Se p 20 02 Phases of asymmetric nuclear matter with broken space symmetries

Isoscalar Cooper pairing in isospin asymmetric nuclear matter occurs between states populating two distinct Fermi-surfaces, each for neutrons and protons. The transition from a BCS-like to the normal (unpaired) state, as the isospin asymmetry is increased, is intervened by superconducting phases which spontaneously break translational and rotational symmetries. One possibility is the formation of a condensate with a periodic crystalline-like structure where Cooper pairs carry net momentum (the nuclear LOFF-phase). Alternatively, perturbations of the Fermi-surfaces away from spherical symmetry allow for minima in the condensate free-energy which correspond to a states with quadrupole deformations of Fermi-surfaces and zero momentum of the Cooper pairs. In a combined treatment of these phases we show that, although the Cooper pairing with finite momentum might arise as a local minimum , the lowest energy state features deformed Fermi-surfaces and Cooper pairs with vanishing total momentum.