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Partial wave scattering cross section in spherical well

  1. Apr 23, 2013 #1
    1. The problem statement, all variables and given/known data

    Consider the spherical well such that V(r<a) = -V0 and V(r≥a) = 0. Calculate the l = 0 partial wave scattering cross section in the low energy limit for this potential.

    2. Relevant equations

    σ = [itex]\frac{4 \pi}{k^2} * \Sigma (2l+1)*sin^2(\delta_l)[/itex]

    3. The attempt at a solution

    For l=0, the above equation just becomes

    σ = [itex]\frac{4 \pi}{k^2} *sin^2(\delta_0)[/itex].

    But how do I get the phase shift [itex]\delta_0[/itex]?
     
  2. jcsd
  3. Apr 25, 2013 #2
    you have to solve the radial part of the wave eqn with l=0.One solution with -V0 potential will be ASinkr type,while outside r=a it will contain the phase shift δ0 type term added.use continuity and differentiability to find δ0 from the wave function determined, at r=a.
     
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