Relativistic random phase approximation applied to atoms of the He isoelectronic sequence

Abstract

A relativistic version of the random phase approximation (RPA) is used to study allowed and forbidden radiative transitions in atoms. The theory is applied to the He isoelectronic sequence to test its utility. Precise numerical solutions to the relativistic RPA equations are obtained describing the transitions $1{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\to 2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{} \mathrm{}\left(M1\mathrm{}\right)\mathrm{}$, $1{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\to 2{}_{}{}^{1,3}{}_{}{}^{}P_1^{}{}_{}{}^{} \mathrm{}\left(E1\mathrm{}\right)\mathrm{}$, and $1{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\to 2{}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{} \mathrm{}\left(M2\mathrm{}\right)\mathrm{}$. The resulting excitation energies and transition probabilities are in good agreement with accurate nonrelativistic calculations for low-$Z$ elements. For intermediate- and high-$Z$ elements where relativistic effects are more important, the results are expected to be very accurate also. Extensive comparison shows good agreement of the calculated forbidden transition rates with available beamfoil measurements and the calculated transition energies with several lines from solar corona for high-$Z$ ($Z\sim 25$) elements.