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.

The pygmy dipole strength, the neutron radius of 208{}^{208}Pb and the symmetry energy

The accurate characterization of the nuclear symmetry energy and its density dependence is one of the outstanding open problems in nuclear physics. A promising nuclear observable in order to constrain the density dependence of the symmetry energy at saturation is the neutron skin thickness of medium and heavy nuclei. Recently, a low-energy peak in the isovector dipole response of neutron-rich nuclei has been discovered that may be correlated with the neutron skin thickness. The existence of this correlation is currently under debate due to our limited experimental knowledge on the microscopic structure of such a peak. We present a detailed analysis of Skyrme Hartree-Fock (HF) plus random phase approximation (RPA) predictions for the dipole response in several neutron-rich nuclei and try to elucidate whether models of common use in nuclear physics confirm or dismiss its possible connection with the neutron skin thickness. Finally, we briefly present theoretical results for parity violating electron scattering on ${}^{208}$Pb at the conditions of the PREx experiment and discuss the implications for the neutron skin thickness of ${}^{208}$Pb and the slope of the symmetry energy.Comment: Contribution to the 2nd Iberian Nuclear Astrophysics Meeting on Compact Stars proceeding

RPA calculations with Gaussian expansion method

The Gaussian expansion method (GEM) is extensively applied to the calculations in the random-phase approximation (RPA). We adopt the mass-independent basis-set that has been tested in the mean-field calculations. By comparing the RPA results with those obtained by several other available methods for Ca isotopes, using a density-dependent contact interaction and the Woods-Saxon single-particle states, we confirm that energies, transition strengths and widths of their distribution are described by the GEM bases to good precision, for the $1^-$, $2^+$ and $3^-$ collective states. The GEM is then applied to the self-consistent RPA calculations with the finite-range Gogny D1S interaction. The spurious center-of-mass motion is well separated from the physical states in the $E1$ response, and the energy-weighted sum rules for the isoscalar transitions are fulfilled reasonably well. Properties of low-energy transitions in $^{60}$Ca are argued in some detail.Comment: 30 pages including 12 figure

Continuum particle-vibration coupling method in coordinate-space representation for finite nuclei

In this paper we present a new formalism to implement the nuclear particle-vibration coupling (PVC) model. The key issue is the proper treatment of the continuum that is allowed by the coordinate space representation. Our formalism, based on the use of zero-range interactions such as the Skyrme forces, is microscopic and fully self-consistent. We apply it to the case of neutron single-particle states in Ca-40, Pb-208, and O-24. The first two cases are meant to illustrate the comparison with the usual (i.e., discrete) PVC model. However, we stress that the present approach allows one to calculate properly the effect of PVC on resonant states. We compare our results with those from experiments in which the particle transfer in the continuum region has been attempted. The latter case, namely O-24, is chosen as an example of a weakly-bound system. Such a nucleus, being double magic and not displaying collective low-lying vibrational excitations, is characterized by quite pure neutron single-particle states around the Fermi surface

Pairing collectivity in medium-mass neutron-rich nuclei near drip-line

We look for collective excitations originating from the strong surface pairing in unstable nuclei near the neutron drip-line. The soft dipole excitation is such a pairing mode as it exhibits a character of core-vs-dineutron motion. Possibility of the hydrodynamic phonon mode (the Anderson-Bogoliubov mode) is also discussed.Comment: 9 pages, a talk presented at Collective Motion in Nuclei under Extreme Conditions (COMEX2), June 20-23, 2006, St. Goar, German

Linear response strength functions with iterative Arnoldi diagonalization

We report on an implementation of a new method to calculate RPA strength functions with iterative non-hermitian Arnoldi diagonalization method, which does not explicitly calculate and store the RPA matrix. We discuss the treatment of spurious modes, numerical stability, and how the method scales as the used model space is enlarged. We perform the particle-hole RPA benchmark calculations for double magic nucleus 132Sn and compare the resulting electromagnetic strength functions against those obtained within the standard RPA.Comment: 9 RevTeX pages, 11 figures, submitted to Physical Review

Instabilities in the Nuclear Energy Density Functional

In the field of Energy Density Functionals (EDF) used in nuclear structure and dynamics, one of the unsolved issues is the stability of the functional. Numerical issues aside, some EDFs are unstable with respect to particular perturbations of the nuclear ground-state density. The aim of this contribution is to raise questions about the origin and nature of these instabilities, the techniques used to diagnose and prevent them, and the domain of density functions in which one should expect a nuclear EDF to be stable.Comment: Special issue "Open Problems in Nuclear Structure Theory" of Jour.Phys.G - accepted. 7 pages, 2 figure

Error analysis of nuclear mass fits

We discuss the least-square and linear-regression methods, which are relevant for a reliable determination of good nuclear-mass-model parameter sets and their errors. In this perspective, we define exact and inaccurate models and point out differences in using the standard error analyses for them. As an illustration, we use simple analytic models for nuclear binding energies and study the validity and errors of models' parameters, and uncertainties of its mass predictions. In particular, we show explicitly the influence of mass-number dependent weights on uncertainties of liquid-drop global parameters.Comment: 10 RevTeX pages, 9 figures, submitted to Physical Review