Complex representation of the quantumstatistical second virial coefficient

doi:10.1016/0375-9601(69)90525-8

Physics Letters A

Volume 29, Issue 8, 30 June 1969, Pages 466-467

https://doi.org/10.1016/0375-9601(69)90525-8 Get rights and content

Abstract

Using the resolvent representation the second virial coefficient of quantum systems is expressed by contour integrals over complex scattering quantities (e.g. Jost functions).

References (5)

K.M. Watson
Phys. Rev.
(1956)
B.J. Baumgartl
Z. Physik
(1967)

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This paper is devoted to the investigation of the connections between the quantum-statistical second virial coefficient and the modern nonrelativistic scattering theory. Using the resolvent representation of the binary density operator, path integral representations of the second virial coefficient in the complex energy plane are given. Especially in the case of spherically symmetric potentials a new useful representation of the second virial coefficient in terms of the Jost functions of scattering theory is derived. For more general potentials the resolvent is expressed in terms of the complex T-matrix.
In the case that there is an energy gap at E = 0 the representations in terms of the phase shifts (Beth-Uhlenbeck), the scattering amplitudes (Landau) and the T-matrix (Baumgartl) are obtained as special cases in a straightforward way. Using the advantages of the closed complex representation it was shown, that the thermodynamic functions are, under certain restrictions for the potential, analytic functions of the interaction parameter η at the point η = 0.

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Complex representation of the quantumstatistical second virial coefficient

Abstract

Phys. Rev.

Z. Physik