ASYMPTOTIC-EXPANSION FOR DELTA-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 delta(r). All terms up to x-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 greater-than-or-equal-to 5, the accuracy of the asymptotic expansion exceeds what-has been achieved variationally. The asymptotic expansion for the specific mass correction to <delta(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.