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We present recent results on the structure of the one-valence-particle $^{41}$Ca and $^{49}$Ca, and one-valence-hole $^{47}$Ca, nuclei. The isotopes of interest were populated via the cold-neutron capture reactions $^{40}$Ca(n,$\gamma$), $^{48}$Ca(n,$\gamma$) and $^{46}$Ca(n,$\gamma$), respectively. The experiments were performed at the Institut Laue-Langevin, within the EXILL campaign, which employed a large array of HPGe detectors. The $\gamma$ decay and level schemes of these nuclei were investigated by $\gamma$-ray coincidence relationships, leading to the identification of 41, 10, and 6 new transitions in $^{41}$Ca, $^{47}$Ca, and $^{49}$Ca, respectively. Branching ratios and intensities were extracted for the $\gamma$ decay from each state, and $\gamma$-ray angular correlations were performed to establish a number of transition multipolarities and mixing ratios, thus helping in the spin assignment of the states. The experimental findings are discussed along with microscopic, self-consistent beyond-mean-field calculations performed with the Hybrid Configuration Mixing model, based on a Skyrme SkX Hamiltonian. The latter suggests that a fraction of the low-spin states of the $^{41}$Ca, $^{49}$Ca, and $^{47}$Ca nuclei is characterized by the coexistence of either 2p-1h and 1p-2h excitations, or couplings between single-particle/hole degrees of freedom and collective vibrations (phonons) of the doubly-magic "core".

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.

The Energy Density Functional theory is one of the most used methods developed in nuclear structure. It is based on the assumption that the energy of the ground state is a functional only of the density profile. The method is extremely successful within the effective force approach, noticeably the Skyrme or Gogny forces, in reproducing the nuclear binding energies and other bulk properties along the whole mass table. Although the Density Functional is in this case represented formally as the Hartree-Fock mean field of an effective force, the corresponding single-particle states in general do not reproduce the phenomenology particularly well. To overcome this difficulty, a strategy has been developed where the effective force is adjusted to reproduce directly the single particle energies, trying to keep the ground state energy sufficiently well reproduced. An alternative route, that has been developed along several years, for solving this problem is to introduce the mean field fluctuations, as represented by the collective vibrations of the nuclear system, and their influence on the single particle dynamics and structure. This is the basis of the particle-vibration coupling model. In this paper we present a formal theory of the particle-vibration coupling model based on the Green' s function method. The theory extends to realistic effective forces the macroscopic particle-vibration coupling models and the (microscopic) Nuclear Field Theory. It is formalized within the functional derivative approach to many-body theory. An expansion in diagrams is devised for the single particle self-energy and the phonon propagator. Critical aspects of the particle-vibration coupling model are analysed in general. Applications at the lowest order of the expansion are presented and discussed., Comment: J. Phys. G (in press)

The influence of the particle-phonon coupling on pairing correlations in finite systems is studied by solving the Dyson equation including the anomalous (pairing) Green function. We develop a formalism which allows to solve this equation with a minimum of approximations. The resulting expressions are used for the study of quasiparticles in finite nuclei. The solution of the Dyson equation is compared with the exact diagonalization of the particle-phonon coupled Hamiltonian, and a simpler treatment based on Bloch-Horowitz perturbation theory.

▪ Abstract We review the present knowledge of multiphonon giant resonances in nuclei. Theoretical concepts approaching the intrinsic structure and excitation mechanisms of multiphonon states are discussed. The available experimental results are summarized, including a brief description of applied techniques. This review emphasizes electromagnetic excitations of double dipole resonances. Open questions and possible routes toward a solution are addressed.

Shell-model calculations of solar neutrino absorption cross sections for $^{40}$Ar, the proposed component of the ICARUS detector, are presented. It is found that low-lying Gamow-Teller transitions lead to a significant enhancement of the absorption rate over that expected from the Fermi transition between the isobaric analog states, leading to an overall absorption rate of 6.7 SNU. We also note that the pertinent Gamow-Teller transitions in $^{\sss 40}$Ar are experimentally accessible from the $\beta$-decay of the mirror nucleus $^{\sss 40}$Ti. Predictions for the branching ratios to states in $^{\sss 40}$Sc are presented, and the theoretical halflife of 53~ms is found to be in good agreement with the experimental value of $56^{+18}_{-12}$~ms.

