The ground state of chargeless fermions with finite magnetic moment

We consider the ground state of a system of chargeless fermions, such as neutrinos, of mass m and magnetic moment m interacting through long-range magnetic dipole interaction, within the framework of a {Hartree-Fock} variational approach. At high densities the uniform paramagnetic state becomes unstable towards a ferromagnetic state with quadrupolar deformation of the Fermi surface. The exchange energy which is attractive dominates the repulsive kinetic energy. If we let the density be a variable, then above a certain density the system will collapse to an infinite density state unless another short-range interaction stops the collapse. In the case of large deformations, the possibility of a purely dipolar deformation exists.