1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

3D Rectangular Scattering Potential

  1. Nov 1, 2011 #1
    1. The problem statement, all variables and given/known data

    There is a constant potential, V0, in the region -a<x<a, -a<y<a, -b<z<b, and V=0 otherwise. Particles of mass m are incident on the scatterer with wave vector k in the x direction with a flux at the origin of one particle per second per cm^2. There is a detector with cross-sectional area A is located at a large distance R from the origin, in the direction with polar coordinates (theta, phi). Assumptions: a<<b, k*a<<1, V0<<hbar^2/(m*b^2), k*b not necessarily small. We want to find the counting rate in the detector. The problem also asks how the answer would change if the k vector was parallel to z instead.

    2. Relevant equations

    It seems that due to the small potential, we can use the Born approximation, which gives the scattering amplitude [itex]f(k\prime,k)=-\frac{m}{2 \pi \hbar^2}\int exp(i (k-k\prime)\cdot r\prime) V(r\prime) d^{3}r\prime)[/itex].


    3. The attempt at a solution

    In spherical coordinates, the Born approximation isn't bad to calculate. However, in this rectangular case, I can't get a nice looking result out of the integration above. I'm interested to see if anyone thinks there is a different way to do the problem, or if I should just keep trying the integral. As for the second part of the problem, it doesn't seem like the Born approximation would necessarily hold when the particle sees a longer range potential. But hopefully this part will become more clear when I can figure out the first part.

    Thanks for your help!
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Similar Discussions: 3D Rectangular Scattering Potential
Loading...