<section id="vavref">
<stitle>Vavilov theory</stitle>
<par>Vavilov<cite refid="bib-VAVI"/> derived a more accurate
straggling distribution by introducing the kinematic limit on the
maximum transferable energy in a single collision, rather than using
<inlinemath><math><msub><mi>E</mi><mrow><mtext>max</mtext></mrow></msub>
<mo>=</mo><mi>∞</mi></math></inlinemath>.
Now we can write<cite refid="bib-SCH1"/>:
<eqnarray ><subeqn><math><mi>f</mi> <mfenced open='(' close=')'>
<mi>ε</mi><mo>,</mo><mi>δ</mi><mi>s</mi></mfenced>
<mo>=</mo> <mfrac><mrow><mn>1</mn></mrow>
<mrow><mi>ξ</mi></mrow>
</mfrac><msub><mi>φ</mi><mrow><mi>v</mi></mrow></msub>
<mfenced open='(' close=')'>
<msub><mi>λ</mi><mrow><mi>v</mi></mrow></msub><mo>,</mo>
<mi>κ</mi><mo>,</mo><msup><mi>β</mi><mrow><mn>2</mn></mrow>
</msup></mfenced></math></subeqn></eqnarray>
where
<eqnarray><subeqn><math><msub><mi>φ</mi><mrow><mi>v</mi></mrow></msub>
<mfenced open='(' close=')'>
<msub><mi>λ</mi><mrow><mi>v</mi></mrow></msub><mo>,</mo>
<mi>κ</mi><mo>,</mo>
<msup><mi>β</mi><mrow><mn>2</mn></mrow></msup></mfenced>
<mo>=</mo>
<mfrac><mrow><mn>1</mn></mrow>
<mrow><mn>2</mn><mi>π</mi><mi>i</mi></mrow>
</mfrac>
<msubsup><mo>∫</mo>
<mrow><mi>c</mi><mo>+</mo><mi>i</mi><mi>∞</mi></mrow>
<mrow><mi>c</mi><mo>-</mo><mi>i</mi><mi>∞</mi></mrow></msubsup>
<mi>φ</mi><mfenced open='(' close=')'><mi>s</mi></mfenced>
<msup><mi>e</mi><mrow><mi>λ</mi><mi>s</mi></mrow></msup>
<mi>d</mi><mi>s</mi><mspace width='2cm'/><mi>c</mi><mo>≥</mo><mn>0</mn>
</math></subeqn>
<subeqn><math><mi>φ</mi><mfenced open='(' close=')'><mi>s</mi></mfenced>
<mo>=</mo><mo>exp</mo><mfenced open='[' close=']'><mi>κ</mi>
<mrow><mo>(</mo><mn>1</mn><mo>+</mo><msup><mi>β</mi>
<mrow><mn>2</mn></mrow></msup><mi>γ</mi><mo>)</mo></mrow>
</mfenced><mo>exp</mo><mfenced open='[' close=']'><mi>ψ</mi>
<mfenced open='(' close=')'><mi>s</mi></mfenced></mfenced>
<mo>,</mo> </math></subeqn>
The original document (formatted by LaTeX).
PDF display optimized for screen viewing.
Browser display using the techexplorer plugin.
Conversion to HTML with embedded MathML rendered with a plugin (e.g., WebEQ and Java applets).