STUDY OF SOME INTERELECTRONIC PROPERTIES IN HELIUM-LIKE ATOMS

By means of the optimum M-term Hylleraas-type wavefunctions with 1 less-than-or-equal-to M less-than-or-equal-to 6 we study various interelectronic properties of the Helium-like atoms with nuclear charge Z = 1, 2, 3, 5 and 10. Let h(u) denote the spherically averaged electron-pair density of a finite many-electron system. Firstly we found that the intracule function h(u)/u(alpha) of the above-mentioned atoms is (i) monotonically decreasing from the origin for alpha greater-than-or-equal-to alpha1 and (ii) convex for alpha greater-than-or-equal-to alpha2 where alpha1 and alpha2 are positive constants which depend on Z and M. Then we show that the electron-electron cusp condition, i.e. that h'(0) = h(0), may be extended in the sense that the inequality h(u) - h'(u) greater-than-or-equal-to 0 is valid for any u greater-than-or-equal-to 0. Thirdly, it is shown that the inequalities involving three interelectronic moments [u(n)] recently found by the authors are, at times, of great quality. Finally the goodness of some bounds to the characteristics of the maximum of h(u) and to the total interelectronic repulsion energy is discussed in detail.