Semiclassical Approximation to Coulomb Excitation Integrals

Several numerical comparisons are made of the quantum-mechanical and semiclassical treatments of Coulomb excitation in the case of nonzero excitation. A detailed comparison is made of the part of the matrix element involving the impinging particle and also of the angular momentum weighting factors. It is found that the total cross section is approximated very well by the semiclassical treatment. The partial cross sections caused by different values of the orbital angular momentum $L$ are represented by the semiclassical method with reasonable accuracy but the representation of radial integrals by their semiclassical approximations is even more accurate, especially for low $L$, the weighting factors containing $L$ explicitly being appreciably different in the two cases.