Triplet Pairing in Neutron Matter

Abstract

The separation method developed earlier by us [Nucl. Phys. {\bf A598} 390 (1996)] to calculate and analyze solutions of the BCS gap equation for ${}^1$S${}_0$ pairing is extended and applied to ${}^3$P${}_2$--${}^3$F${}_2$ pairing in pure neutron matter. The pairing matrix elements are written as a separable part plus a remainder that vanishes when either momentum variable is on the Fermi surface. This decomposition effects a separation of the problem of determining the dependence of the gap components in a spin-angle representation on the magnitude of the momentum (described by a set of functions independent of magnetic quantum number) from the problem of determining the dependence of the gap on angle or magnetic projection. The former problem is solved through a set of nonsingular, quasilinear integral equations, providing inputs for solution of the latter problem through a coupled system of algebraic equations for a set of numerical coefficients. An incisive criterion is given for finding the upper critical density for closure of the triplet gap. The separation method and its development for triplet pairing exploit the existence of a small parameter, given by a gap-amplitude measure divided by the Fermi energy. The revised BCS equations admit analysis revealing universal properties of the full set of solutions for ${}^3$P${}_2$ pairing in the absence of tensor coupling, referring especially to the energy degeneracy and energetic order of these solutions. The angle-average approximation introduced by Baldo et al. is illuminated in terms of the separation-transformed BCS problem and the small parameter expansion...

References in corpus (7)

• The equation of state for nucleon matter and neutron star structure
• 3P_2-3F_2 pairing in neutron matter with modern nucleon-nucleon potentials
• Pairing in low-density Fermi gases
• Universalities of Triplet Pairing in Neutron Matter
• Nucleon-Nucleon Phase Shifts and Pairing in Neutron Matter and Nuclear Matter
• Minimal Relativity and ${}^3{S}_1$-${}^3{D}_1$ Pairing in Symmetric Nuclear Matter
• ^1S_0 pairing correlations in relativistic nuclear matter and the two-nucleon virtual state

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• 3PF2 pairing in high-density neutron matter
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• Phase Transitions in Nucleonic Matter and Neutron-Star Cooling
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• Superfluid Phase Transitions in Dense Neutron Matter
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• Phase structure of neutron ${}^3{P}_2$ superfluids in strong magnetic fields in neutron stars
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• Do Neutron Star Gravitational Waves Carry Superfluid Imprints?
• Microscopic description of axisymmetric vortices in ${}^3{P}_2$ superfluids
• Domain walls in neutron ${}^3{P}_2$ superfluids in neutron stars
• Pairing in pure neutron matter
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• New eigen-mode of spin oscillations in the triplet superfluid condensate in neutron stars
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• From odd-even staggering to the pairing gap in neutron matter
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• Core structures of vortices in Ginzburg-Landau theory for neutron ${}^3{P}_2$ superfluids
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• Symmetry classification of uniform states in spin-2 Bose-Einstein condensates and neutron ${}^3{P}_2$ superfluids