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.

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

scholarly journals Explicit Green operators for quantum mechanical Hamiltonians. II. Edge-type singularities of the helium atom

2019 ◽  
Vol 13 (07) ◽  
pp. 2050122
Author(s):  
Heinz-Jürgen Flad ◽  
Gohar Flad-Harutyunyan ◽  
Bert-Wolfgang Schulze
Keyword(s):  
Asymptotic Behavior ◽  
Helium Atom ◽  
Hydrogen Molecule ◽  
Second Order ◽  
Quantum Mechanical ◽  
Electron Systems ◽  
Explicit Formulas ◽  
Edge Type ◽  
Oppenheimer Approximation ◽  
Hamiltonian Operators

We extend our approach of asymptotic parametrix construction for Hamiltonian operators from conical to edge-type singularities which is applicable to coalescence points of two particles of the helium atom and related two electron systems including the hydrogen molecule. Up to second-order, we have calculated the symbols of an asymptotic parametrix of the nonrelativistic Hamiltonian of the helium atom within the Born–Oppenheimer approximation and provide explicit formulas for the corresponding Green operators which encode the asymptotic behavior of the eigenfunctions near an edge.

Quantum-statistical second virial coefficient and scattering theory

Physica ◽  
1971 ◽  
Vol 51 (1) ◽  
pp. 146-164 ◽  
Author(s):  
D. Kremp ◽  
W.D. Kraeft ◽  
W. Ebeling
Keyword(s):  
Scattering Theory ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Quantum Statistical

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.

Sign in / Sign up

Export Citation Format

Share Document