Abstract:
A limitation common to all extensions of random-phase approximation including only particle-hole configurations is that they violate to some extent the energy weighted sum rules. Considering one such extension, the improved RPA (IRPA), already used to study the electronic properties of metallic clusters, we show how it can be generalized in order to eliminate this drawback. This is achieved by enlarging the configuration space, including also elementary excitations corresponding to the annihilation of a particle (hole) and the creation of another particle (hole) on the correlated ground state. The approach is tested within a solvable 3-level model.

Abstract:
Second RPA calculations with a Skyrme force are performed to describe both high- and low-lying excited states in $^{16}$O. The coupling between 1 particle-1 hole and 2 particle-2 hole as well as that between 2 particle-2 hole configurations among themselves are fully taken into account and the residual interaction is never neglected, not resorting therefore to a generally used approximate scheme where only the first kind of coupling is considered. The issue of the rearrangement terms in the matrix elements beyond standard RPA is addressed and discussed. As a general feature of second RPA results, a several-MeV shift of the strength distribution to lower energies is systematically found with respect to RPA distributions. A much more important fragmentation of the strength is also naturally provided by second RPA due to the huge number of 2 particle-2 hole configurations. A better description of the excitation energies of the low-lying 0$^+$ and 2$^+$ states is obtained with second RPA with respect to RPA.

Abstract:
Working within an exactly solvable 3 level model, we discuss am extension of the Random Phase Approximation (RPA) based on a boson formalism. A boson Hamiltonian is defined via a mapping procedure and its expansion truncated at four-boson terms. RPA-type equations are then constructed and solved iteratively. The new solutions gain in stability with respect to the RPA ones. We perform diagonalizations of the boson Hamiltonian in spaces containing up to four-phonon components. Approximate spectra exhibit an improved quality with increasing the size of these multiphonon spaces. Special attention is addressed to the problem of the anharmonicity of the spectrum.

Abstract:
Low-energy dipole excitations are analyzed for the stable isotopes $^{40}$Ca and $^{48}$Ca in the framework of the Skyrme-second random-phase approximation. The corresponding random-phase approximation calculations provide a negligible strength distribution for both nuclei in the energy region from 5 to 10 MeV. The inclusion and the coupling of 2 particle-2 hole configurations in the second random-phase approximation lead to an appreciable dipole response at low energies for the neutron-rich nucleus $^{48}$Ca. The presence of a neutron skin in the nucleus $^{48}$Ca would suggest the interpretation of the low-lying response in terms of a pygmy excitation. The composition of the excitation modes (content of 1 particle-1 hole and 2 particle-2 hole configurations), their transition densities and their collectivity (number and coherence of the different contributions) are analyzed. This analysis indicates that, in general, these excitations cannot be clearly interpreted in terms of oscillations of the neutron skin against the core with the exception of the peak with the largest $B(E1)$ value, which is located at 9.09 MeV. For this peak the neutron transition density dominates and the neutron and proton transition densities oscillate out of phase in the internal part of the nucleus leading to a strong mixing of isoscalar and isovector components. Therefore, this state shows some features usually associated to pygmy resonances.

Abstract:
Quadrupole transition densities in neutron-rich nuclei in the vicinity of the neutron drip-line are calculated in the framework of the Random Phase Approximation. The continuum is treated by expansion in oscillator functions. We focus on the states which contribute to the usual Giant Quadrupole Resonance, and not on the low-lying strength which is also expected in such nuclei and whose collective character is still under debate. We find that, due to the large neutron skin in these nuclei, the isoscalar and isovector modes are in general strongly mixed. We further show that the transition densities corresponding to the GQR states can be reasonably well described by the collective model in terms of in phase and out of phase oscillations of neutron and proton densities which have different radii.

