Spatially inhomogeneous condensate in asymmetric nuclear matter - art. no.025801

We study the isospin singlet pairing in asymmetric nuclear matter with nonz ero total momentum of the condensate Cooper pairs. The quasiparticle excita tion spectrum is fourfold split compared to the usual BCS spectrum of the s ymmetric, homogeneous matter. A twofold splitting of the spectrum into sepa rate branches is due to the finite momentum of the condensate, the isospin asymmetry, or the finite quasiparticle lifetime. The coupling of the isospi n singlet and tripler paired states leads to further twofold splitting of e ach of these branches. The gap equation is solved numerically in the isospi n singlet channel in the case where the pairing in the isospin tripler chan nel and the renormalization of the single particle energies are neglected. We find nontrivial solutions with finite total momentum of Cooper pairs. Th e corresponding condensate has a periodic spatial structure which carries a isospin density wave at constant total number of particles. The phase tran sition from the BCS to the inhomogeneous superconducting phase is found to be first order and occurs when the density asymmetry alpha = (rho (n) - rho (p))/(rho (n) + rho (p)) (defined in terms of partial densities of neutron s rho (n) and protons rho (p)) is increased above 0.25. The transition from the inhomogeneous superconducting to the unpaired normal state is second o rder. The maximal values of the critical total momentum (in units of the Fe rmi momentum) and the critical density asymmetry at which condensate disapp ears are P-c. /p(F) = 0.3 and alpha (c) = 0.41 (assuming free single partic le spectrum). The possible spatial forms of the ground state of the inhomog eneous superconducting phase are briefly discussed.