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 ru.

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Extensive variational computations are reported for the ground state energy of the non-relativistic two-electron atom. Several different sets of basis functions were systematically explored, starting with the original scheme of Hylleraas. The most rapid convergence is found with a combination of negative powers and a logarithm of the coordinate s = r 1 + r 2 . At N=3091 terms we pass the previous best calculation (Korobov's 25 decimal accuracy with N=5200 terms) and we stop at N=10257 with E = -2.90372 43770 34119 59831 11592 45194 40444 . . .Previous mathematical analysis sought to link the convergence rate of such calculations to specific analytic properties of the functions involved. The application of that theory to this new experimental data leaves a rather frustrating situation, where we seem able to do little more than invoke vague concepts, such as "flexibility." We conclude that theoretical understanding here lags well behind the power of available computing machinery. *