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We use different types of determinantal Hartree-Fock (HF) wave functions tocalculate variational bounds for the ground state energy of spin-half fermionsin volume V_0, with mass m, electric charge zero, and magnetic moment mu, whichare interacting through long range magnetic dipole-dipole interaction. We findthat at high densities when the average inter particle distance r_0 becomessmall compared to the magnetic length r_m, a ferromagnetic state withspheroidal occupation function, involving quadrupolar deformation, gives alower energy compared to the variational energy for the uniform paramagneticstate. This HF variational bound to the ground state energy turns out to have alower energy than our earlier calculation in which instead of a determinantalwavefunction we had used a positive semi-definite single particle densitymatrix operator whose eigenvalues, having quadrupolar deformation, were allowedto take any value from 0 to 1. This system is of course still unstable towardsinfinite density collapse, but we show here explicitly that a suitable shortrange repulsive (hard core) interaction of strength U_0 and range a can stopthis collapse.The existence of a stable high density ferromagnetic state withspheroidal occupation function is possible as long as the ratio of hard-coreand magnetic dipole coupling constants is not very small compared to 1.Comment: A shorter version of this paper will appear in Pramana - Journal of  Physic

pramāna

Hartree-Fock variational bounds for ground state energy of chargeless fermions with finite magnetic moment in the presence of a hard core potential: A stable ferromagnetic state