λTransition of Liquid Helium

Abstract

The partition function of liquid helium proposed by Feynman, $q=\Sigma g\left(L\right)\mathrm{}\exp \mathrm{}(-aTL)\mathrm{}$, is calculated for a simple cubic lattice using an approximation corresponding to Bethe's method for the Ising model. It is shown that a second-order transition occurs at $a{T}_{\lambda }=\ln 4$, or $T_{\lambda }=\frac{2.9m}{m^{\prime }}°$K ($m$ and $m^{\prime }$ representing the true and the effective masses of a helium atom). The nature of the approximation is discussed.