Raman Scattering by Hydrogenic Systems

We have calculated the cross section for Raman scattering of light from a hydrogenic atom, for a wide range of photon energies. The calculation assumes the photon encounters the atom in its ground state and excites it to the $2s$ state. Since various contributions to the matrix element may be isolated in the computation, the calculation allows one to obtain a notion of the relative importance of various classes of intermediate states in a given frequency range. We also point out that the Raman efficiency $S$ may be expressed in terms of the derivative of the electronic polarizability tensor with respect to a parameter that measures the degree of excitation of the atom. Thus, the formal expression for $S$ assumes an appearance identical to the expression encountered in the phenomenological theory of the first-order Raman effect in solids.