Hyperspherical Adiabatic Formalism of the Boltzmann Third Virial

Details Hyperspherical Adiabatic Formalism of the Boltzmann Third Virial Hyperspherical Adiabatic Formalism of the Boltzmann Third Virial

2001-05-22

arxiv.org/abs/physics/0105074v1

Physics

Chemical Physics

7 pages, published in the Proceedings of the Bogolyubov Conference on Problems of Theoretical and Mathematical Physics (Moscow

Scientific paper

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.

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