We obtain the best upper bound for the ground-state energy of a system of chargeless fermions of mass $m$, spin $s=1∕2$, and magnetic moment $\mu \vec{s}$ as a function of its density in the fully spin-polarized Hartree-Fock determinantal state, specified by a prolate spheroidal plane-wave single-particle occupation function $n_{\uparrow }\left(\vec{k}\right)$, by minimizing the total energy $E$ at each density with respect to the variational spheroidal deformation parameter ${\beta }_2,0⩽{\beta }_2⩽1$. We find that at high densities, this spheroidal ferromagnetic state is the most likely ground state of the system, but it is still unstable towards the infinite-density collapse. This optimized ferromagnetic state is shown to be a stable ground state of the dipolar system at high densities, if one has an additional repulsive short-range hardcore interaction of sufficient strength and nonvanishing range.

• Received 25 June 2007

DOI:https://doi.org/10.1103/PhysRevE.76.062101