Equilibrium Theory of Liquid Helium-Four at Absolute Zero

Abstract

In this paper we develop a microscopic theory of liquid helium-four at absolute zero. Our method of attack is a free adaptation of the Bohm-Pines technique for describing the degenerate electron gas, and is an improvement in several ways on the collective treatment of liquid helium carried through by Bohm and Salt using the same technique. In consequence of our approach, we are able to treat the collective motions rather accurately and to give a microscopic derivation of the Feynman theory of liquid helium. We also show precisely how the latter is related to quantum hydrodynamics and how the Feynman-Cohen state vector for the excited states is the natural and rigorous outcome of relaxing a little the condition that density fluctuations in the liquid do not affect its kinetic energy. The ground-state wave function is computed and shown to be, to a very good approximation, of the same form as that postulated by Chester and his collaborators. This implies strongly that Bose condensation exists in liquid helium and that it is closely related to short-range correlations in the system. Lastly, we separate the microscopic Hamiltonian operator into truly independent collective and single-particle parts and verify that the coupling between the phonon modes and the short-range correlations can induce a velocity-dependent interaction between helium atoms. This new interaction is under certain conditions an attractive one and may play a role in determining the anomalous thermal properties of the liquid.