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It is shown that under lowering density or temperature a nucleon Fermi superfluid can undergo a phase transition to a new superfluid state corresponding to superposition of states with singlet-triplet (ST) and triplet-singlet (TS) pairing of nucleons (in spin and isospin spaces). Such states arise as a result of branching from one-gap solution of the self-consistent equations, describing ST pairing of nucleons. The density and temperature dependence of the order parameters for new two-gap solutions is determined in the model with Skyrme effective forces.

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