Theory of Liquid Helium Three

The present work contains a detailed study of two types of heat-capacity anomalies present in liquid ${\mathrm{He}}^3$. One of these is the plateau formation at intermediate pressures, $p\lesssim 10$ atm. The other anomaly consists in the appearance of a flat constant-pressure heat-capacity maximum, followed by a shallow minimum, between the temperatures of 0.15 and 0.30°K, and the pressures of 10 and 30 atm, approximately. At somewhat higher pressures, over a small pressure range, only the heat-capacity maximum becomes observable. These heat-capacity anomalies originate with the competition of the thermal excitations of the spin and nonspin degrees of freedom, within the theoretical approach advanced here. The observation of the predicted low-amplitude heat-capacity extrema in compressed liquid ${\mathrm{He}}^3$ may require heat-capacity measurements of increased accuracy, preferably at higher pressures. The problem of the heat-capacity behavior at low and very low temperatures has also been explored under a restrictive hypothesis. It will be assumed that the nature of the thermal excitations which appear in incontrovertible and independent heat-capacity data, available only at saturation and at temperatures above 0.2°K, persists on the spin and nonspin degrees of freedom down to the absolute zero. With the recently established universal character of the nuclear-paramagnetic-susceptibility ratio law of liquid ${\mathrm{He}}^3$, down to 0.05°K, the stated assumption leads one to predict that the ratio of the total heat capacity to the temperature approaches parabolically in temperature its finite limit at the absolute zero. In the present theory, deviations from this behavior require a new paramagnetic-susceptibility law at the lowest temperatures.