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

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

Skyrme functional with tensor terms from \textit{ab initio} calculations of neutron-proton drops

A new Skyrme functional devised to account well for standard nuclear properties as well as for spin and spin-isospin properties is presented. The main novelty of this work relies on the introduction of tensor terms guided by \textit{ab initio} relativistic Brueckner-Hartree-Fock calculations of neutron-proton drops. The inclusion of tensor term does not decrease the accuracy in describing bulk properties of nuclei, experimental data of some selected spherical nuclei such as binding energies, charge radii, and spin-orbit splittings can be well fitted. The new functional is applied to the investigation of various collective excitations such as the Giant Monopole Resonance (GMR), the Isovector Giant Dipole Resonance (IVGDR), the Gamow-Teller Resonance (GTR), and the Spin-Dipole Resonance (SDR). The overall description with the new functional is satisfactory and the tensor terms are shown to be important particularly for the improvement of the Spin-Dipole Resonance results. Predictions for the neutron skin thickness based on the non-energy weighted sum rule of the Spin-Dipole Resonance are also given.Comment: 16 pages, 12 figure

Regularization of zero-range effective interactions in finite nuclei

The problem of the divergences which arise in beyond mean-field calculations, when a zero-range effective interaction is employed, has not been much considered so far. Some of us have proposed, quite recently, a scheme to regularize a zero-range Skyrme-type force when it is employed to calculate the total energy, at second-order perturbation theory level, in uniform matter. Although this scheme looked promising, the extension for finite nuclei is not straightforward. We introduce such procedure in the current paper, by proposing a regularization procedure that is similar, in spirit, to the one employed to extract the so-called V_{\rm low-k} from the bare force. Although this has been suggested already by B.G. Carlsson and collaborators, the novelty of our work consists in setting on equal footing uniform matter and finite nuclei; in particular, we show how the interactions that have been regularized in uniform matter behave when they are used in a finite nucleus with the corresponding cutoff. We also address the problem of the validity of the perturbative approach in finite nuclei for the total energy.Comment: Accepted in Phys. Rev. C (https://journals.aps.org/prc/accepted/4207aPfaIc313f02133c78b61b9c320e0a4e115d5

Coulomb exchange functional with generalized gradient approximation for self-consistent Skyrme Hartree-Fock calculations

We perform the self-consistent Skyrme Hartree-Fock calculation with the Coulomb exchange functional in the form of generalized gradient approximation (GGA). It is found that the Perdew-Burke-Ernzerhof GGA (PBE-GGA) Coulomb exchange functional is able to reproduce the exact-Fock energy for the nuclei in a large region of the nuclear chart with one adjustable parameter. The remaining error of Coulomb exchange energy by the GGA with respect to the exact-Fock energy dominantly comes from the functional-driven error.Comment: 22 pages, 6 figures, 3 table

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

Particle-vibration coupling for giant resonances beyond the diagonal approximation

A self-consistent particle-vibration coupling (PVC) model without diagonal approximation is presented. The diagonal approximation, that neglects completely the interaction between the doorway states, has been removed by taking into account the interaction between the two particle-holes inside the doorway states. As applications, isoscalar giant monopole, dipole, and quadrupole resonances in 16O are investigated based on the use of Skyrme functionals. The diagonal approximation is found to clearly impact the strength distribution of the giant quadrupole resonance, and the description of the experimental data is improved without this approximation. The impact of the diagonal approximation is analyzed in detail, especially its effect on the eigenenergies and the induced coupling between neutron and proton particle-hole configurations. The latter is a direct and physically sound effect of the improvement on our formalism. The importance of using self-consistently the full effective interaction in the PVC vertex, and the effect of its renormalization via the subtraction method, are also discussed. For completeness, we also analyze the dependence of our results on the Skyrme parametrization.Comment: 22 pages, 18 figure