COMPACT EXPRESSIONS FOR THE ELECTRON-ELECTRON DISTRIBUTION FUNCTION FOR THE S-2 STATES OF 3-ELECTRON SYSTEMS

The electron-electron distribution function P(r(ij)) has been evaluate d in closed form for the S-2 states of three-electron systems that are described by Hylleraas-type wave functions. The function P(r(ij)) can be reduced to the form P(r(ij)) = Sigma(I=1)(3) Sigma(k=1)(gI) A(IK)r (ij)(K)e(-alpha Irij). Numerical values of the expansion coefficients A(IK), Summation limits g(I), and exponents alpha(I) are determined fo r the ground states of selected members of the lithium isoelectronic s eries. A discussion is given on the necessary conditions that must be imposed on the basis set in order that P(r(ij)) be given by the analyt ical formula presented above. Expectation values for several moments ( r(ij)(n)) and (delta(r(ij))) are evaluated.