Second Virial Coefficients ofHe3andHe4

Abstract

The second virial coefficients of He' and He4 have been calculated at closely spaced temperatures over the range 0. 3'K to 60'K using the Lennard-Jones 12 -6 potential with constants determined by de Boer and Michels. The necessary phase shifts were calculated on a high-speed electronic digital computer. The resulting He4 second virial coefficients agree very well with the available experimental data. They also join nicely at 60'K with the coeKcients calculated from the high-temperature. classical equation with quantum corrections. The second cross virial coefficients for He3, He4 have also been calculated. The deviation of a gaseous solution of He3 and He4 from an ideal solution is comparatively small at temperatures above about 2'K, while at very low temperatures pronounced quantum solution imperfection appears.

Quantum second virial coefficient calculation for the 4He dimer on a recent potential

“…Therefore, the quantity G(q), which is necessary to calculate the second virial coefficient, will converge for a maximum angular momentum, l max . 6,23 By angular momentum conservation, one can estimate this maximum at l max ≈ kR max , in which R max is the potential range. The quantity l max is the maximum angular momentum required to achieve cross section convergence.…”

“…The classical second virial coefficient is not appropriate to describe the helium equation of state at temperatures lower than 100 K. 22 Instead, the exact quantum second virial coefficient expression relating the phase shift and the energy of bound state is used for an accurate system description. 6,23,24 The molar virial expansion is represented in the form (3) in which e is the He 2 binding energy for zero angular momentum, k B is Boltzmann's constant and (4) with  = 2.556 Å. The dimensionless variables q and q 0 were conveniently introduced in formulating the problem and are related to the collision energy and temperature, respectively.…”

“…The results obtained in the present work will be compared to experimental data for the helium-helium system. [22][23][24] …”

“…[16][17][18][19][20] The most recent potential has not been tested against thermodynamic and transport property data, 21 such as the quantum second virial coefficients. In the present work, a study of this recent potential was conducted using second virial coefficient data at low temperature.The quantum virial coefficient can be determined by evaluating the quantum ideal gas term, the scattering phase shift dependence on angular momentum [22][23][24][25][26][27][28][29] and the bound states by Levinson's theorem. [25][26] This low-temperature second virial coefficient calculation is an important step to test the quality of the potential under consideration.…”

Quantum Phenomena and the Mobility of Potassium Ions in Argon

“…Two interaction potentials were considered for the Ar-K + problem, one described by Kumar and Robson (1973) and the other by Skullerud (1973). -Both potentials were of the form given by Mason and Schamp (1958),…”