Liquid helium-4 in the static fluctuation approximation

In this work liquid helium-4 is studied for the first time within the frame work of the so-called static fluctuation approximation. This is based on th e replacement of the square of the local-field operator with its mean value . A closed set of nonlinear integral equations is derived for weakly as wel l as for strongly interacting systems. This set is solved numerically by an iteration method for a realistic interhelium potential. The thermodynamic properties are then obtained for both the weakly interacting system, liquid He-4 in Vycor glass, and the strongly interacting system, liquid He-4. It turns out, however, that the present quadratic-fluctuation approximation is valid in the latter, strongly interacting case only in the low-temperature limit (less than or equal to0.15 K). Our results are presented in a set of figures. The role of the interaction is emphasized and the functional depe ndence of key thermodynamic quantities on the temperature is derived for bo th weakly and strongly interacting He-4 systems.