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<h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Absorptionskoeffizient</span></h1>
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<p>Der <b>Absorptionskoeffizient</b>, auch <b>Dämpfungskonstante</b> oder <b>linearer Schwächungskoeffizient</b>, ist ein Maß für die Verringerung der <a href="Intensit%C3%A4t_(Physik)" title="Intensität (Physik)">Intensität</a> <a href="Elektromagnetische_Strahlung" class="mw-redirect" title="Elektromagnetische Strahlung">elektromagnetischer Strahlung</a> beim Durchgang durch ein gegebenes Material. Er wird in der <a href="Optik" title="Optik">Optik</a> und in Bezug auf <a href="R%C3%B6ntgenstrahlung" title="Röntgenstrahlung">Röntgenstrahlung</a> und <a href="Gammastrahlung" title="Gammastrahlung">Gammastrahlung</a> verwendet. Sein übliches Formelsymbol ist in der Optik <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> oder <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">
<msup>
<mi>α<!-- α --></mi>
<mo>′</mo>
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<annotation encoding="application/x-tex">{\displaystyle \alpha '}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/6cb0468d39268c4405a9286d2cba77c2e4631fed.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.172ex; height:2.509ex;" alt="{\displaystyle \alpha '}" loading="lazy"></span>, bei Röntgen- und Gammastrahlung <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 \mu }">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>μ<!-- μ --></mi>
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<annotation encoding="application/x-tex">{\displaystyle \mu }</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/9fd47b2a39f7a7856952afec1f1db72c67af6161.svg" 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 }" loading="lazy"></span>. Seine <a href="Dimension_(Physik)" class="mw-redirect" title="Dimension (Physik)">Dimension</a> ist 1/Länge, die übliche Einheit 1/cm. Ein großer Absorptionskoeffizient bedeutet, dass das Material die betrachtete Strahlung relativ stark abschirmt, ein kleiner dagegen, dass es durchlässiger für die Strahlung ist.
</p><p>In der Bezeichnung Absorptionskoeffizient ist der Begriff <a href="Absorption_(Physik)" title="Absorption (Physik)">Absorption</a> <i>nicht</i> im engeren Sinn der Abgabe von <a href="Strahlungsenergie" title="Strahlungsenergie">Strahlungsenergie</a> an das Medium zu verstehen. Zur hier gemeinten Intensitätsabnahme (<a href="Extinktion_(Optik)" title="Extinktion (Optik)">Extinktion</a>) tragen vielmehr auch <a href="Streuprozess" class="mw-redirect" title="Streuprozess">Streuprozesse</a> bei, die die Strahlung nur aus ihrer Richtung ablenken.
</p>
<div class="mw-heading mw-heading2"><h2 id="Anwendung">Anwendung</h2></div>
<p>Gemäß dem <a href="Lambert-Beer%E2%80%99sches_Gesetz" class="mw-redirect" title="Lambert-Beer’sches Gesetz">Lambert-Beerschen Gesetz</a> klingt die Intensität <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 I}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>I</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle I}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/535ea7fc4134a31cbe2251d9d3511374bc41be9f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\displaystyle I}" loading="lazy"></span> nach Durchlaufen eines Absorbers der Dicke <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 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="./_assets_/eb734a37dd21ce173a46342d1cc64c92/bf368e72c009decd9b6686ee84a375632e11de98.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.088ex; height:1.676ex;" alt="{\displaystyle z}" loading="lazy"></span> bzw. in einer Eindringtiefe <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 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="./_assets_/eb734a37dd21ce173a46342d1cc64c92/bf368e72c009decd9b6686ee84a375632e11de98.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.088ex; height:1.676ex;" alt="{\displaystyle z}" loading="lazy"></span> <a href="Exponentiell" class="mw-redirect" title="Exponentiell">exponentiell</a> ab:
