Microscopic Models for the Particle-Vibration Coupling in Exotic Nuclei

Recent results obtained, often in fruitful collaboration with Japanese colleagues in the study of the interplay between single-particle and collective degrees of freedom are reviewed.Comment: 8 pages. Proceedings of the Italy-Japan Meeting On Heavy Ion Physics 200

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.

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

SU(2,1) Dynamics of Multiple Giant Dipole Resonance Coulomb Excitation

We construct a three-dimensional analytically soluble model of the nonlinear effects in Coulomb excitation of multiphonon Giant Dipole Resonances (GDR) based on the SU(2,1) algebra. The full 3-dimensional model predicts further enhancement of the Double GDR (DGDR) cross sections at high bombarding energies. Enhancement factors for DGDR measured in thirteen different processes with various projectiles and targets at different bombarding energies are well reproduced with the same value of the nonlinearity parameter with the exception of the anomalous case of $^{136}$Xe which requires a larger value.Comment: 10 pages, 3 Postscript figures, late

Dipole states in stable and unstable nuclei

A nuclear structure model based on linear response theory (i.e., Random Phase Approximation) and which includes pairing correlations and anharmonicities (coupling with collective vibrations), has been implemented in such a way that it can be applied on the same footing to magic as well as open-shell nuclei. As applications, we have chosen to study the dipole excitations both in well-known, stable isotopes like $^{208}$Pb and $^{120}$Sn as well as in the neutron-rich, unstable $^{132}$Sn nucleus, by addressing in the latter case the question about the nature of the low-lying strength. Our results suggest that the model is reliable and predicts in all cases low-lying strength of non collective nature.Comment: 16 pages, 6 figures; submitted for publicatio

Sum Rules of the Multiple Giant Dipole States

Various sum rules for multiple giant dipole resonance states are derived. For the triple giant dipole resonance states, the energy-weighted sum of the transition strengths requires a model to be related to those of the single and double giant dipole resonance states. It is also shown that the non-diagonal matrix elements of the double commutator between the dipole operator and the nuclear Hamiltonian give useful identities for the excitation energy and transition strength of each excited state. Using those identities, the relationship between width of the single dipole state and those of the multiple ones is qualitatively discussed.Comment: 8 pages, 1 figure, using PTPTeX styl

Self-consistent description of multipole strength: systematic calculations

We use the quasiparticle random phase approximation with a few Skyrme density functionals to calculate strength functions in the Jpi = 0+, 1-, and 2+ channels for even Ca, Ni, and Sn isotopes, from the proton drip line to the neutron drip line. We show where and how low-lying strength begins to appear as N increases. We also exhibit partial energy-weighted sums of the transition strength as functions of N for all nuclei calculated, and transition densities for many of the interesting peaks. We find that low-energy strength increases with N in all multipoles, but with distinctive features in each. The low-lying 0+ strength near the neutron at large N barely involves protons at all, with the strength coming primarily from a single two-quasineutron configuration with very large spatial extent. The low-lying 1- strength is different, with protons contributing to the transition density in the nuclear interior together with neutrons at large radii. The low-lying 2+ transition strength goes largely to more localized states. The three Skyrme interactions we test produce similar results, differing most significantly in their predictions for the location of the neutron drip line, the boundaries of deformed regions, energies of and transition strengths to the lowest 2+ states between closed shells, and isovector energy-weighted sum rules.Comment: 43 pages, 48 figures, 1 tabl

Anharmonic collective excitation in a solvable model

We apply the time-dependent variational principle, the nuclear field theory, and the boson expansion method to the Lipkin model to discuss anharmonicities of collective vibrational excitations. It is shown that all of these approaches lead to the same anharmonicity to leading order in the number of particles. Comparison with the exact solution of the Lipkin model shows that these theories reproduce it quite well.Comment: RevTex, 18 pages, 4 postscript figure

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