Rayleigh Scattering and the Electromagnetic Susceptibility of Atoms

Rayleigh scattering of light by atoms is considered from the point of view of relativistic electron theory. The relationship between the coherent $S$-matrix element and the frequency-dependent electric and magnetic multipole susceptibilities of the atom is established. Single-particle radial equations are derived for the perturbed electron orbitals, assuming that the atom is described by a relativistic Hartree-Fock-Slater (RHFS) wave function. These equations reduce to the inhomogeneous Schrödinger equations commonly used to evaluate electric polarizabilities when relativistic (fine-structure) effects are neglected. Numerical solutions to the radial equations are obtained for the noble gases. The electric- and magnetic-dipole susceptibilities are compared with previous nonrelativistic calculations as well as with experimental values. The magnetic susceptibilities are found to be essentially independent of frequency, and to agree to within 1% with static experimental values for all of the noble gases except He. The accuracy of the electric polarizability decreases from about 5% for He and Ne to about 50% for Xe. Relativistic effects are almost entirely negligible for magnetic susceptibilities; they are noticeable only in the case of Xe. In the electric polarizability calculations, relativistic effects are completely masked by the crude nature of the RHFS computational techniques.