</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 {\begin{aligned}I(z)&=I_{0}\cdot e^{-\alpha z}\\&=I_{0}\cdot \exp \left(-2n''\,{\frac {\omega }{c}}\,z\right)\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>
<mi>I</mi>
<mo stretchy="false">(</mo>
<mi>z</mi>
<mo stretchy="false">)</mo>
</mtd>
<mtd>
<mi></mi>
<mo>=</mo>
<msub>
<mi>I</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>0</mn>
</mrow>
</msub>
<mo>⋅<!-- ⋅ --></mo>
<msup>
<mi>e</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>−<!-- − --></mo>
<mi>α<!-- α --></mi>
<mi>z</mi>
</mrow>
</msup>
</mtd>
</mtr>
<mtr>
<mtd></mtd>
<mtd>
<mi></mi>
<mo>=</mo>
<msub>
<mi>I</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>0</mn>
</mrow>
</msub>
<mo>⋅<!-- ⋅ --></mo>
<mi>exp</mi>
<mo><!-- --></mo>
<mrow>
<mo>(</mo>
<mrow>
<mo>−<!-- − --></mo>
<mn>2</mn>
<msup>
<mi>n</mi>
<mo>″</mo>
</msup>
<mspace width="thinmathspace"></mspace>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>ω<!-- ω --></mi>
<mi>c</mi>
</mfrac>
</mrow>
<mspace width="thinmathspace"></mspace>
<mi>z</mi>
</mrow>
<mo>)</mo>
</mrow>
</mtd>
</mtr>
</mtable>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}I(z)&=I_{0}\cdot e^{-\alpha z}\\&=I_{0}\cdot \exp \left(-2n''\,{\frac {\omega }{c}}\,z\right)\end{aligned}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/516d5abb77e8657e659e0efcd05b16d158cb477e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:27.65ex; height:7.843ex;" alt="{\displaystyle {\begin{aligned}I(z)&=I_{0}\cdot e^{-\alpha z}\\&=I_{0}\cdot \exp \left(-2n''\,{\frac {\omega }{c}}\,z\right)\end{aligned}}}" loading="lazy"></span></dd></dl>
<p>mit
</p>
<ul><li>der eingestrahlten Intensität <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 I_{0}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>I</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>0</mn>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle I_{0}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/893d08e90ea73781dc133414d661529d0651ca80.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.077ex; height:2.509ex;" alt="{\displaystyle I_{0}}" loading="lazy"></span></li>
<li>dem Absorptionskoeffizienten <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 =2n''\,{\frac {\omega }{c}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>α<!-- α --></mi>
<mo>=</mo>
<mn>2</mn>
<msup>
<mi>n</mi>
<mo>″</mo>
</msup>
<mspace width="thinmathspace"></mspace>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>ω<!-- ω --></mi>
<mi>c</mi>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \alpha =2n''\,{\frac {\omega }{c}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/2cabd2165dfe5c5c1dbf9e28e98f134a9e67a7a7.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:10.949ex; height:4.676ex;" alt="{\displaystyle \alpha =2n''\,{\frac {\omega }{c}}}" loading="lazy"></span>
<ul><li>dem <a href="Extinktionskoeffizient" title="Extinktionskoeffizient">Extinktionskoeffizienten</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 n''}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msup>
<mi>n</mi>
<mo>″</mo>
</msup>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle n''}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/2e0cc872b3fe6eb303b8e4a13c26bd7dccc1f7e5.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.532ex; height:2.509ex;" alt="{\displaystyle n''}" loading="lazy"></span> des Materials</li>
<li>der <a href="Kreisfrequenz" title="Kreisfrequenz">Kreisfrequenz</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 \omega }">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>ω<!-- ω --></mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \omega }</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/48eff443f9de7a985bb94ca3bde20813ea737be8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.446ex; height:1.676ex;" alt="{\displaystyle \omega }" loading="lazy"></span> der verwendeten Strahlung (hängt mit deren <a href="Energie" title="Energie">Energie</a> zusammen)</li>
