Comparison of Semiclassical and Quantum-Mechanical Coulomb Excitation Integrals for LargeL

Semiclassical and quantum-mechanical integrals occurring in the theory of Coulomb excitation are compared in the limit of distant collisions which corresponds to setting the usual parameter $\eta =0\mathrm{}$. The integrals are expanded in powers of the energy of excitation and are found to agree up to and including those of second order, provided the geometric mean of the initial and final energy is used in the semiclassical calculation. The results are generalized to include an arbitrary power law for the dependence of the interaction energy on radius. The agreement remains unchanged.