A generalized Uhlenbeck and Beth formula for the third cluster coefficient

Journal Article · Tue Nov 15 04:00:00 EST 2016 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2016.08.011· OSTI ID:22617423

Larsen, Sigurd Yves ^[1]; Lassaut, Monique ^[2]; Amaya-Tapia, Alejandro ^[3]

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1. Department of Physics, Temple University, Philadelphia, PA 19122 (United States)
2. Institut de Physique Nucléaire, CNRS-IN2P3, Université Paris-Sud, Université Paris-Saclay, F-91406 Orsay Cedex (France)
3. Instituto de Ciencias Fi ´sicas, Universidad Nacional Autónoma de México, AP 48-3, Cuernavaca, Mor. 62251 (Mexico)

Relatively recently (Amaya-Tapia et al., 2011), we presented a formula for the evaluation of the third Bose fugacity coefficient–leading to the third virial coefficient–in terms of three-body eigenphase shifts, for particles subject to repulsive forces. An analytical calculation for a 1-dim. model, for which the result is known, confirmed the validity of this approach. We now extend the formalism to particles with attractive forces, and therefore must allow for the possibility that the particles have bound states. We thus obtain a true generalization of the famous formula of Uhlenbeck and Beth (Uhlenbeck and Beth, 1936; Beth and Uhlenbeck, 1937) and of Gropper (Gropper, 1936, 1937) for the second virial. We illustrate our formalism by a calculation, in an adiabatic approximation, of the third cluster in one dimension, using McGuire’s model as in our previous paper, but with attractive forces. The inclusion of three-body bound states is trivial; taking into account states having asymptotically two particles bound, and one free, is not.

• OSTI ID: 22617423
• Journal Information: Annals of Physics, Journal Name: Annals of Physics Vol. 374; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ADIABATIC APPROXIMATION
BOUND STATE
THREE-BODY PROBLEM