The transition temperature in liquid helium

Abstract

The partition function for an imperfect Bose-Einstein assembly of atoms is evaluated following Feynman’s method, as modified by Kikuchi. The ‘effective mass’ approximation is avoided, and instead a factor depending explicitly on interatomic forces is introduced. This factor is evaluated approximately for pairs of atoms interacting with a Lennard-Jones potential. The calculation involves only the properties of the individual helium atoms and disregards collective excitations. No adjustable parameters are used. A peak in the specific heat at 2-0°K is found (experimental, 2·2°K), and this transition temperature decreases with density. There is another transition at about 3·0°K which is probably a liquid-gas transition. If the interatomic forces are very weak one would only get this second transition; the λ transition does not occur at all unless the forces are of the order of magnitude of those actually found in helium.