APPROXIMATE SEPARATION OF THE HYPERRADIUS IN THE MANY-PARTICLE SCHRODINGER-EQUATION

For large values of d = 3N, the radial distribution function of an N-particle system is sharply peaked near the hyperradius r(m) = (d - 2)/2k0, where k0 = (2\E\)1/2. This fact allows an approximate separation of the hyperradius, leading to many-dimensional hydrogenlike radial solutions. Kindred applications to dimensional scaling are also discussed, where d = DN, with D the spatial dimension. For the large D regime, illustrative analytic formulas are obtained giving the energy and effective nuclear charge for the lowest few S states of the helium atom.