<li>der <a href="Lichtgeschwindigkeit" title="Lichtgeschwindigkeit">Lichtgeschwindigkeit</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 c}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>c</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle c}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/86a67b81c2de995bd608d5b2df50cd8cd7d92455.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}" loading="lazy"></span>.</li></ul></li></ul>
<div class="mw-heading mw-heading3"><h3 id="Herleitung">Herleitung</h3></div>
<p>Ersetzt man in
</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 {\vec {E}}={\vec {E}}_{0}\cdot e^{i\left[{\vec {k}}\,{\vec {r}}-\omega t\right]}={\vec {E}}_{0}\cdot e^{i\left[kz-\omega t\right]}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>E</mi>
<mo stretchy="false">→<!-- → --></mo>
</mover>
</mrow>
</mrow>
<mo>=</mo>
<msub>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>E</mi>
<mo stretchy="false">→<!-- → --></mo>
</mover>
</mrow>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>0</mn>
</mrow>
</msub>
<mo>⋅<!-- ⋅ --></mo>
<msup>
<mi>e</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
<mrow>
<mo>[</mo>
<mrow>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>k</mi>
<mo stretchy="false">→<!-- → --></mo>
</mover>
</mrow>
</mrow>
<mspace width="thinmathspace"></mspace>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>r</mi>
<mo stretchy="false">→<!-- → --></mo>
</mover>
</mrow>
</mrow>
<mo>−<!-- − --></mo>
<mi>ω<!-- ω --></mi>
<mi>t</mi>
</mrow>
<mo>]</mo>
</mrow>
</mrow>
</msup>
<mo>=</mo>
<msub>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>E</mi>
<mo stretchy="false">→<!-- → --></mo>
</mover>
</mrow>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>0</mn>
</mrow>
</msub>
<mo>⋅<!-- ⋅ --></mo>
<msup>
<mi>e</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
<mrow>
<mo>[</mo>
<mrow>
<mi>k</mi>
<mi>z</mi>
<mo>−<!-- − --></mo>
<mi>ω<!-- ω --></mi>
<mi>t</mi>
</mrow>
<mo>]</mo>
</mrow>
</mrow>
</msup>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\vec {E}}={\vec {E}}_{0}\cdot e^{i\left[{\vec {k}}\,{\vec {r}}-\omega t\right]}={\vec {E}}_{0}\cdot e^{i\left[kz-\omega t\right]}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7d8a9ecb6fdbb3d2e6be3c6886c58092574e29f8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:32.785ex; height:4.176ex;" alt="{\displaystyle {\vec {E}}={\vec {E}}_{0}\cdot e^{i\left[{\vec {k}}\,{\vec {r}}-\omega t\right]}={\vec {E}}_{0}\cdot e^{i\left[kz-\omega t\right]}}" loading="lazy"></span></dd></dl>
<p>die <a href="Kreiswellenzahl" class="mw-redirect" title="Kreiswellenzahl">Kreiswellenzahl</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 k}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>k</mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle k}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/c3c9a2c7b599b37105512c5d570edc034056dd40.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}" loading="lazy"></span> aus dem <a href="Wellenvektor" title="Wellenvektor">Wellenvektor</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 {\vec {k}}=k\,{\hat {e}}_{z}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>k</mi>
<mo stretchy="false">→<!-- → --></mo>
</mover>
</mrow>
</mrow>
<mo>=</mo>
<mi>k</mi>
<mspace width="thinmathspace"></mspace>
<msub>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>e</mi>
<mo stretchy="false">^<!-- ^ --></mo>
</mover>
</mrow>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mi>z</mi>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\vec {k}}=k\,{\hat {e}}_{z}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/c95e9c13137c27cb206887dbab5cdaa3e90cbde2.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.201ex; height:3.176ex;" alt="{\displaystyle {\vec {k}}=k\,{\hat {e}}_{z}}" loading="lazy"></span> wie folgt
