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We study the phase diagram of isospin-asymmetrical nuclear matter in thedensity-temperature plane, allowing for four competing phases of nuclearmatter: (i) the unpaired phase, (ii) the translationally and rotationallysymmetric, but isospin-asymmetrical BCS condensate, (iii) the current-carryingLarkin-Ovchinnikov-Fulde-Ferrell phase, and (iv) the heterogeneousphase-separated phase. The phase diagram of nuclear matter composed of thesephases features two tri-critical points in general, as well as crossovers fromthe asymmetrical BCS phase to a BEC of deuterons plus a neutron gas, both forthe homogeneous superfluid phase (at high temperatures) and for theheterogeneous phase (at low temperatures). The BCS-BEC type crossover in thecondensate occurs as the density is reduced. We analyze in detail someintrinsic properties of these phases, including the Cooper-pair wave function,the coherence length, the occupation numbers of majority and minority nucleoniccomponents, and the dispersion relations of quasiparticle excitations about theground state. We show by explicit examples that the physics of the individualphases and the transition from weak to strong coupling can be well understoodby tracing the behavior of these quantities.

BCS-BEC crossovers and unconventional phases in dilute nuclear matter