General energy bounds for systems of bosons with soft cores - art. no. 052510

We study a bound system of N identical bosons interacting by model pair pot entials of the form V(r) = lambda sgn(p)r(p) + mu /r(2), lambda >0, mu grea ter than or equal to0. By using a variational trial function and the "equiv alent two-body method," we find explicit upper and lower bound formulas for the N-particle ground-state energy in arbitrary spatial dimensions d great er than or equal to3 for the two cases p = 2 and p = - 1. It is demonstrate d that the upper bound can be systematically improved with the aid of a spe cial large-N limit in collective field theory.