Third Bose fugacity coefficient in one dimension, as a function of asymptotic quantities

Journal Article · Tue Feb 15 04:00:00 EST 2011 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2010.10.004· OSTI ID:21579846

Amaya-Tapia, A ^[1]; Larsen, S Y ^[2]; Lassaut, M ^[3]

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1. Instituto de Ciencias Fisicas, Universidad Nacional Autonoma de Mexico AP 48-3, Cuernavaca, Mor. 62251 (Mexico)
2. Department of Physics, Temple University, Philadelphia, PA 19122 (United States)
3. Institut de Physique Nucleaire, IN2P3-CNRS, Universite Paris-Sud 11, F-91406 Orsay Cedex (France)

In one of the very few exact quantum mechanical calculations of fugacity coefficients, [L.R. Dodd, A.M. Gibbs. J. Math. Phys. 15 (1974) 41] obtained b{sub 2} and b{sub 3} for a one dimensional Bose gas, subject to repulsive delta-function interactions, by direct integration of the wave functions. For b{sub 2}, we have shown [A. Amaya-Tapia, S.Y. Larsen, M. Lassaut. Mol. Phys. 103 (2005) 1301-1306. < (arXiv:physics/0405150)>] that Dodd and Gibbs' result can be obtained from a phase shift formalism, if one also includes the contribution of oscillating terms, usually contributing only in one dimension. Now, we develop an exact expression for b{sub 3}-b{sub 3}{sup 0} (where b{sub 3}{sup 0} is the free particle fugacity coefficient) in terms of sums and differences of three-body eigenphase shifts. Further, we show that if we obtain these eigenphase shifts in a Distorted-Born approximation, then, to first order, we reproduce the leading low temperature behaviour, obtained from an expansion of the twofold integral of Dodd and Gibbs. The contributions of the oscillating terms cancel. The formalism that we propose is not limited to one dimension, but seeks to provide a general method to obtain virial coefficients, fugacity coefficients, in terms of asymptotic quantities. The exact one dimensional results allow us to confirm the validity of our approach in this domain.

• OSTI ID: 21579846
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 2 Vol. 326; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
ASYMPTOTIC SOLUTIONS
BORN APPROXIMATION
BOSE-EINSTEIN GAS
BOSONS
CALCULATION METHODS
DELTA FUNCTION
FUNCTIONS
INTEGRALS
INTERACTIONS
MANY-BODY PROBLEM
MATHEMATICAL SOLUTIONS
MECHANICS
ONE-DIMENSIONAL CALCULATIONS
PHASE SHIFT
QUANTUM MECHANICS
TEMPERATURE RANGE
TEMPERATURE RANGE 0065-0273 K
THREE-BODY PROBLEM
WAVE FUNCTIONS