Tripler pairing in neutron matter

The separation method developed earlier by us [Nucl. Phys. A 598 390 (1996) ] to calculate and analyze solutions of the BCS gap equation for S-1(0) pai ring is extended and applied to (3)p(2)-(3) F-2 pairing in purl neutron mat ter. The pairing matrix elements are written as a separable part plus a rem ainder 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 m agnetic quantum number) from (ii) the problem of determining the dependence of the gap on angle or magnetic projection. The former problem is solved t hrough a set of nonsingular, quasilinear integral equations, providing inpu ts for solution of the latter problem through a coupled system of algebraic equations for a set of numerical coefficients. An incisive criterion is gi ven for finding the upper critical density for closure of the triplet gap. The separation method and its development for triplet pairing exploit the e xistence of a small parameter, given by a gap-amplitude measure divided by the Fermi energy. The revised BCS equations admit analysis revealing univer sal properties of the full set of solutions for P-3(2) pairing in the absen ce of tensor coupling, referring especially to the energy degeneracy and en ergetic order of these solutions. The angle-average approximation introduce d by Baldo et al. is illuminated in terms of the separation-transformed BCS problem and the small parameter expansion. Numerical calculations of P-3(2 ) pairing parameters and gap functions, with and without coupling to the F- 3(2) 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 int eraction and associated single-particle energies will be required if a reli able quantitative description of nucleonic superfluids is to be achieved, ( C) 2001 Elsevier Science B.V. All rights reserved.