The Low-Temperature Properties of Gaseous Helium. II

Some earlier calculations of the second virial and viscosity coefficients of gaseous helium have been extended, using as before the exact quantum formulae. A brief discussion of the atomic interaction, which is expressed in the form V(σ ) = - ɛ f(σ ), where σ = r/r₀, r₀ is the atomic separation when V is a minimum, and f(1) = 1, is followed by the results of the new calculations and their interpretation. Several interactions, with widely varying values of ɛ r₀², have been employed, and inferences about the actual interaction are made by interpolating the available experimental data, a method particularly suitable for interpreting future results. The results of some calculations by de Boer and Michels have been incorporated. It is found that the present data for the second virial coefficient, between 2 and 4\cdot 3 degrees K, indicate for ɛ r₀² a value about 122 × 10^-16 erg A². Though the separate determination of r₀ and ɛ is not likely to be very precise unless calculations are extended to temperatures much beyond the present limit (11 degrees K), the assumption of a probable value for the first van der Waals coefficient leads to the values r₀ = 2\cdot 93 A, ɛ = 14\cdot 2 × 10^-16 erg. The influence of possible variations in the function f(σ ) are discussed and shown to be of secondary importance, and these results are based on a reasonable form for f(σ ) with two parameters. Comparisons are also made with two viscosity measurements below 5 degrees K, but the inferences from these are not at all in agreement with the evidence from the equation of state.