ELECTRON-ELECTRON COALESCENCE AND INTERELECTRONIC LOG-MOMENTS IN ATOMIC SYSTEMS

A measure of the spatial electron-electron coalescence in atomic and m olecular systems is given by the local quantity [delta(u)], u = r12 be ing the interelectronic vector and delta the three-dimensional Dirac d elta function. Here it is argued that there exists a function H(s, t), s > t > - 3, which depends on two interelectronic moments [u(alpha)] and plays an important role in the electron correlation problem. In pa rticular it is rigorously fulfilled that for an arbitrary but fixed s, [GRAPHICS]. Additionally, specific values of the function H(s, t) are shown to be related to the log-moments [mu(t)ln u]; e.g., the interel ectronic mean logarithmic radius [ln u] is expressed in terms of H(0, 0) in a simple manner. From a numerical point of view, the values of t he quantities [u(t)] and [u(t)ln u] as well as the values of the two-m oment function H(s, t) are calculated in the two-electron atoms with n uclear charge Z = 1, Z 3, 5 and 10 by means of the optimum 20-term Hyl leraas-type wave functions. Finally, further bounds to [delta(u)] vali d for the aforementioned two-electron atoms are found by means of log- moments.