Angular Coefficients of Atomic Matrix Elements Involving Interelectronic Coordinates

A method for determining the angular coefficients of atomic matrix elements is illustrated. The angular coefficients of matrix elements for $r_{\mathrm{ij}}^a{\mathrm{,r}}_{\mathrm{ij}}^a{r}_{\mathrm{jk}}^b{\mathrm{,r}}_{\mathrm{ij}}^a{r}_{\mathrm{jk}}^b{r}_{\mathrm{ki}}^c{\mathrm{,r}}_{\mathrm{ij}}^a{r}_{\mathrm{jk}}^b{r}_{\mathrm{kl}}^c$ , and $r_{\mathrm{ij}}^a{r}_{\mathrm{jk}}^b{r}_{\mathrm{kl}}^c{r}_{\mathrm{li}}^d$ are evaluated using single‐particle states of definite angular momentum. The use of tensor operators enables a separation into angular and radial parts. The atomic matrix elements are then expressed as sums over products of n‐j symbols and radial integrals. These sums are restricted by the values of the single‐particle state angular momenta, and in all cases the effects of single‐particle couplings disappear. The calculation does not require the use of a particular coordinate system, as is the case for multiple products of spherical harmonics.