</p>
<dl><dd><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 k={\frac {\omega }{c}}n={\frac {\omega }{c}}(n'+\mathrm {i} n'')}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>k</mi>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>ω<!-- ω --></mi>
<mi>c</mi>
</mfrac>
</mrow>
<mi>n</mi>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>ω<!-- ω --></mi>
<mi>c</mi>
</mfrac>
</mrow>
<mo stretchy="false">(</mo>
<msup>
<mi>n</mi>
<mo>′</mo>
</msup>
<mo>+</mo>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">i</mi>
</mrow>
<msup>
<mi>n</mi>
<mo>″</mo>
</msup>
<mo stretchy="false">)</mo>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle k={\frac {\omega }{c}}n={\frac {\omega }{c}}(n'+\mathrm {i} n'')}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/a4df4c69c1d8bb5babb26e287dac54e54c5b17e0.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:23.275ex; height:4.676ex;" alt="{\displaystyle k={\frac {\omega }{c}}n={\frac {\omega }{c}}(n'+\mathrm {i} n'')}" loading="lazy"></span>,</dd></dl></dd></dl>
<p>(darin ist <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 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="./_assets_/eb734a37dd21ce173a46342d1cc64c92/a601995d55609f2d9f5e233e36fbe9ea26011b3b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}" loading="lazy"></span> der <a href="Komplexer_Brechungsindex" class="mw-redirect" title="Komplexer Brechungsindex">komplexe Brechungsindex</a>)
</p><p>so erhält man:
</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 {\begin{aligned}{\vec {E}}&={\vec {E}}_{0}\cdot e^{\mathrm {i} \left[(n'+\mathrm {i} n''){\frac {\omega }{c}}z-\omega t\right]}\\&={\vec {E}}_{0}\cdot e^{-n''{\frac {\omega }{c}}z}\cdot e^{\mathrm {i} \left[n'{\frac {\omega }{c}}z-\omega t\right]}\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">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>E</mi>
<mo stretchy="false">→<!-- → --></mo>
</mover>
</mrow>
</mrow>
</mtd>
<mtd>
<mi></mi>
<mo>=</mo>
<msub>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>E</mi>
<mo stretchy="false">→<!-- → --></mo>
</mover>
</mrow>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>0</mn>
</mrow>
</msub>
<mo>⋅<!-- ⋅ --></mo>
<msup>
<mi>e</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">i</mi>
</mrow>
<mrow>
<mo>[</mo>
<mrow>
<mo stretchy="false">(</mo>
<msup>
<mi>n</mi>
<mo>′</mo>
</msup>
<mo>+</mo>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">i</mi>
</mrow>
<msup>
<mi>n</mi>
<mo>″</mo>
</msup>
<mo stretchy="false">)</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>ω<!-- ω --></mi>
<mi>c</mi>
</mfrac>
</mrow>
<mi>z</mi>
<mo>−<!-- − --></mo>
<mi>ω<!-- ω --></mi>
<mi>t</mi>
</mrow>
<mo>]</mo>
</mrow>
</mrow>
</msup>
</mtd>
</mtr>
<mtr>
<mtd></mtd>
<mtd>
<mi></mi>
<mo>=</mo>
<msub>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mover>
<mi>E</mi>
<mo stretchy="false">→<!-- → --></mo>
</mover>
</mrow>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>0</mn>
</mrow>
</msub>
<mo>⋅<!-- ⋅ --></mo>
<msup>
<mi>e</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>−<!-- − --></mo>
<msup>
<mi>n</mi>
<mo>″</mo>
</msup>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>ω<!-- ω --></mi>
<mi>c</mi>
</mfrac>
</mrow>
<mi>z</mi>
</mrow>
</msup>
<mo>⋅<!-- ⋅ --></mo>
<msup>
<mi>e</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">i</mi>
</mrow>
<mrow>
<mo>[</mo>
<mrow>
<msup>
<mi>n</mi>
<mo>′</mo>
</msup>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>ω<!-- ω --></mi>
<mi>c</mi>
</mfrac>
</mrow>
<mi>z</mi>
<mo>−<!-- − --></mo>
<mi>ω<!-- ω --></mi>
<mi>t</mi>
</mrow>
<mo>]</mo>
</mrow>
</mrow>
</msup>
</mtd>
</mtr>
