_accidents" title="List of civilian radiation accidents">List of civilian radiation accidents</a></li> <li><a href="/wiki/1996_San_Juan_de_Dios_radiotherapy_accident" title="1996 San Juan de Dios radiotherapy accident">1996 Costa Rica accident</a></li> <li><a href="/wiki/Goi%C3%A2nia_accident" title="Goiânia accident">1987 Goiânia accident</a></li> <li><a href="/wiki/1984_Moroccan_radiation_accident" title="1984 Moroccan radiation accident">1984 Moroccan accident</a></li> <li><a href="/wiki/1990_Clinic_of_Zaragoza_radiotherapy_accident" class="mw-redirect" title="1990 Clinic of Zaragoza radiotherapy accident">1990 Zaragoza accident</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related articles</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Half-life" title="Half-life">Half-life</a></li> <li><a href="/wiki/Nuclear_physics" title="Nuclear physics">Nuclear physics</a></li> <li><a href="/wiki/Radioactive_source" title="Radioactive source">Radioactive source</a></li> <li><a href="/wiki/Radiation_hardening" title="Radiation hardening">Radiation hardening</a></li> <li><a href="/wiki/Havana_syndrome" title="Havana syndrome">Havana syndrome</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><div role="note" class="hatnote navigation-not-searchable selfref">See also the categories <a href="/wiki/Category:Radiation_effects" title="Category:Radiation effects">Radiation effects</a>, <a href="/wiki/Category:Radioactivity" title="Category:Radioactivity">Radioactivity</a>, <a href="/wiki/Category:Radiobiology" title="Category:Radiobiology">Radiobiology</a>, and <a href="/wiki/Category:Radiation_protection" title="Category:Radiation protection">Radiation protection</a></div></div></td></tr></tbody></table></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; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" 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