Theory of the Melting Anomaly of Helium Four

Abstract

The melting anomaly of ${\mathrm{He}}^{4}$ predicted earlier will be accounted for in detail by two different methods. In the first or thermodynamic approach, the thermal properties of the liquid and solid at melting are used to evaluate the temperature derivative of the melting pressure and the ensuing difference between the melting pressure at temperature $T$ and absolute zero. In the second method, these same melting-pressure functions are derived theoretically from the elementary excitation spectra of the liquid. In the elaboration of the latter approach, the thermal properties of liquid ${\mathrm{He}}^{4}$ II, arising from the approximate high-energy branch of its elementary excitations, will be given exactly. Both methods yield similar results in quantitative agreement with recent melting-pressure data over most of the region explored.