Abstract:
The evolution of the Dipole Response in nuclei with strong neutron excess is studied in the Hartree-Fock plus Random Phase Approximation with Skyrme forces. We find that the neutron excess increases the fragmentation of the isovector Giant Dipole Resonance, while pushing the centroid of the distribution to lower energies beyond the mass dependence predicted by the collective models. The radial separation of proton and neutron densities associated with a large neutron excess leads to non vanishing isoscalar transition densities to the GDR states, which are therefore predicted to be excited also by isoscalar nuclear probes. The evolution of the isoscalar compression dipole mode as a function of the neutron excess is finally studied. We find that the large neutron excess leads to a strong concentration of the strength associated with the isoscalar dipole operator $\sum_ir^3_iY_{10}$, that mainly originates from uncorrelated excitations of the neutrons of the skin.

Abstract:
We carry out a microscopic analysis of the ground and excited states of the Na_8 metal cluster within the jellium model. We perform a series of configuration interaction calculations on a Hartree-Fock basis and construct eigenstates of the Hamiltonian which carry up to 4-particle 4-hole components. Based on the analysis of the dipole transition strengths, we single out those states which can be interpreted as the collective dipole plasmon and its double excitations. These modes are found to possess a high degree of harmonicity, deviations from the harmonic limit remaining, however, of the order of 10%.

Abstract:
Citrus tristeza virus (CTV) outbreaks were detected in Sicily island, Italy for the first time in 2002. To gain insight into the evolutionary forces driving the emergence and phylogeography of these CTV populations, we determined and analyzed the nucleotide sequences of the p20 gene from 108 CTV isolates collected from 2002 to 2009. Bayesian phylogenetic analysis revealed that mild and severe CTV isolates belonging to five different clades (lineages) were introduced in Sicily in 2002. Phylogeographic analysis showed that four lineages co-circulated in the main citrus growing area located in Eastern Sicily. However, only one lineage (composed of mild isolates) spread to distant areas of Sicily and was detected after 2007. No correlation was found between genetic variation and citrus host, indicating that citrus cultivars did not exert differential selective pressures on the virus. The genetic variation of CTV was not structured according to geographical location or sampling time, likely due to the multiple introduction events and a complex migration pattern with intense co- and re-circulation of different lineages in the same area. The phylogenetic structure, statistical tests of neutrality and comparison of synonymous and nonsynonymous substitution rates suggest that weak negative selection and genetic drift following a rapid expansion may be the main causes of the CTV variability observed today in Sicily. Nonetheless, three adjacent amino acids at the p20 N-terminal region were found to be under positive selection, likely resulting from adaptation events.

Abstract:
We perform microscopic calculations of the inelastic cross sections for the double and triple excitation of giant resonances induced by heavy ion probes within a semicalssical coupled channels formalism. The channels are defined as eigenstates of a bosonic quartic Hamiltonian constructed in terms of collective RPA phonons. Therefore, they are superpositions of several multiphonon states, also with different numbers of phonons and the spectrum is anharmonic. The inclusion of (n+1) phonon configurations affects the states whose main component is a n-phonon one and leads to an appreacible lowering of their energies. We check the effects of such further anharmonicities on the previous published results for the cross section for the double excitation of Giant Resonances. We find that the only effect is a shift of the peaks towards lower energies, the double GR cross section being not modified by the explicity inclusion of the three-phonon channels in the dynamical calculations. The latters give an important contribution to the cross section in the triple GR energy region which however is still smaller than the experimental available data. The inclusion of four phonon configurations in the structure calculations does not modify the results.

Abstract:
Using a microscopic approach beyond RPA to treat anharmonicities, we mix two-phonon states among themselves and with one-phonon states. We also introduce non-linear terms in the external field. These non-linear terms and the anharmonicities are not taken into account in the "standard" multiphonon picture. Within this framework we calculate Coulomb excitation of 208Pb and 40Ca by a 208Pb nucleus at 641 and 1000MeV/A. We show with different examples the importance of the non-linearities and anharmonicities for the excitation cross section. We find an increase of 10 % for 208Pb and 20 % for 40Ca of the excitation cross section corresponding to the energy region of the double giant dipole resonance with respect to the "standard" calculation. We also find important effects in the low energy region. The predicted cross section in the DGDR region is found to be rather close to the experimental observation.