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 crystallinelike structure where Cooper pairs carry net momentum (the nuclear Larkin-Ovchinnikov-Fulde-Ferrell-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 are deformed Fermi surfaces and Cooper pairs with vanishing total momentum.