We analyze the sensitivity of $beta$-decay rates in 78 Ni and 100,132 Sn to a correction term in Skyrme energy-density functionals (EDF) which modifies the radial shape of the nucleon effective mass. This correction is added on top of several Skyrme
parametrizations which are selected from their effective mass properties and predictions about the stability properties of 132 Sn. The impact of the correction on high-energy collective modes is shown to be moderate. From the comparison of the effects induced by the surface-peaked effective mass in the three doubly magic nuclei, it is found that 132 Sn is largely impacted by the correction, while 78 Ni and 100 Sn are only moderately affected. We conclude that $beta$-decay rates in these nuclei can be used as a test of different parts of the nuclear EDF: 78 Ni and 100 Sn are mostly sensitive to the particle-hole interaction through the B(GT) values, while 132 Sn is sensitive to the radial shape of the effective mass. Possible improvements of these different parts could therefore be better constrained in the future.
The effects of the phonon-phonon coupling on the beta-decay rates of neutron-rich nuclei are studied in a microscopic model based on Skyrme-type interactions. The approach uses a finite-rank separable approximation of the Skyrme-type particle-hole (p
-h) residual interaction. Very large two-quasiparticle spaces can thus be treated. A redistribution of the Gamow-Teller (G-T) strength is found due to the tensor correlations and the 2p-2h fragmentation of G-T states. As a result, the beta-decay half-lives are decreased significantly. Using the Skyrme interaction SGII together with a volume-type pairing interaction we illustrate this reduction effect by comparing with available experimental data for the Ni isotopes and neutron-rich N=50 isotones. We give predictions for 76Fe and 80Ni in comparison with the case of the doubly-magic nucleus 78Ni which is an important waiting point in the r-process.
First calculations for deformed nuclei with the Fayans functional are carried out for the uranium and lead isotopic chains. The ground state deformations and deformation energies are compared to Skyrme-Hartree-Fock-Bogolyubov results of HFB-17 and HF
B-27 functionals. For the uranium isotopic chain, the Fayans functional predictions are rather similar properties compared to HFB-17 and HFB-27. However, there is a disagreement for the lead isotopic chain. Both of the Skyrme HFB functionals predict rather strong deformations for the light Pb isotopes which does not agree with the experimental data on charge radii and magnetic moments of the odd Pb isotopes. On the other hand, the Fayans functional predicts a spherical ground state for all of the lead isotopes, in accordance with the data and the known in literature results obtained with the Gogny D1S force and SLy6 functional as well. The deformation energy curves are calculated and compared to four Skyrme functionals, SLy4, Sly6, SkM* and UNEDF1, for $^{238}$U nucleus and several lead deficient Pb isotopes. In the first case, the Fayans functional result is rather close to SkM* and UNEDF1 which, in particularly the latter one, describe the first and second barriers in $^{238}$U rather well. For the light lead isotopes, the Fayans deformation energy curves are qualitatively close to those of the SLy6 functional.
Nuclear beta decay rates are an essential ingredient in simulations of the astrophysical r-process. Most of these rates still rely on theoretical modeling. However, modern radioactive ion-beam facilities have allowed to measure beta half lives of som
e nuclei on or close to the r-process path. These data indicate that r-process half lives are in general shorter than anticipated in the standard theoretical predictions based on the Finite Range Droplet Model (FRDM). The data have also served as important constraints for improved predictions of half lives based on continuum QRPA calculations on top of the energy-density functional theory. Although these calculations are yet limited to spherical nuclei, they include the important r-process waiting point nuclei close to and at the neutron magic numbers $N=50, 82$ and 126. We have studied the impact of these new experimental and theoretical half lives on r-process nucleosynthesis within the two astrophysical sites currently favored for the r process: the neutrino-driven wind from the freshly born neutron star in a supernova explosion and the ejecta of the merger of two neutron stars. We find that the, in general, shorter beta decay rates have several important effects on the dynamics of r-process nucleosynthesis. At first, the matter flow overcomes the waiting point nuclei faster enhancing matter transport to heavier nuclei. Secondly, the shorter half lives result also in a faster consumption of neutrons resulting in important changes of the conditions at freeze-out with consequences for the final r-process abundances. Besides these global effects on the r-process dynamics, the new half lives also lead to some local changes in the abundance distributions.
Single-particle levels of seven magic nuclei are calculated within the Energy Density Functional (EDF) method by Fayans et al. Thr
Dipole magnetic moments of several long isotopic chains are analyzed within the self-consistent Finite Fermi System theory based on the Generalized Energy Density Functional method with exact account for the pairing and quasi-particle continuum. New
data for nuclei far from the beta-stability valley are included in the analysis. For a number of semi-magic isotopes of the tin and lead chains a good description of the data is obtained, with accuracy of 0.1 - 0.2 mu_N. A chain of non-magic isotopes of copper is also analyzed in detail. It is found that the systematic analysis of magnetic moments of this long chain yields rich information on the evolution of the nuclear structure of the Cu isotopes. In particular, it may give a signal of deformation for the ground state of some nuclei in the chain.
