Tunnel model for quantum liquids

Abstract

In the tunnel model, a fluid is regarded as being composed of lines of molecules which move almost one-dimensionally in lines or tunnels, the walls of which are formed by neighbouring lines of molecules. This model has been used, with good success, to describe the properties of classical hard spheres and classical simple liquids. For quantum fluids the energy levels of a one-dimensional line of molecules must be calculated. This has been done only for a system of hard spheres. For more complicated systems the energy levels must be approximated. In this paper the tunnel model is applied to liquid ⁴He at absolute zero and to liquid H₂. The lowest energy level has been approximated and the hard-sphere energy levels are used to estimate the higher energy levels. The agreement with experiment is generally good except in the critical region.