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<h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Diffusion de Mott</span></h1>
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<p>La <b>diffusion de Mott</b> est la <a href="Diffusion_des_particules" title="Diffusion des particules">diffusion</a> d'un <a href="Lepton" title="Lepton">lepton</a> de <a href="Spin" title="Spin">spin</a> 1/2 sur une <a href="Particule_%C3%A9l%C3%A9mentaire" title="Particule élémentaire">particule</a> ponctuelle de spin 1/2, de <a href="Masse" title="Masse">masse</a> finie et de <a href="Charge_%C3%A9lectrique" title="Charge électrique">charge électrique</a> <span class="mwe-math-element mwe-math-element-inline"><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}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>e</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle e}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/cd253103f0876afc68ebead27a5aa9867d927467.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.083ex; height:1.676ex;" alt="{\displaystyle e}" loading="lazy"></span>. Elle ne dépend que de la <a href="Cin%C3%A9matique" title="Cinématique">cinématique</a>, et sa <a href="Section_efficace" title="Section efficace">section efficace</a> s'écrit :
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><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 {d\sigma }{d\Omega }}=\left({\frac {\alpha \cos {\frac {\theta }{2}}}{2E\sin ^{2}{\frac {\theta }{2}}}}\right)^{2}{\frac {E}{E'}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi>d</mi>
<mi>σ<!-- σ --></mi>
</mrow>
<mrow>
<mi>d</mi>
<mi mathvariant="normal">Ω<!-- Ω --></mi>
</mrow>
</mfrac>
</mrow>
<mo>=</mo>
<msup>
<mrow>
<mo>(</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi>α<!-- α --></mi>
<mi>cos</mi>
<mo><!-- --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>θ<!-- θ --></mi>
<mn>2</mn>
</mfrac>
</mrow>
</mrow>
<mrow>
<mn>2</mn>
<mi>E</mi>
<msup>
<mi>sin</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo><!-- --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>θ<!-- θ --></mi>
<mn>2</mn>
</mfrac>
</mrow>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>E</mi>
<msup>
<mi>E</mi>
<mo>′</mo>
</msup>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\frac {d\sigma }{d\Omega }}=\left({\frac {\alpha \cos {\frac {\theta }{2}}}{2E\sin ^{2}{\frac {\theta }{2}}}}\right)^{2}{\frac {E}{E'}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f06095f674d1b3605ae9962e1b936933cbccd141.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.505ex; width:24.995ex; height:8.676ex;" alt="{\displaystyle {\frac {d\sigma }{d\Omega }}=\left({\frac {\alpha \cos {\frac {\theta }{2}}}{2E\sin ^{2}{\frac {\theta }{2}}}}\right)^{2}{\frac {E}{E'}}}" loading="lazy"></span>,</dd></dl>
<p>où <span class="mwe-math-element mwe-math-element-inline"><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}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>E</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle E}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}" loading="lazy"></span> est l'<a href="%C3%89nergie" title="Énergie">énergie</a> du lepton dans le référentiel de la particule ponctuelle au repos, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta }">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>θ<!-- θ --></mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \theta }</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/6e5ab2664b422d53eb0c7df3b87e1360d75ad9af.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }" loading="lazy"></span> l'angle de diffusion, <span class="mwe-math-element mwe-math-element-inline"><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<!-- α --></mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b79333175c8b3f0840bfb4ec41b8072c83ea88d3.svg" 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 }" loading="lazy"></span> la <a href="Constante_de_structure_fine" title="Constante de structure fine">constante de structure fine</a>, et l'énergie de recul <span class="mwe-math-element mwe-math-element-inline"><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'}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msup>
<mi>E</mi>
<mo>′</mo>
</msup>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle E'}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/a574600572696493d48300245a45b8de0638ce21.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.479ex; height:2.509ex;" alt="{\displaystyle E'}" loading="lazy"></span> est définie comme
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><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'={\frac {E}{1+{\frac {2E}{M}}\sin ^{2}{\frac {\theta }{2}}}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msup>
<mi>E</mi>
<mo>′</mo>
</msup>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>E</mi>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mn>2</mn>
<mi>E</mi>
</mrow>
<mi>M</mi>
</mfrac>
</mrow>
<msup>
<mi>sin</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
<mo><!-- --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>θ<!-- θ --></mi>
<mn>2</mn>
</mfrac>
</mrow>
</mrow>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle E'={\frac {E}{1+{\frac {2E}{M}}\sin ^{2}{\frac {\theta }{2}}}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/bbe1bc41ae2cf73d136b4066e96f9575a087de8b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.505ex; width:19.672ex; height:6.843ex;" alt="{\displaystyle E'={\frac {E}{1+{\frac {2E}{M}}\sin ^{2}{\frac {\theta }{2}}}}}" loading="lazy"></span>,</dd></dl>
<p>avec <span class="mwe-math-element mwe-math-element-inline"><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="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f82cade9898ced02fdd08712e5f0c0151758a0dd.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.442ex; height:2.176ex;" alt="{\displaystyle M}" loading="lazy"></span> la masse de la particule ponctuelle.
</p>
<div class="mw-heading mw-heading2"><h2 id="Notes_et_références"><span id="Notes_et_r.C3.A9f.C3.A9rences"></span>Notes et références</h2></div>
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