BOUNDS TO THE CENTRAL ELECTRON-PAIR DENSITY WITH APPLICATIONS TO 2-ELECTRON ATOMS

The local electron-electron quantity [delta(r12)] of atomic systems, w hich plays an important role in the realization of the so-called corre lation cusp condition, as well as in the description of the relativist ic and radiative corrections to the ground-state energy, is investigat ed by means of the interelectronic radial expectation values [r12alpha ], alpha > -3. Starting from the unimodal character of the spherically averaged electron-pair density h(r12) and the recently found inequali ty h(r12) > h'(r12), upper U(k) and lower L(k) bounds, k = 0, 1, 2,... , to the electron-pair density at the origin or central electron-pair density h (0), which is equal to the quantity [delta(r12)], are found analytically. For the two-electron atoms with Z = 1, 2, 3, 5, and 10, the quality of these bounds is analyzed by means of the optimum 20-ter m Hylleraas-type wave functions recently obtained by two of us [T. Kog a and K. Matsui, Z. Phys. D (to be published)]. It is shown that the a ccuracy of both types of bounds increases with k for fixed Z, being gr eater for the lower bounds than for the upper bounds when k is small. Both bounds are of similar quality for big values of k. Moreover, any desired accuracy may be reached by increasing the k value.