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

Spin-free 1 matrices $\gamma \left(\overrightarrow{\mathrm{r}}\right|{\overrightarrow{\mathrm{r}}}^{\prime })\text{'}\mathrm{s}$ 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 $\gamma \left(\overrightarrow{\mathrm{r}}\right|{\overrightarrow{\mathrm{r}}}^{\prime })\text{'}\mathrm{s}$ are then Fourier transformed to momentum space in order to obtain radial momentum distributions $I_0\mathrm{}\left(p\right)\text{'}\mathrm{s}$. The analytical method developed here allows $I_0\mathrm{}\left(p\right)\text{'}\mathrm{s}$. 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 $I_0\mathrm{}\left(p\right)\text{'}\mathrm{s}$, 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.