Partial wave scattering cross section in spherical well

[QuantumIsHard]

Homework Statement

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.

Homework Equations

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

The Attempt at a Solution

For l=0, the above equation just becomes

σ = $\frac{4 \pi}{k^2} *sin^2(\delta_0)$.

But how do I get the phase shift $\delta_0$?

 

[andrien]

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.