Second Virial Coefficients of Helium from the Exp-Six Potential

Kilpatrick, John E.; Keller, W.E.; Hammel, E.F.

doi:10.1103/physrev.97.9

Cited by 107 publications

(10 citation statements)

References 7 publications

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“…This form for the potential is convenient and it is used in the present calculation. More recent measurements at low temperatures by Keller 15 indicate that the potential should be somewhat more attractive.…”

Section: Introductionmentioning

confidence: 99%

Ground State of LiquidHe4

1965

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The properties of the ground state of liquid He 4 are studied using a variational wave function of the form Hi^fiUj). The Lennard-Jones 12-6 potential is used with parameters determined from the gas data by deBoer and Michiels. The configuration space integrals are performed by a Monte Carlo technique for 32 and 108 atoms in a cube with periodic boundary conditions. With /W=exp[-(2.6 A/f) 5 ], the groundstate energy is found to be -0.78X10" 15 ergs/atom, which is 20% above the experimental value. The liquid structure factor and the two-particle correlation function are in reasonably good agreement with the x-ray and neutron scattering experiments. Lltydr= f E [Whif(rv)+V(ry)\*dT.This integral can be written in terms of the two-particle correlation function, defined as ^Rx-R^p-s ( E $(Ri-r<)A 448 w. L. MCMILLAN m 6 7 12 -J I -1 J QP°«°CU J H J H i i 1 -1

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Section: Introductionmentioning

confidence: 99%

Ground State of LiquidHe4

1965

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“…2 "~ agreed well within the estimated accuracy. Franck and Martin (1961) and Martin (1966) also obtained good results with Keesom's values, whereas Osborne et al (1967) found very good agreement at 4.2% mith the virial coefficients of Kilpatrick et al (1955). Kilpatrick's calculations are based on data given by Keller (1955).…”

Section: P=a+-+dt+et~mentioning

confidence: 90%

Processes of Fragmentation and Fission in Interactions Between High Energy Particles and Nuclei

Perfilov¹,

Lozhkin²,

Shamov³

1960

Sov. Phys. Usp.

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A carbon resistance thermometer with very convenient characteristics has been developed. It allows accurate measurement of temperatures and temperature differences over a wide temperature range using a Wheatstone bridge. By varying the ratios of the constituents in the carbon mixture, the resistance and sensitivity can be varied more or less predictably. A sixth degree polynomial, fitted to calibration points in liquid helium, hydrogen and nitrogen only, gives an accurate (R, T ) relation over the whole temperature region. This is demonstrated with a calibration against a gas thermometer.In a separate experiment the superconducting transition temperature of lead has been determined. By interpolating with the polynomial without reference to the gas thermometer, a value of 7 . 1 9 0 "~ has been obtained, in very good agreement with literature.

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“…At the present time, no well-justified decision is available on the degree of fitness of the original analytical approximations to the pair potential energies of two isolated He 4 atoms, <pi(r) and <pn(r). There appear to be indications, 11 as far as the helium vapor second virial coefficient is concerned, that <pn (r) tends to overestimate, in absolute value, the pair potential energy. The problem of the degree of approximation achieved on the pair forces, [-grad^i(r)] and [-grad^n(r)], was not raised so far, because the intervention of the forces, in the rather fragmentary status of the theory of liquids, seemed to be remote.…”

Section: Very Large Values Of Both Approximate Kinetic Energies [E Ktmentioning

confidence: 99%

“…on the approximate evaluations of the In (4.3) and (4.4) the second virial coefficients measured recently by Keller 10 in this Laboratory, as well as the empirical function B(T) and its extrapolation 11 below 2°K have been used. In contrast with the vapor energies per atom e(T), the latent heats at r^2.50°K are of questionable accuracy, above all around the lambda point.…”

Section: Average Kinetic Energies and Root Mean Square Forces Per Atomentioning

confidence: 99%

Interatomic Correlations in LiquidHe4

Goldstein

1955

Phys. Rev.

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The direct correlation functions, of generally short-range character over most of the liquid temperature interval, have been obtained with the liquid He 4 x-ray scattering data of Reekie, using the 701 IBM Electronic Calculator. The geometrical simplicity of these functions when compared with the indirect correlation functions, of more intuitive physical significance, is automatically demonstrated. They closely satisfy two types of integral test relations, and this fact proves their over-all correct character and the internal consistency of the numerical analysis.The previously obtained indirect correlation functions will be used here in studying the interference properties of the liquid in slow-neutron scattering processes, in the limiting static approximation. At temperatures not too close to the critical region, the static interference integrals are always negative as a result of the preponderant destructive interference effects arising from the local density defects from the mean density, outweighing the local density excesses. At short and moderate neutron wavelengths, where the use of the static interference integrals is better justified, the total slow-neutron scattering cross sections in liquid He 4 , and in liquids in general, always increase with increasing temperature. The static interference integrals will be shown to provide an additional integral test on the indirect correlation functions. The latter were found to satisfy this test relation with good accuracy.Part of this paper is devoted to a numerical evaluation of mean kinetic energies per liquid He 4 atom as a function of the temperature. The existence of a large zero-point kinetic energy of the liquid as compared with the kinetic energy of thermal origin is demonstrated. Furthermore, the previously given qualitative proof of the kinetic energy origin of the lambda transition could be made semiquantitative. Finally, root-mean-square forces acting on a liquid atom are evaluated, this physical quantity of elementary character having become, in principle at least, accessible through the experimental investigation of slow-neutron scattering properties of liquids.

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Second Virial Coefficients of Helium from the Exp-Six Potential

Cited by 107 publications

References 7 publications

Ground State of LiquidHe4

Ground State of LiquidHe4

Processes of Fragmentation and Fission in Interactions Between High Energy Particles and Nuclei

Interatomic Correlations in LiquidHe4

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