Sudhanshu S Jha
Articles written in Pramana – Journal of Physics
Volume 64 Issue 1 January 2005 pp 17-29
Swapnil S Jawkar Sudhanshu S Jha
Using the general formulation for obtaining chemical potential
Volume 68 Issue 5 May 2007 pp 819-830 Research Articles
We use different determinantal Hartree–Fock (HF) wave functions to calculate true variational upper bounds for the ground state energy of 𝑁 spin-half fermions in volume $V_{0}$, with mass 𝑚, electric charge zero, and magnetic moment 𝜇, interacting through magnetic dipole–dipole interaction. We ﬁnd that at high densities when the average interparticle distance $r_{0}$ becomes small compared to the magnetic length $r_{m} \equiv 2m\mu^{2}/\hbar^{2}$, a ferromagnetic state with spheroidal occupation function $n_{\uparrow} (\vec{k})$, involving quadrupolar deformation, gives a lower upper bound compared to the variational energy for the uniform paramagnetic state or for the state with dipolar deformation. This system is unstable towards inﬁnite density collapse, but we show explicitly that a suitable short-range repulsive (hard core) interaction of strength $U_{0}$ and range a can stop this collapse. The existence of a stable equilibrium high density ferromagnetic state with spheroidal occupation function is possible as long as the ratio of coupling constants $\Gamma_{cm} \equiv (U_{0}a^{3}/\mu^{2})$ is not very smallcompared to 1.
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