Theoretical understanding of the nuclear incompressibility: where do we stand ?

The status of the theoretical research on the compressional modes of finite nuclei and the incompressibility $K_\infty$ of nuclear matter, is reviewed. It is argued that the recent experimental data on the Isoscalar Giant Monopole Resonance (ISGMR) allow extracting the value of $K_\infty$ with an uncertainity of about $\pm$ 12 MeV. Non-relativistic (Skyrme, Gogny) and relativistic mean field models predict for $K_\infty$ values which are significantly different from one another, namely $\approx$ 220-235 and $\approx$ 250-270 MeV respectively. It is shown that the solution of this puzzle requires a better determination of the symmetry energy at, and around, saturation. The role played by the experimental data of the Isoscalar Giant Dipole Resonance (ISGDR) is also discussed.Comment: To appear in the proceedings of the COMEX1 conference (special issue of Nucl. Phys. A). Few changes and corrections compared to the previous version. General conclusion unchange

Microscopic linear response calculations based on the Skyrme functional plus the pairing contribution

A self-consistent Quasiparticle-Random-Phase-Approximation (QRPA) model which employs the canonical Hartree-Fock-Bogoliubov (HFB) basis and an energy-density functional with a Skyrme mean field part and a density-dependent pairing, is used to study the monopole collective excitations of spherical even-even nuclei. The influence of the spurious state on the strength function of the isoscalar monopole excitations is clearly assessed. We compare the effect of different kinds of pairing forces (volume pairing, surface pairing and mixed pairing) on the monopole excitation strength function. The energy of the Isoscalar Giant Monopole Resonance (ISGMR), which is related to the nuclear incompressibility $K_{\infty}$, is calculated for tin isotopes and the results are discussed.Comment: Accepted for publication in Phys. Rev.

New Skyrme energy density functional for a better description of the Gamow-Teller Resonance

We present a new Skyrme energy density functional (EDF) named SAMi [Phys. Rev. C 86 031306(R)]. This interaction has been accurately calibrated to reproduce properties of doubly-magic nuclei and infinite nuclear matter. The novelties introduced in the model and fitting protocol of SAMi are crucial for a better description of the Gamow-Teller Resonance (GTR). Those are, on one side, the two-component spin-orbit potential needed for describing different proton high-angular momentum spin-orbit splitings and, on the other side, the careful description of the empirical hierarchy and positive values found in previous analysis of the spin (G_0) and spin-isospin (G_0^') Landau-Migdal parameters: 0 < G_0 < G_0^', a feature that many of available Skyrme forces fail to reproduce. When employed within the self-consistent Hartree-Fock plus Random Phase Approximation, SAMi produces results on ground and excited state nuclear properties that are in good agreement with experimental findings. This is true not only for the GTR, but also for the Spin Dipole Resonance (SDR) and the Isobaric Analog Resonance (IAR) as well as for the non charge-exchange Isoscalar Giant Monopole (ISGMR) and Isovector Giant Dipole (IVGDR) and Quadrupole Resonances (IVGQR).Comment: Proceedings of the Nuclear Physics Workshop "Marie & Pierre Curie" Kazimierz 2012. To appear in Physica Script

Isovector spin-singlet (T=1, S=0) and isoscalar spin-triplet (T=0, S=1) pairing interactions and spin-isospin response

We review several experimental and theoretical advances that emphasise common aspects of the study of T=1 and T=0 pairing correlations in nuclei. We first discuss several empirical evidences of the special role played by the T=1 pairing interaction. In particular, we show the peculiar features of the nuclear pairing interaction in the low density regime, and possible outcomes such as the BCS-BEC crossover in nuclear matter and, in an analogous way, in loosely bound nuclei. We then move to the competition between T=1 and T=0 pairing correlations. The effect of such competition on the low-lying spectra is studied in N=Z odd-odd nuclei by using a three-body model; it is shown that the inversion of the 0+ and 1+ states near the ground state, and the strong magnetic dipole transitions between them, can be considered as a clear manifestation of strong T=0 pairing correlations in these nuclei. The effect of T=0 pairing correlations is also quite evident if one studies charge-changing transitions. The Gamow-Teller (GT) states in N=Z+2 nuclei are studied here by using self-consistent HFB+QRPA calculations in which the T=0 pairing interaction is taken into account. Strong GT states are found, near the ground state of daughter nuclei; these are compared with available experimental data from charge-exchange reactions, and such comparison can pinpoint the value of the strength of the T=0 interaction. Pair transfer reactions are eventually discussed: while two-neutron transfer has been long proposed as a tool to measure the T=1 superfluidity in the nuclear ground states, the study of deuteron transfer is still in its infancy, despite its potential interest in revealing effects coming from both T=1 and T=0 interactions.Comment: Paper submitted to Physica Scripta for inclusion in the Focus Issue entitled "Focus Issue on Nuclear Structure: Celebrating the 75 Nobel Prize" (by A. Bohr and B.R. Mottelson). arXiv admin note: text overlap with arXiv:nucl-th/0512021 by other author

