NEW METHOD IN BARDEEN-COOPER-SCHRIEFFER THEORY AND SUPERFLUIDITY OF NEUTRON MATTER

A new method for solving the equation of superfluidity for the gap Del ta(p) in the spectrum E(p) of single-particle excitations of a superfl uid uniform and isotropic Fermi system is outlined. The initial nonlin ear integral equation with a singular kernel that have a pole on the F ermi surface at Delta=0 is reduced to a system of two equations. Of th ese, one, for the gap-shape function chi(0)(p), is a linear integral e quation, while the other, for the gap amplitude Delta(F) is a nonlinea r algebraic equation. This transformation makes it possible to develop a new iterative procedure for determining Delta(p). In contrast to th e traditional procedure, the new one is reliable, irrespective of the sign of effective interaction between particles; moreover, it converge s extremely fast: even the first iteration of the new procedure ensure s accuracy higher than that resulting from several tens of standard it erations. The new form of the equation for Delta is used to seek bifur cation points-that is, density (rho) values at which there first arise s a nontrivial solution to the problem. It is shown that these points are associated with the poles rho(c) of the function chi(0)(p, rho)I w hereas the behavior of the gap amplitude Delta(F) in the vicinity of t he critical point is determined by the residues at these poles. Here, the density function and the amplitude of the gap follow an exponentia l law, as in the limit of low densities, but with a different exponent . The results of numerical calculations performed for superfluid neutr on matter at various densities and for various potentials of nn intera ction are discussed. It is found that the shape of the gap as specifie d by the function chi(0)(p) is weakly sensitive to the choice of mi-in teraction potentials, provided that the different potentials are fitte d to the same scattering data. The proposed computational scheme is ap plied to pairing with nonzero orbital angular momenta L. Such pairing is realized in dense systems, where the mean interparticle distance is comparable with the range of effective forces. It is shown that, in t he absence of tensor and spin-orbit forces, in which case the orbital angular momentum L and the spin S are conserved quantities, the shape of the gap is independent of the projection m of the orbital angular m omentum L onto the z axis. Under such conditions, the amplitude of the gap is maximal at m=0. Equations are obtained for finding critical po ints in the system with tensor forces. It is demonstrated that, when t ensor forces are taken into account, the phase diagram of neutron matt er becomes richer: there appear new intervals of rho where this matter is superfluid.