On the surface nature of the nuclear pairing

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 S0 and the complementary one, S′. The gap equation is solved in the model space in terms of the effective interaction Veffp 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|.