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.
Keywords
Cite
@article{arxiv.physics/0105074,
title = {Hyperspherical Adiabatic Formalism of the Boltzmann Third Virial},
author = {Sigurd Yves Larsen},
journal= {arXiv preprint arXiv:physics/0105074},
year = {2007}
}
Comments
7 pages, published in the Proceedings of the Bogolyubov Conference on Problems of Theoretical and Mathematical Physics (Moscow-Dubna-Kiev, September 27 - October 6, 1999)