The nuclear symmetry energy and other isovector observables from the point of view of nuclear structure

In this contribution, we review some works related with the extraction of the symmetry energy parameters from isovector nuclear excitations, like the giant resonances. Then, we move to the general issue of how to assess whether correlations between a parameter of the nuclear equation of state and a nuclear observable are robust or not. To this aim, we introduce the covariance analysis and we discuss some counter-intuitive, yet enlightening, results from it.Comment: To be published in the proceedings of the 2014 Zakopane Conference on Nuclear Physics (Acta Physica Polonica B

Dipole states in stable and unstable nuclei

A nuclear structure model based on linear response theory (i.e., Random Phase Approximation) and which includes pairing correlations and anharmonicities (coupling with collective vibrations), has been implemented in such a way that it can be applied on the same footing to magic as well as open-shell nuclei. As applications, we have chosen to study the dipole excitations both in well-known, stable isotopes like $^{208}$Pb and $^{120}$Sn as well as in the neutron-rich, unstable $^{132}$Sn nucleus, by addressing in the latter case the question about the nature of the low-lying strength. Our results suggest that the model is reliable and predicts in all cases low-lying strength of non collective nature.Comment: 16 pages, 6 figures; submitted for publicatio

Exotic modes of excitation in atomic nuclei far from stability

We review recent studies of the evolution of collective excitations in atomic nuclei far from the valley of $\beta$-stability. Collective degrees of freedom govern essential aspects of nuclear structure, and for several decades the study of collective modes such as rotations and vibrations has played a vital role in our understanding of complex properties of nuclei. The multipole response of unstable nuclei and the possible occurrence of new exotic modes of excitation in weakly-bound nuclear systems, present a rapidly growing field of research, but only few experimental studies of these phenomena have been reported so far. Valuable data on the evolution of the low-energy dipole response in unstable neutron-rich nuclei have been gathered in recent experiments, but the available information is not sufficient to determine the nature of observed excitations. Even in stable nuclei various modes of giant collective oscillations had been predicted by theory years before they were observed, and for that reason it is very important to perform detailed theoretical studies of the evolution of collective modes of excitation in nuclei far from stability. We therefore discuss the modern theoretical tools that have been developed in recent years for the description of collective excitations in weakly-bound nuclei. The review focuses on the applications of these models to studies of the evolution of low-energy dipole modes from stable nuclei to systems near the particle emission threshold, to analyses of various isoscalar modes, those for which data are already available, as well as those that could be observed in future experiments, to a description of charge-exchange modes and their evolution in neutron-rich nuclei, and to studies of the role of exotic low-energy modes in astrophysical processes.Comment: 123 pages, 59 figures, submitted to Reports on Progress in Physic

Calculation of stellar electron-capture cross sections on nuclei based on microscopic Skyrme functionals

A fully self-consistent microscopic framework for evaluation of nuclear weak-interaction rates at finite temperature is introduced, based on Skyrme functionals. The single-nucleon basis and the corresponding thermal occupation factors of the initial nuclear state are determined in the finite-temperature Skyrme Hartree-Fock model, and charge-exchange transitions to excited states are computed using the finite-temperature RPA. Effective interactions are implemented self-consistently: both the finite-temperature single-nucleon Hartree-Fock equations and the matrix equations of RPA are based on the same Skyrme energy density functional. Using a representative set of Skyrme functionals, the model is applied in the calculation of stellar electron-capture cross sections for selected nuclei in the iron mass group and for neutron-rich Ge isotopes.Comment: 31 pages, 13 figures, submitted to Physical Review