The Compression-Mode Giant Resonances and Nuclear Incompressibility

The compression-mode giant resonances, namely the isoscalar giant monopole and isoscalar giant dipole modes, are examples of collective nuclear motion. Their main interest stems from the fact that one hopes to extrapolate from their properties the incompressibility of uniform nuclear matter, which is a key parameter of the nuclear Equation of State (EoS). Our understanding of these issues has undergone two major jumps, one in the late 1970s when the Isoscalar Giant Monopole Resonance (ISGMR) was experimentally identified, and another around the turn of the millennium since when theory has been able to start giving reliable error bars to the incompressibility. However, mainly magic nuclei have been involved in the deduction of the incompressibility from the vibrations of finite nuclei. The present review deals with the developments beyond all this. Experimental techniques have been improved, and new open-shell, and deformed, nuclei have been investigated. The associated changes in our understanding of the problem of the nuclear incompressibility are discussed. New theoretical models, decay measurements, and the search for the evolution of compressional modes in exotic nuclei are also discussed.Comment: Review paper to appear in "Progress in Particle and Nuclear Physics

Effects of phonon-phonon coupling on low-lying states in neutron-rich Sn isotopes

Starting from an effective Skyrme interaction we present a method to take into account the coupling between one- and two-phonon terms in the wave functions of excited states. The approach is a development of a finite rank separable approximation for the quasiparticle RPA calculations proposed in our previous work. The influence of the phonon-phonon coupling on energies and transition probabilities for the low-lying quadrupole and octupole states in the neutron-rich Sn isotopes is studied.Comment: 18 page

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

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

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

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

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

Giant resonances in exotic spherical nuclei within the RPA approach with the Gogny force

Theoretical results for giant resonances in the three doubly magic exotic nuclei $^{78}$Ni, $^{100}$Sn and $^{132}$Sn are obtained from Hartree-Fock (HF) plus Random Phase Approximation (RPA) calculations using the D1S parametrization of the Gogny two-body effective interaction. Special attention is paid to full consistency between the HF field and the RPA particle-hole residual interaction. The results for the exotic nuclei, on average, appear similar to those of stable ones, especially for quadrupole and octupole states. More exotic systems have to be studied in order to confirm such a trend. The low energy of the monopole resonance in $^{78}$Ni suggests that the compression modulus in this neutron rich nucleus is lower than the one of stable ones.Comment: 16 pages, 10 figure

Microscopic study of the isoscalar giant resonances in 208Pb induced by inelastic alpha scattering

The energetic beam of (spin and isospin zero) $\alpha$-particles remains a very efficient probe for the nuclear isoscalar giant resonances. In the present work, a microscopic folding model study of the isoscalar giant resonances in $^{208}$Pb induced by inelastic \aPb scattering at $E_{\rm lab}=240$ and 386 MeV has been performed using the (complex) CDM3Y6 interaction and nuclear transition densities given by both the collective model and Random Phase Approximation (RPA) approach. The fractions of energy weighted sum rule around the main peaks of the isoscalar monopole, dipole and quadrupole giant resonances were probed in the Distorted Wave Born Approximation analysis of inelastic \aPb scattering using the double-folded form factors given by different choices of the nuclear transition densities. The energy distribution of the $E0, E1$ and $E2$ strengths given by the multipole decomposition {analyses} of the \aap data under study are compared with those predicted by the RPA calculation.Comment: Accepted for publication in Nuclear Physics