About splitting of energy gap in superfluid neutron matter with spin-triplet anisotropic p-wave pairing at nuclear and supranuclear densities in superstrong magnetic fields

The nonlinear integral equations for the components of the order parameter of dense superfluid neutron matter (SNM) with spin-triplet anisotropic p-wave pairing (similar to pairing in ³He−A₂ in magnetic fields, i.e., with spin S = 1 and orbital moment L = 1 of anisotropic Cooper pairs of neutrons) in superstrong magnetic fields (exceeding the 10¹⁷ G) are solved analytically in the limit of zero temperature. These solutions are derived for the family of so-called BSk-type generalized parameterizations of the effective Skyrme forces (with three terms dependent on density n) in neutron matter. The obtained general solutions for splitting of energy gap in SNM in superstrong magnetic fields are specified for the generalized BSk21 parameterization of the effective Skyrme forces at nuclear density n₀ = 0.17 fm^–3 and at two supranuclear densities n = 1.25n₀ and n = 1.5n₀ for magnetic fields H = Z⋅10¹⁷ G, where 1≤ Z ≤ 10. The main results are the splitting of energy gap and its asymmetry which increase nonlinearly with growing both superstrong magnetic field H and supranuclear density n > n₀. Such effects in SNM might exist in liquid outer core (at densities $n > ∼⁡ n 0$⁠) in strongly magnetized neutron stars known as “magnetars”.