Second Virial Coefficients ofHe3andHe4

The second virial coefficients of ${\mathrm{He}}^3$ and ${\mathrm{He}}^4$ 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 ${\mathrm{He}}^4$ second virial coefficients agree very well with the available experimental data. They also join nicely at 60°K with the coefficients calculated from the high-temperature classical equation with quantum corrections. The second cross virial coefficients for ${\mathrm{He}}^3$, ${\mathrm{He}}^4$ have also been calculated. The deviation of a gaseous solution of ${\mathrm{He}}^3$ and ${\mathrm{He}}^4$ from an ideal solution is comparatively small at temperatures above about 2°K, while at very low temperatures pronounced quantum solution imperfection appears.