High-precision nonrelativistic polarizabilities of the nS state of helium

The static dipole polarizabilities of the 1 1S [Formula: see text] 51S, 23S [Formula: see text] 63S states of helium are presented. Our results are accurate up to at least eight digits. The majority of [Formula: see text]He (infinite mass helium) data are better than the data derived by Yan with Hylleraas coordinates,[Formula: see text] and close to the newest results achieved by another method.[Formula: see text] We demonstrate the results of 4He besides.

Transformation of the integral using Hylleraas coordinates in N-dimensions

The integral ∫ F(r, r′, |r–r′|) dr dr′ where r and r′ are N-dimensional position vectors can be transformed into a simple three-dimensional integral using Hylleraas coordinates. A simple derivation of this result is presented. PACS Nos.: 31.15.–p; 31.15.Ja; 03.65.–w

General methods for evaluating matrix elements of singular operators in two-electron systems

Due to the recent advances in both theory and experiment for the fine structure of two-electron atomic systems, it is necessary to include quantum electrodynamic (QED) effects through orders α6mc2, α7ln(Zα)mc2, and α7mc2, in order to match the experimental precision. These effects can be expressed in terms of a sum of singular operators. A general scheme is given for the evaluation of a wide range of matrix elements of high-order singular QED operators for two-electron atomic systems in Hylleraas coordinates. The scheme presented here can be applied to triplet states with arbitrary angular momentum. A number of useful expressions for the analytical evaluation of radial integrals are derived. An example is given in calculating the Douglas and Kroll terms, and the numerical values of the reduced matrix elements are presented for the 2 3PJ states of helium.