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 r₁₂.