The properties of charge-exchange excitations of $^{208}\mathrm{Pb}$ with \ensuremath{\Delta}L=0, i.e., the isobaric analog and Gamow-Teller resonances, are studied within a self-consistent model making use of an effective force of the Skyrme type. The well-known isobaric analog case is used to assess the reliability of the model. The calculated properties of the Gamow-Teller resonance are compared with recent experimental measurements with the aim of better understanding the microscopic structure of this mode.

We study the properties of the isoscalar monopole resonance in 208 Pb, within the framework of a self-consistent model employing a Skyrme force. Including the coupling of the resonance to a set of particle-hole-phonon configurations, we obtain both a good description of the strength function of the mode and a consistent accout of the neutron decay of the resonance.

The quantal RPA corrections to the nuclear partition function are studied for hamiltonians with a quadrupole-quadrupole interaction. In the path-integral formulation, the RPA corrections are obtained as small amplitude fluctuations around the static paths. For a realistic hamiltonian, the quantal corrections are found to effect the level density mainly by lowering the spectral energies.

The dependence on the single-particle states of the pairing matrix elements of the Gogny force and of the bare low-momentum nucleon-nucleon potential ${v}_{\mathrm{low}\text{\ensuremath{-}}k}$---designed so as to reproduce the low-energy observables avoiding the use of a repulsive core---is studied for a typical finite, superfluid nucleus ($^{120}\mathrm{Sn}$). It is found that the matrix elements of ${v}_{\mathrm{low}\text{\ensuremath{-}}k}$ follow closely those of ${v}_{\mathrm{Gogny}}$ on a wide range of energy values around the Fermi energy ${e}_{F}$, those associated with ${v}_{\mathrm{low}\text{\ensuremath{-}}k}$ being less attractive. This result explains the fact that around ${e}_{F}$ the pairing gap ${\ensuremath{\Delta}}_{\mathrm{Gogny}}$ associated with the Gogny interaction (and with a density of single-particle levels corresponding to an effective k mass ${m}_{k}\ensuremath{\approx}0.7 m$) is a factor of about 2 larger than ${\ensuremath{\Delta}}_{\mathrm{low}\text{\ensuremath{-}}k}$, being in agreement with ${\ensuremath{\Delta}}_{\mathrm{exp}}=1.4$ MeV. The exchange of low-lying collective surface vibrations among pairs of nucleons moving in time-reversal states gives rise to an induced pairing interaction ${v}_{\mathrm{ind}}$ peaked at ${e}_{F}$. The interaction $({v}_{\mathrm{low}\text{\ensuremath{-}}k}+{v}_{\mathrm{ind}}) {Z}_{\ensuremath{\omega}}$ arising from the renormalization of the bare nucleon-nucleon potential and of the single-particle motion (\ensuremath{\omega}-mass and quasiparticle strength ${Z}_{\ensuremath{\omega}}$) associated with the particle-vibration coupling mechanism, leads to a value of the pairing gap at the Fermi energy ${\ensuremath{\Delta}}_{\mathrm{ren}}$ that accounts for the experimental value. An important question that remains to be studied quantitatively is to what extent ${\ensuremath{\Delta}}_{\mathrm{Gogny}}$, which depends on average parameters, and ${\ensuremath{\Delta}}_{\mathrm{ren}}$, which explicitly depends on the parameters describing the (low-energy) nuclear structure, display or not a similar isotopic dependence and whether this dependence is borne out by the data.

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 colo@mi.infn.it, accepted for publication in Phys. Rev. C

In a recent Letter [1] an overall agreement with the experimental data for the excitation of the single and double giant dipole resonances in relativistic heavy ion collision in 136Xe and 208Pb nuclei has been reported. We point out that this agreement is achieved by a wrong calculation of the DGDR excitation mechanism. We also argue that the agreement with the data for the widths of resonances is achieved by an unrealistically large value of a model parameter. [1] Nguyen Dinh Dang, Vuong Kim Au, and Akito Arima, Phys. Rev. Lett. 85 (2000) 1827., Comment: Comment for Phys. Rev. Lett

