Fully Coupled Hartree-Fock Calculations of the Refractive Index, Dynamic Polarizability, and Verdet Coefficients of Helium, Beryllium, and Neon

Abstract

Fully coupled Hartree-Fock calculations of the refractive index, dynamic polarizability, and Verdet coefficients of He, Be, Ne, and the corresponding 2-, 4-, and 10-electron isoelectronic series are presented. The time-dependent Hartree-Fock perturbation equations are derived and solved using a variational method, in which the zero-order and the perturbed wave functions are represented by analytical functions containing adjustable parameters which are optimized according to the variational technique. The numerical results for both the refractive index and the Verdet coefficients are fitted to polynomials in even powers of $\frac{1}{\ensuremath{\lambda}}$, where $\ensuremath{\lambda}$ is the wavelength. In this work it is found that the computed refractive indices differ from the corresponding experimental values due to Cuthbertson and Cuthbertson by a very nearly constant amount. That is, if the computed dynamic polarizabilities are adjusted so as to equal the experimental polarizability $\ensuremath{\alpha}$ at zero frequency, then the experimental and theoretical curves of refractive index versus frequency are nearly identical. This adjustment in $\ensuremath{\alpha}$ is around 5% (for He) and 10% (for Ne) of the experimental static polarizabilities. Finally, the calculated transition frequencies are around 2% too large for He, 17% too large for Ne, and 9% too small for Be.