Parity-violating electric-dipole transitions in helium

We study the parity-violating electric-dipole transitions $\gamma +2\mathrm{}{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}\to 2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ and $\gamma +2\mathrm{}{}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}\to 2{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ in He in order to gain some insight into the reliability of approximate calculations which have been carried out for similar transitions in many-electron atoms. The contributions of the nearest-lying states are computed with a variety of wave functions, including very simple product wave functions, Hartree-Fock functions, and Hylleraas-type wave functions with up to eighty-four parameters. We find that the values for the matrix elements of the parity-violating interaction which are given by the fairly simple wave functions can differ considerably from the values obtained from the very good wave functions, even when these simple wave functions give accurate values for energies and dipole matrix elements. An identity derived in a previous paper, which converts a delta-function matrix element to that of a global operator, is used to obtain alternative values for the matrix elements in question. It is found that use of this identity can substantially improve the results obtained with less accurate wave functions. We discuss the implications of our results for calculations of parity mixing in many-electron atoms.