Spatially inhomogeneous phase of asymmetric nuclear matter

We study the isospin singlet pairing in asymmetric nuclear matter with nonzero total momentum of the condensate Cooper pairs. The corresponding BCS equations are derived and solved within the finite temperature retarded realtime Green’s functions formalism. The quasiparticle excitation spectrum is four-fold split compared to the usual BCS spectrum of the symmetric, homogeneous matter. A two-fold splitting of the spectrum into separate branches is due to the finite-momentum of the condensate, the isospin asymmetry, or the finite quasiparticle life time. The coupling of the isospin singlet and triplet paired states leads to further two-fold splitting of each of these branches. We solve the gap equation numerically in the isospin singlet channel in the case where the pairing in the isospin triplet channel is neglected and find nontrivial solutions with finite total momentum of the pairs. The corresponding phase (nuclear LOFF phase) assumes a periodic spatial structure which carries a isospin density wave at constant total number of particles. The phase transition from the BCS to the LOFF phase is found first order and occurs when the density asymmetry is increased above 0.25. The transition from the LOFF to the unpaired normal state is second order. The maximal values of the critical total momentum (in units of the Fermi momentum) and the critical density asymmetry at which condensate disappears are Pc/pF = 0.3 and αc = 0.41. The possible spatial forms of the ground state of the nuclear LOFF phase are briefly discussed. Typeset using REVTEX 1