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Rutherford cross section in CM frame

  1. Jan 11, 2013 #1
    Hi

    I need to plot the (differential) Rutherford cross section as a function of the scattering angle in the CM frame. the reaction is a typical projectile on stationary target. I know the projectile energy in the lab, θcm and the masses. I am confused over which energy to use though.

    I know that

    [itex]\frac{dσ}{dΩ}=\left(\frac{zZe^{2}}{16\pi\epsilon_{0}E}\right)^{2}*csc(\frac{\theta_{cm}}{2})^{4}[/itex]

    In the following m and M are the masses of projectile and target respectivly and Tp is the projectile kinetic energy in the lab frame.

    Should I use the projectile energy converted to CM?
    [itex]E=\left(\frac{M}{m+M}\right)^{2}*T_{p}[/itex]

    The kinetic energy of the CM frame?
    [itex]E=\left(\frac{m}{m+M}\right)*T_{p}[/itex]

    The total kinetic energy in the CM frame?
    [itex]E=\frac{\sqrt{2MT_{p}+\left(m+M\right)^{2}}}{m+M}[/itex]

    or something else?

    I have looked in several textbooks and googled but have just become more confused since I have seen E defined as "total kinetic enrgy","projectile energy" or just "energy of the particles".

    Any help to clear this up would be greatly appreciated.
     
  2. jcsd
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