Semi-microscopic model of pairing in nuclei

Abstract

A semi-microscopic model for nucleon pairing in nuclei is presented starting from the ab intio BCS gap equation with Argonne v18 force and the self-consistent Energy Density Functional Method basis characterized with the bare nucleon mass. The BCS theory is formulated in terms of the model space S0 with the effective pairing interaction calculated from the first principles in the subsidiary space S0. This effective interaction is supplemented with a small phenomenological addendum containing one phenomenological parameter universal for all medium and heavy atomic nuclei. We consider the latter as a phenomenological way to take into account both the many-body corrections to the BCS theory and the effective mass effects. For protons, the Coulomb interaction is introduced directly. Calculations made for several isotopic and isotonic chains of semi-magic nuclei confirm the validity of the model. The role of the self-consistent basis is stressed.Comment: 22 pages, 9 figures, 3 table

Phonon effects on the double mass differences in magic nuclei

“…The accuracy of such a prescription was estimated in [14] as 0.1-0.2 MeV. Approximately the same accuracy holds for the "developed pairing" approximation in the gap equation, with conservation of the particle number only on average [23], used in all references on the pairing problem cited above.…”

“…To overcome this problem, a two-step renormalization method of solving the gap equation in nuclei was used in Refs. [11,14,15]. The complete Hilbert space of the pairing problem S is split in the model subspace S 0 , which includes the single-particle states with energies less than a separation energy E 0 , and the complementary one, S .…”

“…The modification concerns the spin-orbit and effective tensor terms of the Fayans EDF. This is not very important for the pairing problem [14,15] but there is a noticeable difference between these two EDFs, in favor of DF3-a, in some other problems, e.g., in calculating characteristics of the first 2 + states in semimagic nuclei [21].…”

“…To avoid all these uncertainties, a semimicroscopic model of nuclear pairing was suggested by the Moscow-Catania group [11,14,15]. It starts from the ab initio BCS gap equation with the Argonne NN potential v 18 treated with the two-step method.…”

“…In addition, in Ref. [7] V low-k was found starting from the Argonne potential v 18 , which is different only a little from Argonne v 14 , used in Ref. [3].…”