Importance of Angular Correlations between Atomic Electrons

We present the results of some new calculations on two atomic problems—the correlation energy in the ground state of 2-electron atoms, and elastic scattering of slow electrons from hydrogen atoms—to show the relative importance of various angular components of the complete wave function. We conclude that, as a general rule, the use of just (relative) $s$ and $p$ waves will give quite accurate answers—with only a few percent errors at most; but to obtain higher precision one should abandon the Legendre polynomial expansion and use the coordinate $r_{12}$.