Asymptotic expansion for δ-function matrix elements of helium

This paper extends the methods of asymptotic analysis extensively developed for energy-level calculations of Rydberg states to the evaluation of matrix elements of δ(r). All terms up to ${\mathit{x}}^{\mathrm{-}8}$ in the asymptotic potential are systematically derived from a simple perturbation expansion. The formalism is developed in a way that closely parallels that for the corresponding energy expansion. The results are comparable in accuracy to the energy itself. Detailed numerical comparisons with high-precision variational calculations are presented for the states of helium up to nL=10K (i.e., L=7). For L≥5, the accuracy of the asymptotic expansion exceeds what has been achieved variationally. The asymptotic expansion for the specific mass correction to 〈δ(r)〉 is also obtained. Here the accuracy rivals the variational results even for L=3. Similar methods can be applied to the calculation of a wide variety of other atomic properties.