PRESSURE AND DENSITY OF VACANCIES IN SOLID HE-4

Crystals of He-4 contain vacancies that move around by a quantum-mecha nical hopping process. The density and pressure of these vacancies can be experimentally studied. The accuracy of the experiments is high en ough to detect the effect of the Bose statistics of the vacancies. In this paper we examine the effect of the hard-core repulsion between th e vacancies, which should also have a measurable effect on their behav ior. We set up a virial expansion for a lattice gas of hard-core parti cles, and calculate the second virial coefficient. It turns out that t he vacancies behave as ideal Bose particles at low temperatures, but t hat the hard-core interaction makes them behave more and more like fer mions as the temperature increases.