Confined harmonically interacting spin-polarized fermions

The thermodynamical properties are calculated for a three-dimensional model of $N$ harmonically interacting spin-polarized fermions in a parabolic potential well. The obtained dependences of the chemical potential and of the internal energy on the complete range of the temperature and of the number of particles turn out to obey a scaling law, similar to the scaling from the continuum approximation for the density of states. The calculational technique is based on our path-integral approach of symmetrized density matrices for identical particles in a parabolic confining well.