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Scattering problem

  1. Nov 29, 2007 #1
    Hi , I got stuck on a point of griffiths' scattering problem on "the introduction to elementary particles"
    1. The problem statement, all variables and given/known data
    Consider the case of elastic scattering , A+B-->A+B , in the lab frame (B initially at rest) assuming the target is so heavy (mbc2 >> Ea) that its recoil is negligible . Use (6.34) to determine the differential scattering cross section .


    2. Relevant equations
    Equation (6.34) :
    [tex]\frac{d\sigma}{d\Omega}[/tex]=M[tex]^{2}[/tex][tex]\frac{[tex]\frac{\hbar}{2}[/tex]S}{4\sqrt{\left(p_{1}\bullet p_{2}\right)^{2}-\left(m_{1}m_{2}c^{2}\right)^{2}}[/tex][tex]\left[\left(\frac{cd^{3}p_{3}}{[tex]\left(2\Pi^{3}[/tex][tex]\right)[/tex]2E_{3}}[/tex][tex]\right)[/tex]\left(\frac{cd^{3}p_{4}}{[tex]\left(2\Pi^{3}[/tex][tex]\right)[/tex]2E_{4}}[/tex][tex]\right)[/tex]\bullet\bullet\bullet\left(\frac{cd^{3}p_{n}}{[tex]\left(2\Pi^{3}[/tex][tex]\right)[/tex]2E_{n}}[/tex][tex]\right)[/tex][tex]\right][/tex][tex]\times[/tex][tex]\left(2\Pi^{4}[/tex][tex]\right)[/tex][tex]\delta^{4}\left(P_{1}+P_{2}-P_{3}-P_{4}\bullet\bullet\bullet-P_{n}\right)[/tex]



    3. The attempt at a solution

    [tex]\frac{d\sigma}{d\Omega}[/tex]=M[tex]^{2}[/tex][tex]\frac{[tex]\frac{\hbar}{2}[/tex]S}{16\left(2\Pi\right)^{2}\left|P_{1}\right|m_{2}c}\frac{\rho*d\rho}{\left(\rho^{2}+P_{1}^{2}-2\rho\left|P_{1}\right|cos\theta\right)^{1/2}}\delta\left(\frac{E_{1}+E_{2}}{c}-\rho-\left|P_{4}\right|\right)[/tex]

    I got this formula so far , however , I cannot cancel out the delta function . It seems that it is impossible for me to separate rho and p1 as independent variables when p4 is involved in the delta function .
     
    Last edited: Nov 29, 2007
  2. jcsd
  3. Nov 29, 2007 #2

    Avodyne

    User Avatar
    Science Advisor

    Please fix your tex ... this is too hard to read.
     
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