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

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

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

The Spectral Line Shape of Exotic Nuclei

The quadrupole strength function of $^{28}O$ is calculated making use of the SIII interaction, within the framework of continuum-RPA and taking into account collisions among the nucleons (doorway coupling). The centroid of the giant resonance is predicted at $\approx 14$ MeV, that is much below the energy expected for both isoscalar and isovector quadrupole resonances in nuclei along the stability valley. About half of this width arises from the coupling of the resonance to the continuum and about half is due to doorway coupling. This result is similar to that obtained in the study of giant resonances in light, $\beta$-stable nuclei, and shows the lack of basis for the expectation, entertained until now in the literature, that continuum decay was the main damping mechanism of giant resonances in halo nuclei.Comment: LaTeX file, 7 pages, figures not included but available if requested at [email protected], accepted for publication in Phys. Rev.

The fully self-consistent quasiparticle random phase approximation and its application to the isobaric analog resonances

A microscopic model aimed at the description of charge-exchange nuclear excitations along isotopic chains which include open-shell systems, is developed. It consists of quasiparticle random phase approximation (QRPA) made on top of Hartree-Fock-Bardeen-Cooper-Schrieffer (HF-BCS). The calculations are performed by using the Skyrme interaction in the particle-hole channel and a zero-range, density-dependent pairing force in the particle-particle channel. At variance with the (many) versions of QRPA which are available in literature, in our work special emphasis is put on the full self-consistency. Its importance, as well as the role played by the charge-breaking terms of the nuclear Hamiltonian, like the Coulomb interaction, the charge symmetry and charge independence breaking (CSB-CIB) forces and the electromagnetic spin-orbit, are elucidated by means of numerical calculations of the isobaric analog resonances (IAR). The theoretical energies of these states along the chain of the Sn isotopes agree well with the experimental data in the stable isotopes. Predictions for unstable systems are presented.Comment: 15 pages, 6 figure

Towards a Unified Description of Isoscalar Giant Monopole Resonances in a Self-Consistent Quasiparticle-Vibration Coupling Approach

"Why is the EoS for tin so soft?" is a longstanding question, which prevents us from determining the nuclear incompressibility $K_\infty$ accurately. To solve this puzzle, a fully self-consistent quasiparticle random phase approximation (QRPA) plus quasiparticle-vibration coupling (QPVC) approach based on Skyrme-Hartree-Fock-Bogoliubov is developed. We show that the many-body correlations introduced by QPVC, which shift the ISGMR energy in Sn isotopes by about 0.4 MeV more than the energy in $^{208}$Pb, play a crucial role in providing a unified description of the ISGMR in Sn and Pb isotopes. The best description of the experimental strength functions is given by SV-K226 and KDE0, which are characterized by incompressibility values $K_\infty=$ 226 MeV and 229 MeV, respectively, at mean field level

Effects of the Tensor Force on the Multipole Response in Finite Nuclei

We present a thorough analysis of the effects of the tensor interaction on the multipole response of magic nuclei, using the fully self-consistent Random Phase Approximation (RPA) model with Skyrme interactions. We disentangle the modifications to the static mean field induced by the tensor terms, and the specific features of the residual particle-hole (p-h) tensor interaction, for quadrupole (2+), octupole (3-), and also magnetic dipole (1+) responses. It is pointed out that the tensor force has a larger effect on the magnetic dipole states than on the natural parity states 2+ and 3-, especially at the mean field level. Perspectives for a better assessment of the tensor force parameters are eventually discussed

Giant Quadrupole Resonances in 208Pb, the nuclear symmetry energy and the neutron skin thickness

Recent improvements in the experimental determination of properties of the Isovector Giant Quadrupole Resonance (IVGQR), as demonstrated in the A=208 mass region, may be instrumental for characterizing the isovector channel of the effective nuclear interaction. We analyze properties of the IVGQR in 208Pb, using both macroscopic and microscopic approaches. The microscopic method is based on families of non-relativistic and covariant Energy Density Functionals (EDF), characterized by a systematic variation of isoscalar and isovector properties of the corresponding nuclear matter equations of state. The macroscopic approach yields an explicit dependence of the nuclear symmetry energy at some subsaturation density, for instance S(\rho=0.1 fm^{-3}), or the neutron skin thickness \Delta r_{np} of a heavy nucleus, on the excitation energies of isoscalar and isovector GQRs. Using available data it is found that S(\rho=0.1 fm{}^{-3})=23.3 +/- 0.6 MeV. Results obtained with the microscopic framework confirm the correlation of the \Delta r_{np} to the isoscalar and isovector GQR energies, as predicted by the macroscopic model. By exploiting this correlation together with the experimental values for the isoscalar and isovector GQR energies, we estimate \Delta r_{np} = 0.14 +/- 0.03 fm for 208Pb, and the slope parameter of the symmetry energy: L = 37 +/- 18 MeV

Medium polarization isotopic effects on nuclear binding energies

There exist several effective interactions whose parameters are fitted to force mean field predictions to reproduce experimental findings of finite nuclei and calculated properties of infinite nuclear matter. Exploiting this tecnique one can give a good description of nuclear binding energies. We present evidence that further progress can be made by taking into account medium polarization effects associated with surface and pairing vibrations.Comment: 7 pages, 5 figure