Confined harmonically interacting spin-polarized fermions in a magnetic field: Thermodynamics

We investigate the combined influence of a magnetic field and a harmonic in terparticle interaction on the thermodynamic properties of a finite number of spin-polarized fermions in a confinement potential. This study is an ext ension using our path integral approach of symmetrized density matrices for identical particles. The thermodynamical properties are calculated for a t hree-dimensional model of N harmonically interacting spin-polarized fermion s in a parabolic potential well in the presence of a magnetic held. The fre e energy and the internal energy are obtained for a limited number of parti cles. Deviations from the thermodynamical limit become negligible for about 100 or more particles, but even for a smaller number of fermions present i n the well, scaling relations similar to those of the continuum approximati on to the density of states are already satisfied.