Hyperspherical Adiabatic Formalism of the Boltzmann Third Virial

Abstract

First, we show that, if there are no bound states, we can express the q.m. third cluster - involving 3 and fewer particles in Statistical Mechanics - as a formula involving adiabatic eigenphase shifts. This is for Boltzmann statistics. From this q.m. formulation, in the case of purely repulsive forces, we recover, as h goes to 0, the classical expressions for the cluster. We then discuss difficulties which arise in the presence of 2-body bound states and present a tentative formula involving eigenphase shifts and the 2 and 3 body bound state energies. We emphasize that important difficulties have not been resolved.