Self-consistent Theory of Finite Fermi Systems vs Skyrme-Hartree-Fock method. Spherical nuclei

Recent results of the Fayans energy density functional (EDF) for spherical nuclei are reviewed. A comparison is made with predictions of several Skyrme EDFs. The charge radii and characteristics of the first 2^+ excitations in semi-magic nuclei are briefly discussed. The single-particle spectra of doubly magic nuclei are considered in more detail. The phonon-particle coupling effects are analyzed including the so-called tadpole term.Comment: 6 pages, 7 figures, to appear in the proceedings of the International Conference "Nuclear Structure and Relaited Topics", July 14 - July 18, 2015, Dubna, Russia. arXiv admin note: text overlap with arXiv:1401.131

Particle-phonon coupling effects within theory of finite Fermi systems

Recent results of the study of the particle-phonon coupling (PC) effects in odd magic and semi-magic nuclei within the self-consistent theory of finite Fermi systems are reviewed. In addition to the usual pole diagrams, the non-pole ones are considered. Their contributions are often of a crucial importance. PC corrections to the single-particle energies for $^{40}$Ca and $^{208}$Pb are presented. The quadrupole moments of odd In and Sb isotopes, the odd-proton neighbors of even Sn isotopes, are presented also with accounting for the PC corrections. At last, recently announced problem of extremely high values charge radii of heavy Ca isotopes is solved in terms of a consistent consideration of the PC effects. In all the cases, rather good description of the data is obtained.Comment: 10 pages, 6 figures, to appear in the proceedings of the Fifth Conference on NUCLEI and MESOSCOPIC Physics (NMP17), March 6-10, 2017; East Lansing, Michigan, US

An ab initio theory of double odd-even mass differences in nuclei

Two aspects of the problem of evaluating double odd-even mass differences D_2 in semi-magic nuclei are studied related to existence of two components with different properties, a superfluid nuclear subsystem and a non-superfluid one. For the superfluid subsystem, the difference D_2 is approximately equal to 2\Delta, the gap \Delta being the solution of the gap equation. For the non-superfluid subsystem, D_2 is found by solving the equation for two-particle Green function for normal systems. Both equations under consideration contain the same effective pairing interaction. For the latter, the semi-microscopic model is used in which the main term calculated from the first principles is supplemented with a small phenomenological addendum containing one phenomenological parameter supposed to be universal for all medium and heavy atomic nuclei.Comment: 7 pages, 10 figures, Report at Nuclear Structure and Related Topics, Dubna, Russia, July 2 - July 7, 201

Magnetic moments of odd-odd spherical nuclei

Magnetic moments of more than one hundred odd-odd spherical nuclei in ground and excited states are calculated within the self-consistent TFFS based on the EDF method by Fayans {\it et al}. We limit ourselves to nuclei with a neutron and a proton particle (hole) added to the magic or semimagic core. A simple model of no interaction between the odd nucleons is used. In most the cases we analyzed, a good agreement with the experimental data is obtained. Several cases are considered where this simple model does not work and it is necessary to go beyond. The unknown values of magnetic moments of many unstable odd and odd-odd nuclei are predicted including sixty values for excited odd-odd nuclei.Comment: 10 page

Self-consistent account for phonon induced corrections to quadrupole moments of odd nuclei. Pole and non-pole diagrams

Recent results of the description of quadrupole moments of odd semi-magic nuclei are briefly reviewed. They are based on the self-consistent theory of finite Fermi systems with account for the phonon-particle coupling (PC) effects. The self-consistent model for describing the PC effects was developed previously for magnetic moments. Account for the non-pole diagrams is an important ingredient of this model. In addition to previously reported results for the odd In and Sb isotopes, which are the proton-odd neighbors of even tin nuclei, we present new results for odd Bi isotopes, the odd neighbors of even lead isotopes. In general, account for the PC corrections makes the agreement with the experimental data significantly better.Comment: 8 pages, 4 figures. Presented at ICNFP1

Phonon coupling effects in magnetic moments of magic and semi-magic nuclei

Phonon coupling (PC) corrections to magnetic moments of odd neighbors of magic and semi-magic nuclei are analyzed within the self-consistent Theory of Finite Fermi Systems (TFFS) based on the Energy Density Functional by Fayans et al. The perturbation theory in g_L^2 is used where g_L is the phonon-particle coupling vertex. A model is developed with separating non-regular PC contributions, the rest is supposed to be regular and included into the standard TFFS parameters. An ansatz is proposed to take into account the so-called tadpole term which ensures the total angular momentum conservation with g_L^2 accuracy. An approximate method is suggested to take into account higher order terms in g_L^2. Calculations are carried out for four odd-proton chains, the odd Tl, Bi, In and Sb ones. Different PC corrections strongly cancel each other. In the result, the total PC correction to the magnetic moment in magic nuclei is, as a rule, negligible. In non-magic nuclei considered it is noticeable and, with only one exception, negative. On average it is of the order of -(0.1 - 0.5) \mu_N and improves the agreement of the theory with the data. Simultaneously we calculated the gyromagnetic ratio g_L^{ph} of all low-lying phonons in 208Pb. For the 3^-_1 state it is rather close to the Bohr-Mottelson model prediction whereas for other L-phonons, two 5^- and six positive parity states, the difference from the Bohr-Mottelson values is significant.Comment: 21 pages, 24 figure