Predicting the borderline between the classical and quantum regimes in ⁴He gas from the second virial coefficient

Abstract

The second Virial coefficient in both classical and quantum regimes of 4He gas is investigated in the temperature range 4.2–10 K. Full quantum mechanical and classical treatments are undertaken to calculate this coefficient. The main input in computing the quantum coefficient is the “effective” phase shifts. These are determined within the framework of the Galitskii–Migdal–Feynman formalism, using two interatomic potentials. The borderline between the classical and quantum regimes is found to depend on the temperature, the number density, and the interparticle potential.

Scattering Properties of Argon Gas in the Temperature Range 87.3-120 K

“…The validity of the GMF formalism in the low-density regime has been demonstrated repeatedly over the years [10][11][12][13][14]. The reason for this choice of temperature range is to enable us to compare our results to other results available in the literature, both experimental and theoretical.…”

“…For a many-bosonic system, the operator Q Q is the product of two distributions as follows [12,13,28]:…”

“…In this paper, the Galitskii-Migdal-Feynman (GMF) formalism [10][11][12][13][14] is applied to Ar gas for studying its scattering and thermodynamic properties in the temperature range 87.3-120 K, using the Hartree-Fock dispersion (HFD-B3) interatomic potential, with special emphasis on the quantum second virial coefficient [15]. The validity of the GMF formalism in the low-density regime has been demonstrated repeatedly over the years [10][11][12][13][14].…”

“…It can also be viewed as a generalized scattering amplitude, or as a "dressed" Lippmann-Schwinger t-matrix (which describes the scattering of two particles in free space). The GMF T -matrix was originally derived for many-fermionic systems, but was later adapted to manybosonic systems [12,13]. This formalism is used to calculate the "effective" phase shifts that incorporate manybody effects; they are functions of the density and temperature.…”

Equation of state of Krypton gas in the temperature-range 120-130 K

“…The main goals of this study are to find out an equation of state for Kr gas and to calculate some of its thermodynamic properties in the temperature range 120-130 K at various densities using the Galitskii-Migdal Feynman (GMF) formalism (Ghassib et al, 1976;Bishop et al, 1976;Joudeh et al, 2010;Ghassib et al, 2014;Mosameh et al, 2014). This formalism can be viewed as an independent-pair model ،dressed by a many-body medium.…”