Stieltjes-integral approximations to photoabsorption and dispersion profiles in atomic helium

Abstract

Variational calculations in Hilbert space and theorems from the theory of moments are employed in the construction of Stieltjes-integral approximations to the electric-dipole absorption and dispersion profiles in atomic helium. A spectrum of discrete transition frequencies and oscillator strengths obtained from variationally determined pseudostates furnishes accurate approximations to the necessary dipole spectral sums. Solution of the appropriate moment equations, or transformation to a basis set of principal pseudostates, provides the principal frequencies and strengths necessary for Stieltjes imaging the absorption profile, and for the evaluation of the associated dispersion profile. Rapid convergence is obtained to values in excellent agreement with the available experimental absorption cross section, refractive index, and Verdet coefficient, and with semiempirical estimates of the closely related dynamic dipole shielding factor and Rayleigh-scattering cross section. Moreover, comparison of the discrete pseudospectrum of frequencies and strengths with its Stieltjes average indicates the presence of approximations to autoionizing states and inelastic thresholds in the variationally determined photoabsorption profile. These results suggest that the Stieltjes technique for determining photoabsorption and dispersion profiles is a useful complement to more conventional methods which require the explicit construction of discrete and continuum eigenfunctions.