On the surface nature of the nuclear pairing

Abstract

The surface nature of nuclear pairing is confirmed microscopically. A two-step approach is used in which the full Hilbert space S is split into the model subspace S 0 and the complementary one, S′. The gap equation is solved in the model space in terms of the effective interaction V eff p which obeys the Bethe–Goldstone-type equation in the complementary subspace. The simplest nuclear systems with one-dimensional inhomogeneity are considered, i.e. semi-infinite nuclear matter and the nuclear slab. Numerical solution is carried out for the separable representation of the Paris NN-potential. The equation for the effective pairing interaction is solved directly, without use of any form of local approximation. A version of the local approximation, the local potential approximation, is suggested which works sufficiently well even in the surface region. The effective pairing interaction obtained in our calculations reveals a strong variation in the surface region changing from a strong attraction outside the nuclear matter to almost zero value inside. The effective interaction is found to be dependent on the chemical potential μ. At μ=−8 MeV , it reproduces qualitatively the phenomenological density-dependent effective pairing interaction, with the surface dominance, which was found previously in the self-consistent finite Fermi systems theory and in the new version of the energy functional method by Fayans et al. As | μ| decreases, the surface attraction becomes stronger. The gap equation was solved in semi-infinite matter and in the slab system with the help of the method by Khodel, Khodel and Clark which was suggested recently for nuclear matter. This method extended to non-homogeneous systems turned out to be very efficient in this case. The gap Δ found for both the systems exhibits a strong variation in the surface region with a pronounced maximum near the surface. The surface effect in Δ turned out to be μ-dependent being enhanced at small | μ|.