Algebraic 1 Matrices and Radial Momentum Distributions from Hylleraas-Type Wave Functions.S1Ground States of He and He-Like Ions

Abstract

Spin-free 1 matrices $\ensuremath{\gamma}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}|{\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}}^{\ensuremath{'}})'\mathrm{s}$ are obtained in algebraic form from simple Hylleraas-type (HY) wave functions for the $^{1}S$ ground states of He and several He-like ions. The algebraic $\ensuremath{\gamma}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}|{\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}}}^{\ensuremath{'}})'\mathrm{s}$ are then Fourier transformed to momentum space in order to obtain radial momentum distributions ${I}_{0}(p)'\mathrm{s}$. The analytical method developed here allows ${I}_{0}(p)'\mathrm{s}$. to be calculated in a direct manner from HY wave functions. Although the present emphasis is on the method rather than on the goodness of individual ${I}_{0}(p)'\mathrm{s}$, results for the $^{1}S$ He and ${\mathrm{Li}}^{+}$ ground states are obtained from six-term HY functions which incorporate 99.1 and 98.0%, respectively, of the correlation energy.