The low-temperature properties of gaseous helium

Abstract

Helium is unique in that it persists as a monatomic gas down to tempera­tures so low that quantum effects become important. These effects arise in two more or less distinct ways. Quantum mechanics must be used in dealing with the relative motion of the gas atoms, leading to modification of the classical formulae even it the Boltzmann statistics are employed in describing the behaviour of the atomic assembly. It is further necessarv, however, to allow for the symmetry properties of the atoms by making use of the Bose-Einstein instead of the classical statistics. Usually the quantiza­tion of the relative motion introduces the more important deviations from classioal theory, but it is of interest to examine also whether it is possible to show, by comparison with experiment, that the Bose-Einstein statistics are the correct ones to use in dealing with helium atoms. In this paper we take account of both these quantum effects in determining theoretical values for the viscosity and second virial coefficients of helium, in the temperature range 0-25°K. Experimental values of these coefficients have been obtained at a number of temperatures in this range; comparison of observed and calculated values then leads to interesting conclusions concerning the inter­action of helium atoms, the validity of the quantum theory at these low temperatures and the correct statistics to apply. At the same time results are obtained for the total collision area of helium atoms capable of experi­mental tests by molecular ray methods. The classical limit of the viscosity formula has been discussed by Massey and Mohr (1933) and by Uhlenbeck and Uehling (1933), and of that for the second virial coefficient by Uhlenbeck and Leth (1936). No classical analogue of the total cross-section exists (Massey and Mohr 1933). In an accompanying paper by one of us (R. A. B.) the classical theory of the equation of state of helium and also of neon and argon is discussed and the conclusions drawn therefrom used to supplement those of this paper in providing information as to the form of the interaction of helium atoms. A complete knowledge of this interaction may be important for a discussion of the remarkable properties of liquid helium.