The λ-Phenomenon of Liquid Helium and the Bose-Einstein Degeneracy

Nature ◽  
1938 ◽  
Vol 141 (3571) ◽  
pp. 643-644 ◽  
Author(s):  
F. LONDON
Keyword(s):  
Liquid Helium ◽  
Bose Einstein

Liquid helium and the properties of a Bose–Einstein gas. III. The density dependence of hard-core models

1970 ◽  
Vol 48 (11) ◽  
pp. 1340-1364
Author(s):  
D. F. Goble
Keyword(s):  
Density Dependence ◽  
Liquid Helium ◽  
Hard Core ◽  
Ladder Approximation ◽  
Model Systems ◽  
Coordinate Space ◽  
Core Boundary ◽  
T Matrix ◽  
Bose Einstein ◽  
Space Method

We have used the results of a previous paper by Goble and Trainor to compute the density dependence of the hard-core Bose–Einstein gas in the t-matrix ladder approximation, utilizing the coordinate-space method of Brueckner and Sawada as modified by Parry and ter Haar, and the pseudopotential treatment of the hard-core boundary condition presented by Liu and Wong. Various thermodynamic parameters of these model systems are compared with the properties of liquid helium four. The disagreements which are found are shown to be primarily related to differences in the magnitudes of the Landau parameters.

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.

Liquid helium and the properties of a Bose–Einstein gas. I. A numerical study of hard-core models

1968 ◽  
Vol 46 (7) ◽  
pp. 839-854 ◽  
Author(s):  
D. F. Goble ◽  
L. E. H. Trainor
Keyword(s):  
Liquid Helium ◽  
Numerical Study ◽  
Hard Core ◽  
Ladder Approximation ◽  
Pseudopotential Method ◽  
Coordinate Space ◽  
Core Potential ◽  
Soft Core Potential ◽  
Reasonable Choice ◽  
Bose Einstein

The properties of a hard-sphere, Bose–Einstein gas are investigated numerically in the t-matrix, ladder approximation, using both the coordinate-space treatment of Brueckner and Sawada, as modified by Parry and ter Haar, and the pseudopotential method of Liu and Wong. For each treatment, the form of the excitation spectrum and the thermodynamic properties of the gas at low temperatures are compared with the corresponding properties of liquid helium. The pseudopotential method gives better agreement for a reasonable choice of the radius of the "hard-core" interaction. This result is not surprising since the actual potential corresponding to the pseudopotential of Liu and Wong is intermediate between the "soft-core" potential of Brueckner and Sawada and a true "hard-core" potential.

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