The Giant Dipole Resonance as a quantitative constraint on the symmetry energy

The possible constraints on the poorly determined symmetry part of the effective nuclear Hamiltonians or effective energy functionals, i.e., the so-called symmetry energy S(rho), are very much under debate. In the present work, we show that the value of the symmetry energy associated with Skyrme functionals, at densities rho around 0.1 fm^{-3}, is strongly correlated with the value of the centroid of the Giant Dipole Resonance (GDR) in spherical nuclei. Consequently, the experimental value of the GDR in, e.g., 208Pb can be used as a constraint on the symmetry energy, leading to 23.3 MeV < S(rho=0.1 fm^{-3}) < 24.9 MeV.Comment: 5 pages, 2 figures, submitte

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

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

Low-lying dipole response: isospin character and collectivity in 68{}^{68}Ni, 132{}^{132}Sn and 208{}^{208}Pb

The isospin character, the collective or single-particle nature, and the sensitivity to the slope of the nuclear symmetry energy of the low-energy isovector dipole response (known as pygmy dipole resonance) are nowadays under debate. In the present work we study, within the fully self-consistent non-relativistic mean field (MF) approach based on Skyrme Hartree-Fock plus Random Phase Approximation (RPA), the measured even-even nuclei ${}^{68}$Ni, ${}^{132}$Sn and ${}^{208}$Pb. To analyze the model dependence in the predictions of the pygmy dipole strength, we employ three different Skyrme parameter sets. We find that both the isoscalar and the isovector dipole responses of all three nuclei show a low-energy peak that increases in magnitude, and is shifted to larger excitation energies, with increasing values of the slope of the symmetry energy at saturation. We highlight the fact that the collectivity associated with the RPA state(s) contributing to this peak is different in the isoscalar and isovector case, or in other words it depends on the external probe. While the response of these RPA states to an isovector operator does not show a clear collective nature, the response to an isoscalar operator is recognizably collective, for {\it all} analyzed nuclei and {\it all} studied interactions.Comment: Submitted to Phys. Rev.

QRPA plus Phonon Coupling Model and the Photoabsorbtion Cross Section for 18,20,22^{18,20,22}O

We have calculated the electric dipole strength distributions in the unstable neutron rich oxygen isotopes $^{18,20,22}$O, in a model which include up to four quasi-particle-type configurations. The model is the extension, to include the effect of the pairing correlations, of a previous model very successful around closed shell nuclei, and it is based on the quasi-particle-phonon coupling. Low-lying dipole strength is found, which exhausts between 5 and 10% of the Thomas-Reiche-Kuhn (TRK) energy-weighted-sum-rule (EWSR) below 15 MeV excitation energy, in rather good agreement with recent experimental data. The role of the phonon coupling is shown to be crucial in order to obtain this result.Comment: 16 pages + 6 figure

Response function beyond mean field of neutron-rich nuclei

The damping of single-particle and collective motion in exotic isotopes is a new topic and its study may shed light on basic problems of nuclear dynamics. For instance, it is known that nuclear structure calculations are not able, as a rule, to account completely for the empirical single-particle damping. In this contribution, we present calculations of the single-particle self-energy in the case of the neutron-rich light nucleus $^{28}$O, by taking proper care of the continuum, and we show that there are important differences with the case of nuclei along the valley of stability.Comment: 9 pages, 4 figures. To appear in: Proceedings of the Topical Conference on Giant Resonances, Varenna, May 11-16, 1997 (Nucl. Phys. A, to be published

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

Constraints on the symmetry energy and on neutron skins from the pygmy resonances in 68Ni and 132Sn

Correlations between the behavior of the nuclear symmetry energy, the neutron skins, and the percentage of energy-weighted sum rule (EWSR) exhausted by the Pygmy Dipole Resonance (PDR) in 68Ni and 132Sn have been investigated by using different Random Phase Approximation (RPA) models for the dipole response, based on a representative set of Skyrme effective forces plus meson-exchange effective Lagrangians. A comparison with the experimental data has allowed us to constrain the value of the derivative of the symmetry energy at saturation. The neutron skin radius is deduced under this constraint.Comment: Accepted for publication in PRC Rapid Comminicatio

The halo of the exotic nucleus 11Li: a single Cooper pair

If neutrons are progressively added to a normal nucleus, the Pauli principle forces them into states of higher momentum. When the core becomes neutron-saturated, the nucleus expels most of the wavefunction of the last neutrons outside to form a halo, which because of its large size can have lower momentum. It is an open question how nature stabilizes such a fragile system and provides the glue needed to bind the halo neutrons to the core. Here we show that this problem is similar to that of the instability of the normal state of an electron system at zero temperature solved by Cooper, solution which is at the basis of BCS theory of superconductivity. By mimicking this approach using, aside from the bare nucleon-nucleon interaction, the long wavelength vibrations of the nucleus $^{11}$Li, the paradigm of halo nuclei, as tailored glues of the least bound neutrons, we are able to obtain a unified and quantitative picture of the observed properties of $^{11}$Li.Comment: 16 pages, 1 b/w figures, 2 colour figure

Outer crust of a cold non-accreting magnetar

The outer crust structure and composition of a cold, non-accreting magnetar is studied. We model the outer crust to be made of fully equilibrated matter where ionized nuclei form a Coulomb crystal embedded in an electron gas. The main effects of the strong magnetic field are those of quantizing the electron motion in Landau levels and of modifying the nuclear single particle levels producing, on average, an increased binding of nucleons in nuclei present in the Coulomb lattice. The effect of an homogeneous and constant magnetic field on nuclear masses has been predicted by using a covariant density functional, in which induced currents and axial deformation due to the presence of a magnetic field that breaks time-reversal symmetry have been included self-consistently in the nucleon and meson equations of motion. Although not yet observed, for $B\gtrsim 10^{16}$G both effects contribute to produce different compositions and to enlarge the range of pressures typically present in common neutron stars. Specifically, in such a regime, the magnetic field effects on nuclei favor the appearance of heavier nuclei at low pressures. As $B$ increases, such heavier nuclei are also preferred up to larger pressures. In the most extreme case, the whole outer crust is almost made of ${}_{40}^{92}$Zr$_{52}$.Comment: Published versio