Properties of liquid helium has long since been investigated and many interesting phenomena are known to us. Recently it has become possible to obtain the isotope He³ in pure form and a lot of interesting experiments have been done for various concentrations of He³ in He⁴. At first, ratio of the two components in the vapor and liquid phases was investigated and it was proposed by Taconis, Beenakker, Nier and Aldrich that below the λ-point He³ mixes only with the normal part of He⁴. On the other hand, change of λ-point with the content of He³ was investigated both experimentally and theoretically. Theories of the phenomena were proposed by Stout, Rice, De Boer and Gorter. Their theories are based on the assumption that He³ mixes only with the normal part of He⁴ as proposed by Taconis and others. Experimental investigations were done by Abraham, Weinstock, and Osborne for the range of concentrations of 0%–28% and by Daunt and Heer for concentrations up to 89%.
Now theories thus far proposed are mainly thermodynamical, and it seems that molecular theories have not yet appeared. We shall here investigate the properties of the mixture of He⁴ particles which obey Bose-Einstein statistics and He³ particles which obey Fermi-Dirac statistics.

View full abstract