Triplet pairing in neutron matter Original Research Article

The separation method developed earlier by us [Nucl. Phys. A 598 390 (1996)] to calculate and analyze solutions of the BCS gap equation for 1SView the MathML source pairing is extended and applied to 3PView the MathML source–3FView the MathML source 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 (i) 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 (ii) 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 3PView the MathML source 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. Numerical calculations of 3PView the MathML source pairing parameters and gap functions, with and without coupling to the 3FView the MathML source state, are carried out for pairing matrix elements supplied by (vacuum) two-neutron interactions that fit nucleon–nucleon scattering data. It is emphasized that ab initio evaluation of the in-medium particle–particle interaction and associated single-particle energies will be required if a reliable quantitative description of nucleonic superfluids is to be achieved.