</mtable>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}{\vec {E}}&={\vec {E}}_{0}\cdot e^{\mathrm {i} \left[(n'+\mathrm {i} n''){\frac {\omega }{c}}z-\omega t\right]}\\&={\vec {E}}_{0}\cdot e^{-n''{\frac {\omega }{c}}z}\cdot e^{\mathrm {i} \left[n'{\frac {\omega }{c}}z-\omega t\right]}\end{aligned}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/c2cb8e90ca5d40c0641e71a49c30cd684be94a10.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:28.721ex; height:6.843ex;" alt="{\displaystyle {\begin{aligned}{\vec {E}}&={\vec {E}}_{0}\cdot e^{\mathrm {i} \left[(n'+\mathrm {i} n''){\frac {\omega }{c}}z-\omega t\right]}\\&={\vec {E}}_{0}\cdot e^{-n''{\frac {\omega }{c}}z}\cdot e^{\mathrm {i} \left[n'{\frac {\omega }{c}}z-\omega t\right]}\end{aligned}}}" loading="lazy"></span></dd></dl>
<p>Es gilt <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 I\propto |E|^{2}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>I</mi>
<mo>∝<!-- ∝ --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mo stretchy="false">|</mo>
</mrow>
<mi>E</mi>
<msup>
<mrow class="MJX-TeXAtom-ORD">
<mo stretchy="false">|</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msup>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle I\propto |E|^{2}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/d13763d7d50089dd5e7b8bfe9207d63d6cf35b47.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.394ex; height:3.343ex;" alt="{\displaystyle I\propto |E|^{2}}" loading="lazy"></span>.
</p>
<div class="mw-heading mw-heading3"><h3 id="Extinktionskoeffizient_und_Absorptionsindex"><span id="Absorptionsindex"></span> Extinktionskoeffizient und Absorptionsindex</h3></div>
<p>Aus dem Absorptionskoeffizienten einer Probe lassen sich der Extinktionskoeffizient <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 n''}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msup>
<mi>n</mi>
<mo>″</mo>
</msup>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle n''}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/2e0cc872b3fe6eb303b8e4a13c26bd7dccc1f7e5.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.532ex; height:2.509ex;" alt="{\displaystyle n''}" loading="lazy"></span> und der <b>Absorptionsindex</b> <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 \kappa ={\frac {n''}{n'}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>κ<!-- κ --></mi>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<msup>
<mi>n</mi>
<mo>″</mo>
</msup>
<msup>
<mi>n</mi>
<mo>′</mo>
</msup>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \kappa ={\frac {n''}{n'}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/16f82b3e1d052df6b0cec669a49578db8e4ba0f9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.805ex; height:5.509ex;" alt="{\displaystyle \kappa ={\frac {n''}{n'}}}" loading="lazy"></span> berechnen:
</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 \alpha \,{\frac {c}{2\omega }}=n''=n'\cdot \kappa }">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>α<!-- α --></mi>
<mspace width="thinmathspace"></mspace>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mi>c</mi>
<mrow>
<mn>2</mn>
<mi>ω<!-- ω --></mi>
</mrow>
</mfrac>
</mrow>
<mo>=</mo>
<msup>
<mi>n</mi>
<mo>″</mo>
</msup>
<mo>=</mo>
<msup>
<mi>n</mi>
<mo>′</mo>
</msup>
<mo>⋅<!-- ⋅ --></mo>
<mi>κ<!-- κ --></mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \alpha \,{\frac {c}{2\omega }}=n''=n'\cdot \kappa }</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f67e56e5c189a1e540483eeffc11c7b6f3c3432a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:19.145ex; height:4.676ex;" alt="{\displaystyle \alpha \,{\frac {c}{2\omega }}=n''=n'\cdot \kappa }" loading="lazy"></span></dd></dl>
<div class="mw-heading mw-heading2"><h2 id="Röntgen-_und_Gammastrahlung"><span id="R.C3.B6ntgen-_und_Gammastrahlung"></span>Röntgen- und Gammastrahlung</h2></div>
<p>Als Faustregel für Photonenenergien über 50 <a href="Elektronenvolt" title="Elektronenvolt">keV</a> gilt: Je höher die Energie, weniger dicht das Material und kleiner die <a href="Kernladungszahl" class="mw-redirect" title="Kernladungszahl">Kernladungszahl</a> des Materials, umso geringer ist der lineare Schwächungskoeffizient.