The properties of the giant-dipole resonance (GDR) are calculated as a function of excitation energy, angular momentum, and the compound nucleus particle decay width in the nuclei $^{120}$Sn and $^{208}$Pb, and are compared with recent experimental data. Differences observed in the behavior of the full-width-at-half-maximum of the GDR for $^{120}$Sn and $^{208}$Pb are attributed to the fact that shell corrections in $^{208}$Pb are stronger than in $^{120}$Sn, and favor the spherical shape at low temperatures. The effects shell corrections have on both the free energy and the moments of inertia are discussed in detail. At high temperature, the FWHM in $^{120}$Sn exhibits effects due to the evaporation width of the compound nucleus, while these effects are predicted for $^{208}$Pb., 28 pages in RevTeX plus eight postscript figures. Submitted to Nucl. Phys. A

A systematic study of the full-width-at-half-maximum (FWHM) of the giant-dipole resonance (GDR) as a function of temperature for the nuclei {sup 120}Sn and {sup 208}Pb confirms the overall theoretical picture of the GDR in hot nuclei; in particular, the role played by large-amplitude thermal fluctuations of the nuclear shape. This is confirmed by the good agreement between theory and experiment achieved over a range of temperatures from 1.25--32 MeV and by the differences in the behavior of the FWHM for {sup 120}Sn and {sup 208}Pb, which can be attributed to the presence of strong shell corrections favoring spherical shapes in {sup 208}Pb that are absent in {sup 120}Sn. Finally, the increase in the FWHM over that expected from thermal averaging at temperatures of the order 3.0 MeV is in accordance with the increase expected from the particle evaporation of the compound system.

A microscopic model, entirely based on Skyrme energy density lunctionals, has been developed to study the γ-decay ol giant resonances. In particular, it treats the ground-state decay within the fully self-consistent Random Phase Approximation (RPA) and the decay to low-lying states at the lowest order beyond RPA. This model is applied to 208Pb and the results are compared with experimental data and with previous theoretical results obtained, in the past decades, using phenomenological models.

The energy spectra of α particles emitted in multiple-α decay chains from 59Cu compound nuclei formed in the reaction of 190 MeV 32S on 27Al have been measured. These spectra are sensitive to different regions of the phase space open to the decay of the compound nucleus. A direct test of dynamical effects related to the shape relaxation is obtained by comparing the experimental spectra with results from Monte Carlo statistical model calculations.

The proton escape widths associated with the isobaric analog (IAR) and Gamow-Teller (GTR) resonances of 208Bi are calculated making use of Skyrme forces and complex collective states. In the case of the GTR, the theory is in disagreement with the data by more than an order of magnitude. This discrepancy is even more conspicuous in view of the fact that theory describes correctly the observed decay of the IAR and thus the underlying single-particle spectrum.

The line shape of the plasma resonance in both neutral and charged small sodium clusters is calculated. The overall properties of the multipeak structure observed in the photoabsorption cross section of spherical Na_8 and Na_20 neutral clusters can be understood in terms of Landau damping. Quantal configurations are shown to play an important role. In the case of charged Na_9+ and Na_21^+ clusters a single peak is predicted that carries most of the oscillator strength., This early (1989) jellium matrix-RPA/LDA (TDLDA in Fock space) study: 1) introduced the physics of spectral Landau-damping fragmentation for metal clusters; 2) explained the double line of the neutral Na_20; 3) predicted a 25% strength at high energies (recently seen experimentally); 4) predicted reduced fragmentation for cationic clusters (later seen experimentally)

We calculate, for the first time, the state-dependent pairing gap of a finite nucleus (120Sn) diagonalizing the bare nucleon-nucleon potential (Argonne v14) in a Hartree-Fock basis (with effective k-mass m_k eqult to 0.7 m), within the framework of the BCS approximation including scattering states up to 800 MeV above the Fermi energy to achieve convergence. The resulting gap accounts for about half of the experimental gap. We find that a consistent description of the low-energy nuclear spectrum requires, aside from the bare nucleon-nucleon interaction, not only the dressing of single-particle motion through the coupling to the nuclear surface, to give the right density of levels close to the Fermi energy (and thus an effective mass m* approximately equal to m), but also the renormalization of collective vibrational modes through vertex and self-energy processes, processes which are also found to play an essential role in the pairing channel, leading to a long range, state dependent component of the pairing interaction. The combined effect of the bare nucleon-nucleon potential and of the induced pairing interaction arising from the exchange of low-lying surface vibrations between nucleons moving in time reversal states close to the Fermi energy accounts for the experimental gap., Comment: 5 pages, 4 figures; author list corrected