- #1

Silviu

- 624

- 11

## Homework Statement

This is the problem 3.34 from Goldstein, 3rd Edition:

Consider a truncated repulsive Coulomb potential defined as V=k/r, for r>a and V=k/a, for r<=a. For a total energy E>k/a, obtain expressions for the scattering angle ##\Theta## as a function of ##s/s_0##, where ##s_0## is the impact parameter for which the periapsis occurs at the point r=a.

## Homework Equations

##d^2u/d\theta^2 + u = -m/l^2*dV/du, with u=1/r##

##\Theta(s) = \pi -2\int_{0}^{u_m}(s\cdot du/(\sqrt{1-V(u)/E-s^2u^2}))##, with E - the energy of the particle and ##u_m = 1/r_m, r_m## the distance at the closest approach

## The Attempt at a Solution

I tried to calculate ##r(\theta)## outside and inside the sphere, ##s_0## can be calculated assuming that the potential is k/r all the time, as for ##s_0## the particle doesn't go inside the sphere. But I am not sure how to relate ##\Theta## to s, when I have the potential inside the sphere.