The three body partition function for hard core square well clusters

1980 ◽  
Vol 73 (9) ◽  
pp. 4663-4667 ◽  
Author(s):  
W. H. Zurek ◽  
W. C. Schieve
Keyword(s):  
Partition Function ◽  
Hard Core ◽  
Square Well ◽  
Three Body

scholarly journals Liquid-solid transitions in the three-body hard-core model

2015 ◽  
Vol 109 (2) ◽  
pp. 20003
Author(s):  
Tommaso Comparin ◽  
Sebastian C. Kapfer ◽  
Werner Krauth
Keyword(s):  
Hard Core ◽  
Core Model ◽  
Three Body ◽  
Hard Core Model

The analytical evaluation of the first-order density cluster integral in the radial distribution function

1970 ◽  
Vol 320 (1542) ◽  
pp. 323-348 ◽  
Keyword(s):  
Hard Sphere ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Scattering Data ◽  
X Ray ◽  
Lennard Jones ◽  
X Ray Scattering ◽  
Cluster Integrals ◽  
Square Well ◽  
Three Body

It is shown how to evaluate the two-body, and three-body cluster integrals, ɳ 3 , ɳ * 3 , β 3 , β * 3 (equations (1.1) to (1.4)) for the hard-sphere, square-well and Lennard-Jones ( v :½ v ) potentials; the three-body potential used is the dipole-dipole-dipole potential of Axilrod & Teller. Explicit expressions are presented for the integrals ɳ * 3 , β * 3 using the above potentials; in the case of the first integral, its values for both small and large values of the separation distance are also given, for the Lennard-Jones ( v :½ v ) potential. Similar considerations have been carried out for ɳ 3 and β 3 , except that explicit expressions for the hard-sphere, and square-well potentials are not given, since these had been done before by other authors. The intermediate expressions for the four cluster integrals, are in terms of single integrals, and such expressions are valid for any continuous potential. Numerical results based on some of the expressions in this paper are compared with the results of numerical evaluation of the above integrals by other authors, and the agreement is seen to be good. Making use of the Mikolaj-Pings relation, the above results are used to obtain relationships between the second virial coefficient, and X-ray scattering data, as well as a means of deducing the pair potential at large separations, directly from a knowledge of X-ray scattering data, and the second virial coefficient.

Liquid Helium and the Properties of a Bose–Einstein Gas. IV. The Effect of Various Approximations

1971 ◽  
Vol 49 (24) ◽  
pp. 3099-3114 ◽  
Author(s):  
D. F. Goble
Keyword(s):  
Liquid Helium ◽  
Hard Core ◽  
Quantitative Agreement ◽  
Perturbation Series ◽  
Model System ◽  
Three Body ◽  
Bose Einstein ◽  
Generalized Condensation

On a qualitative basis we have examined the identification of the properties of a hard-core Bose–Einstein (BE) gas with those of liquid helium four below the lambda temperature. It is suggested that the use of the generalized condensation of Girardeau together with the inclusion of "three-body ladders" from the perturbation series may improve the agreement between the hard-core BE model system and the physical helium four system to such an extent that reasonable quantitative agreement may be attained.

Redetermination of hard-core square-well-potential parameters for helium using new constructive methods for the ground state of liquidHe4

1982 ◽  
Vol 25 (1) ◽  
pp. 481-482 ◽  
Author(s):  
George A. Baker ◽  
Manuel de Llano ◽  
Justino Pineda ◽  
William C. Stwalley
Keyword(s):  
Ground State ◽  
Hard Core ◽  
Constructive Methods ◽  
Square Well ◽  
Potential Parameters
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