Symmetry energy from the nuclear collective motion: constraints from dipole, quadrupole, monopole and spin-dipole resonances

The experimental and theoretical studies of Giant Resonances, or more generally of the nuclear collective vibrations, are a well established domain in which sophisticated techniques have been introduced and firm conclusions reached after an effort of several decades. From it, information on the nuclear equation of state can be extracted, albeit not far from usual nuclear densities. In this contribution, which complements other contributions appearing in the current volume, we survey some of the constraints that have been extracted recently concerning the parameters of the nuclear symmetry energy. Isovector modes, in which neutrons and protons are in opposite phase, are a natural source of information and we illustrate the values of symmetry energy around saturation deduced from isovector dipole and isovector quadrupole states. The isotopic dependence of the isoscalar monopole energy has also been suggested to provide a connection to the symmetry energy: relevant theoretical arguments and experimental results are thoroughly discussed. Finally, we consider the case of the charge-exchange spin-dipole excitations in which the sum rule associated with the total strength gives in principle access to the neutron skin and thus, indirectly, to the symmetry energy.Comment: Updated version, with small corrections based on comments/suggestions from the referee. 12 pages, 9 figures; submitted to EPJA "Special Issue on Symmetry Energy

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

Nuclear single-particle states: dynamical shell model and energy density functional methods

We discuss different approaches to the problem of reproducing the observed features of nuclear single-particle (s.p.) spectra. In particular, we analyze the dominant energy peaks, and the single-particle strength fragmentation, using the example of neutron states in 208Pb. Our main emphasis is the interpretation of that fragmentation as due to particle-vibration coupling (PVC). We compare with recent Energy Density Functional (EDF) approaches, and try to present a critical perspective.Comment: 7 pages. Contribution to the "Focus issue on Open Problems in Nuclear Structure", Journal of Physics

Minimal Model of Stochastic Athermal Systems: Origin of Non-Gaussian Noise

For a wide class of stochastic athermal systems, we derive Langevin-like equations driven by non-Gaussian noise, starting from master equations and developing a new asymptotic expansion. We found an explicit condition whereby the non-Gaussian properties of the athermal noise become dominant for tracer particles associated with both thermal and athermal environments. Furthermore, we derive an inverse formula to infer microscopic properties of the athermal bath from the statistics of the tracer particle. We apply our formulation to a granular motor under viscous friction, and analytically obtain the angular velocity distribution function. Our theory demonstrates that the non-Gaussian Langevin equation is the minimal model of athermal systems.Comment: 10 pages, 5 figure

A new Skyrme interaction with improved spin-isospin properties

A correct determination of the spin-isospin properties of the nuclear effective interaction should lead, among other improvements, to an accurate description of the Gamow-Teller Resonance (GTR). These nuclear excitations impact on a variety of physical processes: from the response in charge-exchange reactions of nuclei naturally present in the Earth, to the description of the stellar nucleosynthesis, and of the pre-supernova explosion core-collapse evolution of massive stars in the Universe. A reliable description of the GTR provides also stringent tests for neutrinoless double-$\beta$ decay calculations. We present a new Skyrme interaction as accurate as previous forces in the description of finite nuclei and of uniform matter properties around saturation density, and that account well for the GTR in ${}^{48}$Ca, ${}^{90}$Zr and ${}^{208}$Pb, the Isobaric Analog Resonance and the Spin Dipole Resonance in ${}^{90}$Zr and ${}^{208}$Pb.Comment: Predictions on the IAR and SDR and comparison with the SGII interaction for the GTRs where adde

Restoration of Isospin Symmetry in Highly Excited Nuclei

Explicit relations between the isospin mixing probability, the spreading width $\Gamma_{IAS}^{\downarrow}$ of the Isobaric Analog State (IAS) and the statistical decay width $\Gamma_c$ of the compound nucleus at finite excitation energy, are derived by using the Feshbach projection formalism. The temperature dependence of the isospin mixing probability is discussed quantitatively for the first time by using the values of $\Gamma_{IAS}^{\downarrow}$ and of $\Gamma_c$ calculated by means of microscopic models. It is shown that the mixing probability remains essentially constant up to a temperature of the order of 1 MeV and then decreases to about 1/4 of its zero temperature value, at higher temperature than $\approx$ 3 MeV, due to the short decay time of the compound system.Comment: 13 pages, 1 figure (PostScript file included). To appear in Phys. Lett.

Quasi-particle random phase approximation with quasi-particle-vibration coupling: application to the Gamow-Teller response of the superfluid nucleus 120^{120}Sn

We propose a self-consistent quasi-particle random phase approximation (QRPA) plus quasi-particle-vibration coupling (QPVC) model with Skyrme interactions to describe the width and the line shape of giant resonances in open-shell nuclei, in which the effect of superfluidity should be taken into account in both the ground state and the excited states. We apply the new model to the Gamow-Teller resonance in the superfluid nucleus $^{120}$Sn, including both the isoscalar spin-triplet and the isovector spin-singlet pairing interactions. The strength distribution in $^{120}$Sn is well reproduced and the underlying microscopic mechanisms, related to QPVC and also to isoscalar pairing, are analyzed in detail.Comment: 32 pages, 11 figures, 4 table