Auch bei niedrigeren Energien steigt <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 \mu }">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>μ<!-- μ --></mi>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \mu }</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/9fd47b2a39f7a7856952afec1f1db72c67af6161.svg" 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 }" loading="lazy"></span> mit der <a href="Kernladungszahl" class="mw-redirect" title="Kernladungszahl">Kernladungszahl</a> <i>Z</i> des Materials steil an (proportional zur 4. <a href="Potenz_(Mathematik)" title="Potenz (Mathematik)">Potenz</a>). Deshalb ist <a href="Blei" title="Blei">Blei</a> mit seiner hohen Dichte das bevorzugte Material für <a href="Abschirmung_(Strahlung)" title="Abschirmung (Strahlung)">Abschirmungen</a>.
</p><p>Für praktische Zwecke wird oft der <a href="Massenschw%C3%A4chungskoeffizient" title="Massenschwächungskoeffizient">Massenschwächungskoeffizient</a> bevorzugt. Er ergibt multipliziert mit der <a href="Dichte" title="Dichte">Dichte</a> des Materials den linearen Schwächungskoeffizienten.
</p>
<div class="mw-heading mw-heading2"><h2 id="Siehe_auch">Siehe auch</h2></div>
<ul><li><a href="Halbwertsdicke" class="mw-redirect" title="Halbwertsdicke">Halbwertsdicke</a></li></ul>
<div class="mw-heading mw-heading2"><h2 id="Literatur">Literatur</h2></div>
<ul><li>Peter H. Hertrich: <cite style="font-style:italic">Röntgenaufnahmetechnik: Grundlagen und Anwendungen</cite>. Publicis Publishing, 2004, ISBN 978-3-89578-209-1, <span style="white-space:nowrap">S.<span style="display:inline-block;width:.2em"> </span>38–44</span> (<a rel="nofollow" class="external text" href="https://books.google.de/books?id=kyErRHDfJSUC&pg=PA38#v=onepage">eingeschränkte Vorschau</a> in der Google-Buchsuche).<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/de.wikipedia.org:Absorptionskoeffizient&rft.au=Peter+H.+Hertrich&rft.btitle=R%C3%B6ntgenaufnahmetechnik%3A+Grundlagen+und+Anwendungen&rft.date=2004&rft.genre=book&rft.isbn=9783895782091&rft.pages=38-44&rft.pub=Publicis+Publishing" style="display:none"> </span></li>
<li>Rudolf Nicoletti, Michael Oberladstätter, Franz König: <cite style="font-style:italic">Messtechnik und Instrumentierung in der Nuklearmedizin: eine Einführung</cite>. facultas.wuv Universitäts, 2006, ISBN 978-3-85076-795-8, <span style="white-space:nowrap">S.<span style="display:inline-block;width:.2em"> </span>38–39</span> (<a rel="nofollow" class="external text" href="https://books.google.de/books?id=bn9AP8DsK5MC&pg=PA38#v=onepage">eingeschränkte Vorschau</a> in der Google-Buchsuche).<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/de.wikipedia.org:Absorptionskoeffizient&rft.au=Rudolf+Nicoletti%2C+Michael+Oberladst%C3%A4tter%2C+Franz+K%C3%B6nig&rft.btitle=Messtechnik+und+Instrumentierung+in+der+Nuklearmedizin%3A+eine+Einf%C3%BChrung&rft.date=2006&rft.genre=book&rft.isbn=9783850767958&rft.pages=38-39&rft.pub=facultas.wuv+Universit%C3%A4ts" style="display:none"> </span></li></ul></div><!--htdig_noindex--><div><div class="zim-footer">
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