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.

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A set of potential constants for the He-He exp-six intermolecular potential has been found which leads to calculated results in good agreement with the experimental second virial coefficients of He 4 both at high and at low temperatures and with the high-temperature viscosity and thermal conductivity data. A table of the second virial coefficients of He 3 and He 4 over the temperature range 0.3°K to 60°K is given. The position of a negative discrete energy as a function of some of the parameters of the exp-six potential has been investigated.

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