Analysis of a Model Exhibiting Condensation with Application toHe3

Abstract

A study is made of a certain model Hamiltonian which describes a system of fermions. Making use of the variational results of Girardeau one can obtain, in the limit of infinite volume, an explicit formula for the free energy in terms of the solution of a nonlinear integral equation. It is established that for certain values of the coupling constant the model exhibits condensation, and that qualitatively at least, the isotherms for the model reproduce those for actual physical systems. The model is applied to ${\mathrm{He}}^3$ and it is shown that by a suitable choice for the parameters of the model, reasonable agreement with the low-temperature properties of ${\mathrm{He}}^3$ is obtained. The second virial coefficient for ${\mathrm{He}}^4$ is also reproduced with the same parameter values which give the correct virial coefficient for ${\mathrm{He}}^3$.