Qualitative Aspects of the Quantum Mechanical Second Virial Coefficient

1971 ◽  
Vol 54 (10) ◽  
pp. 4281-4282 ◽  
Author(s):  
Ludwig W. Bruch
Keyword(s):  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Quantum Mechanical

Quantum Mechanical Second Virial Coefficient of a Lennard‐Jones Gas. Helium

1969 ◽  
Vol 50 (9) ◽  
pp. 4034-4055 ◽  
Author(s):  
M. E. Boyd ◽  
S. Y. Larsen ◽  
J. E. Kilpatrick
Keyword(s):  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Quantum Mechanical ◽  
Lennard Jones

Second Virial Coefficient of Low-density Lithium-7 (7Li) Gas in the Temperature Range 1 K40000 K and Beyond

2021 ◽  
Vol 14 (3) ◽  
pp. 239-247
Keyword(s):  
Long Range ◽  
Short Range ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Quantum Mechanical ◽  
Low Density ◽  
Temperature Range ◽  
Repulsive Potentials ◽  
Repulsive Forces ◽  
Good Agreement

Abstract: The second virial coefficient B for low-dense 7Lithium (7Li) gas is calculated over a wide temperature range 1 K40000 K. In the ‘high’-T limit (600 K45000 K), the classical coefficient, Bcl, and the contribution of the first quantum-mechanical correction, Bqc, are computed from standard expressions, using a suitable binary potential. The classical coefficient, Bcl, together with the Boyle temperature, TB, are determined and their values are in good agreement with previous results. In addition, the interface between the classical and quantum regimes is systematically investigated. Furthermore, the calculation of the quantum-mechanical second virial coefficient, Bq, is evaluated using the Beth-Uhlenbeck formula in the temperature range 1 K500 K. A positive value of Bq indicates that the net interaction energy is repulsive, implying that the short-range repulsive forces dominate the long-range attractive forces. However, quite the opposite occurs for negative values of Bq, which are indicative of net attractive interaction. The general behavior of Bq is similar to the potential energy itself, such that the long-range attractive and the short-range repulsive potentials can be deduced from the measurements of Bq. Keywords: Second virial coefficient, Low-density Lithium-7 Gas, Short-range repulsive forces, Long-range attractive forces. PACS: 51.30.+i.

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

2014 ◽  
Vol 92 (9) ◽  
pp. 997-1001 ◽  
Author(s):  
H.B. Ghassib ◽  
A.S. Sandouqa ◽  
B.R. Joudeh ◽  
S.M. Mosameh
Keyword(s):  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Quantum Mechanical ◽  
Interatomic Potentials ◽  
Number Density ◽  
Temperature Range ◽  
Interparticle Potential ◽  
Main Input ◽  
Effective Phase ◽  
Full Quantum

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.

The Quantum Mechanical Second Virial Coefficient for Anisotropic Interactions: Hydrogen Molecule–Helium Atom

1974 ◽  
Vol 52 (19) ◽  
pp. 1914-1925 ◽  
Author(s):  
Sigurd Yves Larsen ◽  
J. D. Poll
Keyword(s):  
Helium Atom ◽  
Scattering Theory ◽  
Hydrogen Molecule ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Bound State ◽  
Quantum Mechanical ◽  
Closed Channel ◽  
Channel Calculation ◽  
Anisotropic Interactions

A derivation of a generalized Uhlenbeck and Beth formula is given which relies neither on the notion of a box nor on formal scattering theory. The expression for the 2nd virial coefficient then involves bound state energies as well as eigenphase shifts associated with the asymptotic description of a coupled (open and closed) channel calculation. The proof and specific details of such a calculation are worked out for the case of a hydrogen molecule interacting with a helium atom.

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