A Contribution to the Theory of Bose-Einstein Liquids

Abstract

Smoothed potential models for liquid ${\mathrm{He}}^4$ and liquid ${\mathrm{He}}^3$ in which each are considered as ideal Bose-Einstein and Fermi-Dirac gases situated in potential wells of potential $-{{\chi }_4}^0$ and $-{{\chi }_3}^0$, respectively, are considered. It is shown that the degeneracy temperature, $T_0$ of pure liquid ${\mathrm{He}}^4$ on this model can be deduced and that the $\lambda$-transition temperatures, $T_{\lambda }$, of solutions of such liquids can be calculated. The calculated values of $T_{\lambda }$ as a function of concentration of ${\mathrm{He}}^3$ appear to be in satisfactory agreement with the observed values. From these considerations, predictions are made regarding the behavior of solutions of two Bose-Einstein liquids; e.g., ${\mathrm{He}}^6$ in ${\mathrm{He}}^4$. It is shown, moreover, that solutions of such model liquids obey the third law of thermodynamics.