Effective mass of $^4$He atom in superfluid and normal phases

TL;DR

This paper derives a temperature-dependent formula for the effective mass of $^4$He atoms in superfluid and normal phases, addressing infra-red divergences and calculating related thermodynamic properties.

Contribution

It presents a novel expression for the effective mass of $^4$He atoms valid at all temperatures except near the critical point, improving understanding of superfluid phase transitions.

Findings

The formula eliminates infra-red divergences across all temperatures.

The temperature dependence of heat capacity and transition temperature are calculated.

The critical index $\eta$ is determined within the random phase approximation.

Abstract

The formula for the temperature dependence of the effective mass of a $^{4}% $He atom in the superfluid and normal phases is obtained.\,\,This expression for the effective mass allows one to eliminate infra-red divergences, being applicable at all temperatures, except for a narrow fluctuation region 0.97~$\lesssim T/T_{\rm c}\leq1$.\,\,In the high and low temperature limits, as well as in the interactionless limit, the obtained expression reproduces the well known results.\,\,The temperature dependence of the heat capacity and the phase transition temperature $T_{\rm c}\approx$~2.18~K are calculated, by using the formula obtained for the effective mass.\,\,In the framework of the approach proposed in this work, the small critical index $\eta$ is determined in the random phase approximation.\,\,The obtained value corresponds to the well known result.