In the framework of the generalized non-relativistic Fermi-liquid approach we study phase transitions in spatially uniform dense pure neutron matter from normal to superfluid states with a spin-triplet p-wave pairing (similar to anisotropic superfluid phases 3He-A1 and 3He-A2) in a steady and homogeneous strong magnetic field H (but , where is the magnetic dipole moment of a neutron, is the cutoff energy and is the Fermi energy in neutron matter with density of particles n). The previously derived general formulas (valid for the arbitrary parametrization of the effective Skyrme interaction in neutron matter) for phase transition (PT) temperatures (which are nonlinear functions of the density n and linear functions of the magnetic field H) are specified here for new generalized BSk20 and BSk21 parameterizations of the Skyrme forces (with additional terms dependent on the density n) in the interval , where is the nuclear density. Our main results are mathematical expressions and figures for PT temperatures in the absence of magnetic field, and (at ), and in strong magnetic fields (which may approach to or even more as in the liquid outer core of magnetars —strongly magnetized neutron stars). These are realistic non-monotone functions with a bell-shaped density profile.
General expressions are obtained in explicit form for the anomalous and normal distribution functions of quasiparticles in nonunitary phases of a superfluid paramagnetic Fermi liquid consisting of electrically neutral fermions with triplet pairing (the pairs have spin s=1 and an arbitrary odd value of the orbital angular momentum l) in a uniform static magnetic field. A generalized Fermi-liquid approach is used which takes into account the exchange Fermi-liquid interaction but does not specify the form of the energy functional of the superfluid Fermi liquid. The results are valid at any temperature in the interval 0⩽T⩽Tc, where Tc is the temperature of the phase transition from the normal to the superfluid state. When an explicit form of the energy functional is specified, the general formulas for the distribution function can be used to describe the various nonunitary phases of a superfluid Fermi liquid of the He3 type in a high magnetic field. In particular, for He3-A1, He3-A2, and the nonunitary two-dimensional phase of He3 in a high magnetic field at 0⩽T⩽Tc, an energy functional quadratic in the distribution function is used to find a system of coupled equations for the order parameter and the effective magnetic field and to obtain an expression is obtained for the nonlinear magnetic susceptibility.
Abstract:Within a generalized non-relativistic Fermi-liquid approach we have found general analytical formulae for phase-transition temperatures T 1 ( H) and T 2 ( H) (which are nonlinear functions of density, , and linear of magnetic field, H) for phase transitions in spatially uniform, dense, pure neutron matter from normal to superfluid states with spin-triplet p-wave pairing (similar to anisotropic superfluid phases 3 He − A 1 and 3 He − A 2 ) in steady and homogeneous sufficiently strong magnetic field (but |µ |H E < ε F ( ), where µ is the magnetic dipole moment of a neutron, E is the cutoff energy and ε F ( ) is the Fermi energy in neutron matter). General formulae for T 1 2 ( H) are valid for arbitrary parameterization of the effective Skyrme forces in neutron matter. We have used for definiteness the so-called SLy2, Gs and RATP parameterizations of the Skyrme forces with different exponents in their power dependence on density (at sub-and supranuclear densities) from the interval 0 7 0 < (S ) < 2 0 , where 0 = 0 17 fm −3 is the nuclear density and (S ) is the the critical density of the ferromagnetic instability in superfluid neutron matter. These phase transitions might exist in the liquid outer core of magnetized neutron stars.
PACS
The nonlinear integral equations for the order parameter and effective magnetic field in pure neutron liquid matter of high densities (which may be of the same order or exceed the symmetric nuclear matter saturation density n0) with spin-triplet p-wave pairing of 3 He-A1,2 type in a strong magnetic field (existing inside the fluid core of neutron stars) were derived using the Skyrme interaction between neutrons. These equations (obtained within the generalized nonrelativistic Fermi-liquid approach) are valid in the temperature interval 0 ≤ T ≤ Tc (Tc is the normal-superfluid transition temperature). For arbitrary parametrization of the Skyrme interaction the approximate analytical solutions of these equations were found for phase transition (PT) temperatures Tc1,2(n, H) and for their splitting as functions linear on the magnetic field H and nonlinear on the neutron matter density n. The result for the splitting of the PT temperatures is represented in graphical form in the particular case with the SkP interaction (for 0.9n0 n 1.4n0).
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.