Scattering problem with a complex potential

A semiclassical method has been generalized and used to study the scattering of a particle from a complex potential. The accuracy of the method is tested by considering a simple potential consisting of a repulsive Coulomb part and an attractive imaginary part of the form $-\frac{i\beta }{r^2}$. The complex phase shifts for the problem can be determined exactly by solving the relevant radial equation. The semiclassical results, including terms of order ${\hslash }^2$, have been found to give good agreement with the exact results.