Ok, so we have a potential energy V(r)= -C/r^4 which exists between an atom and ion at distances greater than contact. Note that C=e^2/2(P^2) where e is charge of ion and P is polarizability of atom. I have to calculate the cross section for an ion of velocity v to strike an atom, while assuming that the ion is much lighter than the atom.
The answer to this is cross section=4pi/v*(sqrt(2C/m)). How do I get this?
The only equations I have are, E=1/2*mv^2, L(angular momentum)=mvb where b is impact parameter. The equation for b is given in terms of scattering angles, I think in this case b= C/mv^2 * cot(beta/2). But here we don't know any scattering angles. And the equation for cross section is cross section=pi*b^2