Thermodynamic Properties of Superfluid 4He at Negative Pressure

We calculate the thermodynamics of superfluid 4He at negative pressures. We use the Landau theory in which thermodynamic properties are expressed as sums over the thermal distribution of elementary excitations. The excitation dispersion curve is taken from the density functional theory developed by Dalfovo et al. To give a good description of the liquid near to the lambda line, we include the interaction between the elementary excitations using a modification of the roton liquid theory of Bedell, Pines, and Fomin. The calculated quantities include the location of the lambda line, the liquid-vapor spinodal, and lines of constant entropy in the pressure-temperature (P-T) plane. We have also calculated the line of minimum density (zero expansion coefficient) in the P-T plane. This joins the lambda line tangentially at about -5.3 bars. Using the critical properties near the lambda line, we find that the line of maximum density in He I also joins the lambda line tangentially at this pressure. For use in cavitation experiments, we have calculated the states on the lambda line reached by isentropic expansion from He I.