Rayleigh Scattering and the Electromagnetic Susceptibility of Atoms

Abstract

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 Schr\"odinger 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.