# Nucleon-nucleon scattering problem

1. Sep 7, 2012

### semc

1. The problem statement, all variables and given/known data
Low-energy (s-wave) neutrons are scattered from protons, and the distribution of recoil
protons is observed and analyzed. Let the neutron scattering angle be $\Theta$ in the laboratory
coordinate system, and let the incident neutron kinetic energy be Tn. Assume that mp = mn. Show that (in the laboratory system):

$\frac{d\sigma}{dTp}$=$\frac{\sigma}{Tn}$

where σ is the total cross section and Tp is the proton kinetic energy after the scattering.

3. The attempt at a solution
I used

$\frac{d\sigma}{dTp}$=$\frac{d\sigma}{d\Theta}$$\frac{d\Theta}{dTp}$

but I can't seem to get the required expression. What is wrong with my method?