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Our current knowledge of the Equation of State of asymmetric nuclear matter around saturation density and of the energy of the Isobaric Analog State in a heavy nucleus such as 208Pb seem to be in contradiction. In Ref. [1], the problem has been highlighted and a solution has been proposed. In the present contribution, we overview the aforementioned work by giving some new details not previously published.

Recent results on the structure of 47Ca will be presented. The nucleus of interest was populated via the cold-neutron capture 46Ca(n,γ) reaction, on a rare 46Ca target, during the EXILL experimental campaign at the nuclear reactor of Institut Laue- Langevin in Grenoble. High-resolution γ-ray spectroscopy, performed with a composite array of HPGe detectors, enabled the identification of new transitions deexciting states between the neutron-capture level and the ground state. Experimental data will be compared with a novel microscopic theoretical model, currently under development, specifically designed to describe the low-lying structure of odd-mass nuclei with one valence particle/hole outside a spherical doubly-magic core, using the Skyrme effective interaction self-consistently.

A completely microscopic beyond mean-field approach has been elaborated to overcome some intrinsic limitations of self-consistent mean-field schemes applied to nuclear systems, such as the incapability to produce some properties of single-particle states (e.g. spectroscopic factors), as well as of collective states (e.g. their damping width and their gamma decay to the ground state or to low lying states). Since commonly used effective interactions are fitted at the mean-field level, one should aim at refitting them including the desired beyond mean-field contributions in the refitting procedure. If zero-range interactions are used, divergences arise. We present some steps towards the refitting of Skyrme interactions, for its application in finite nuclei.

In this work, electron-capture rates on nuclei for stellar conditions are calculated for Ni isotopes, using a self-consistent microscopic model based on the finite-temperature Skyrme Hartree-Fock plus finite-temperature charge-exchange random-phase approximation approach. The results of the calculations show that electron-capture rates obtained either with different Skyrme sets or with different available models can differ by up to a few orders of magnitude.

The effects of the tensor force on the charge-exchange Gamow-Teller (GT) and spin-dipole (SD) states are studied by using the self-consistent Hartree-Fock plus Random Phase Approximation (HF+RPA) approach based on Skyrme zero-range forces. We have found, not surprisingly, that the tensor force has a large effect on the GT strength. In the case of the SD excitations, the tensor force produces a softening of the 1− states, but a hardening of 0− and 2− states: these effects improve the agreement with the experimental findings. We have also studied how to constrain the magnitude of the tensor terms of the Skyrme interaction by using the empirical information on the collective GT and SD excited states in 90Zr and 208Pb.

Experimental and theoretical efforts are being devoted to the study of observables that can shed light on the properties of the nuclear symmetry energy. We present our new results on the excitation energy [1] and polarizability of the Isovector Giant Quadrupole Resonance (IVGQR), which has been the object of new experimental investigation[2]. We also present our theoretical analysis on the parity violating asymmetry at the kinematics of the Lead Radius Experiment (PREx [3]) and highlight its relation with the density dependence of the symmetry energy [4].

A completely microscopic formalism has been developed to treat the observable properties of single-particle states (e.g. energies and spectroscopic factors), as well as of collective states (e.g., their energy centroid, their damping width and their gamma decay to the ground state or to low lying states) beyond mean-field. The phonons are calculated within the fully self–consistent random phase approximation (RPA). The particle-vibration coupling (PVC) is accounted for within the framework of the nuclear field theory (NFT) at the lowest contributing order. All the calculations have been performed using the whole effective Skyrme interaction.

Zero–range effective interactions are commonly used in nuclear physics to describe a many-body system in the mean-field framework. If they are employed in beyond-mean-field models, an artificial ultraviolet divergence is generated by the zero-range of the interaction. We analyze this problem in symmetric nuclear matter with the t0 – t3 Skyrme model. In this case, the second-order energy correction diverges linearly with the momentum cutoff Λ. After that, we extend the work to the case of nuclear matter with the full Skyrme interaction. A strong divergence (∼ Λ5) related to the velocity-dependent terms of the interaction is obtained. Moreover, a global fit can be simultaneously performed for both symmetric and nuclear matter with different neutron-to-proton ratios. These results pave the way for applications to finite nuclei in the framework of beyond mean-field theories.

A new theoretical framework has been established and applied in the calculation of electron capture (EC) and β-decay rates in stellar environment, characterized by high density and temperature. For the description of the nuclear properties, the finite-temperature Hartree Bardeen-Cooper-Schrie_er (FTHBCS) theory based on the relativistic derivative-coupling D3C* interaction is employed. In order to describe the charge-exchange transitions, the finitetemperature proton-neutron quasi-particle random-phase approximation is developed (FT-PNRQRPA) which includes both temperature and pairing correlations. In the FT-HBCS calculations, only the isovector pairing is included, while in the residual interaction of the FT-PNRQRPA both the isovector and isoscalar pairing contribute. In this work, results for EC and β-decay rates are presented in the temperature interval T = 0–1.5 MeV and stellar density ρYe = 107 and 109 g/cm3. Both allowed 0+, 1+ and first-forbidden transitions 0−, 1− and 2− are included in the calculations. It is shown that interplay between pairing correlations and finite-temperature effects can lead to significant changes in rates. It is also important to include de-excitations, i.e. transitions with negative Q-value, that become increasingly significant at higher temperatures especially for p f -shell nuclei.

The Coulomb exchange and correlation energy density functionals for electron systems are applied to nuclearsystems. It is found that the exchange functionals in the generalized gradient approximation provide agreements with the exact-Fock energy with one adjustable parameter within a few dozen keV accuracy, whereas the correlation functionals are not directly applicable to nuclear systems due to the existence of the nuclear force.

A new Skyrme functional has been developed with tensor term guided by ab initio relativistic Brueckner-Hartree-Fock (RBHF) studies on neutron-proton drops. Instead of extracting information on the tensor force from experimental single-particle energy splittings, the RBHF calculations do not contain beyond mean-field effects such as particle-vibration coupling and therefore the information on the tensor force can be obtained without ambiguities. The new functional gives a good description of nuclear ground-state properties aswell as various giant resonances. The description for the evolution of single-particle energy splittings is also improved by the new functional.

In this contribution, we shall describe a formalism that goes beyond the simple time-dependent mean field and is based on particle-vibration coupling (PVC). Such a formalism has been developed with the idea of being self-consistent. It makes use of Skyrme effective forces, and has been used for several applications. We will focus on charge-exchange transitions, namely we will show that our model describes well both the Gamow-Teller giant resonance width, and the low-lying transitions associated with β-decay. In this latter case, including PVC produces a significant improvement of the half-lives obtained at mean-field level, and leads to a good agreement with experimental data. We will end by discussing particle-phonon multiplets in odd nuclei.

The lifetime of the 9/2+ state of 65Cu, at 2534 keV, has been measured by fast timing techniques, in order to establish wether such state arises from a weak coupling between a p3/2 proton and the 3− octupole vibration at 3.56 MeV in the 64Ni core. The 65Cu nucleus was populated by the reaction 7Li + 64Ni at 32 MeV, at the Horia Hulubei National Institute of Physics and Nuclear Engineering (NIPNE) in Bucharest, and its γ-decay was detected by the ROSPHERE array. The measured lifetime coresponds to a B(E3) reduced transition probability to the ground state equal to 8.89 W.u., in agreement with theoretical predictions in the weak coupling limit.