THE ELECTRON CORRELATION CUSP .1. OVERVIEW AND PARTIAL-WAVE ANALYSIS OF THE KAIS FUNCTION

The Kais function is an exact solution of the Schrodinger equation for a pair of electrons trapped in a parabolic potential well with r(12)( -1) electron-electron interaction. Partial wave analysis (PWA) of the Kais function yields E(L) = E + C-1(L + <(C)over bar (2)>)(-3) + O(L(- 5)) where E is the exact energy and E(L) the energy of a renormalized finite sum of partial waves omitting all waves with angular momentum l > L. Slight rearrangement of an earlier result by Hill shows that the corresponding full CI energy differs from E(L) only by terms of order O(L(-5)) with FCI values of C-1 and <(C)over bar (2)) identical to PW A values. The dimensionless <(C)over bar (2)> parameter is weakly depe ndent upon the size of the physical system. Its value is 0.788 for the Kais function, and 0.893 for the less diffuse helium atom, and approa ches <(C)over bar (2)> --> 1 in the limit of an infinitely compact cha rge distribution. The lth energy increment satisfies an approximate vi rial theorem which becomes exact in the high l limit. This analysis, f ormulated to facilitate use of the Maple system for symbolic computing , lays the mathematical ground work for subsequent studies of the elec tron correlation cusp problem. The direction of future papers in this series is outlined.