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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".

This volume presents a comprehensive introduction to the study of nuclear structure at finite temperature. By measuring the frequencies of the high-energy photons emitted or absorbed by an atomic nucleus it is possible to visualize the structure of that nucleus. In such experiments it is observed that the atomic nucleus displays resonant behavior, absorbing or emitting photons within a relatively narrow range of frequencies. To study emission processes one measures the y-decay of compound nuclei, and by this means it is possible to probe the structure of the nucleus at finite temperature. This book is divided into two main parts: the study of giant resonances based on the atomic nucleus ground state (zero temperature), and the study of the y-decay of giant resonances from compound (finite temperature) nuclei. As this work is an outgrowth of their lectures to fourth-year students at the University of Milan, the authors have placed special emphasis on the general concepts that form the foundation of the phenomenon of giant resonances. This basic subject matter is supplemented with material taken from work going on at the forefront of research on the structure of hot nuclei. Thus, this volume will serve as an essential reference for both young researchers and experienced practitioners.

In the present volume, several lectures are devoted to the implement- ations of the Density Functional Theory (DFT) in atomic nuclei, either in the non-relativistic or covariant formalism. By restricting ourselves to the non-relativistic case, in this contribution we deal with two aspects of the theory: firstly, its time-dependent extension and the study of the nuclear vibrational excitations, and secondly, the use of effective interactions beyond the mean field framework. Few recent applications, involving both stable and unstable nuclei, are presented.

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.

We have measured the high-energy γ-ray spectra from the fusion reactions 130 MeV16O +98Mo and 240 MeV48Ti +64Ni, populating the114Sn and112Sn compound nuclei at the excitation energy of 110 MeV. The comparison of the spectra shows a ~36% enhancement of the α-ray yield in the Giant Dipole Resonance region (Eγ > 8 MeV) when the 16 O-induced reaction is considered. This enhancement is interpreted as due to entrance channel effects related to theN/Z asymmetry between the target and the projectile.

High-energyγ-rays from the32S+74Ge reaction at 210 MeV bombarding energy were measured in coincidence with light charged particles detected in a large area hodoscope. Experimental results show that energeticγ-rays in coincidence with light charged particles are essentially emitted in the compound nucleus decay. The parameters of the giant dipole resonance (GDR) have been extracted from alineshape analysis of the experimentalγ-ray spectrum. The derived values of mean energyED, widthΓ and strengthS are in good agreement with results from previous experiments on Sn isotopes obtained by using different experimental techniques.

The giant-dipole resonance (GDR) in ${}^{120}\mathrm{Sn}$ and ${}^{208}\mathrm{Pb}$ is studied as a function of excitation energy, angular momentum, and intrinsic width. Theoretical evaluations of the full width at half maximum (FWHM) for the GDR strength function are compared with recent experimental data and are found to be in overall agreement. Differences observed between ${}^{120}\mathrm{Sn}$ and ${}^{208}\mathrm{Pb}$ are attributed to strong shell corrections in ${}^{208}\mathrm{Pb}$ favoring spherical shapes at low temperatures. At high temperature, the FWHM in ${}^{120}\mathrm{Sn}$ exhibits effects due to the evaporation width of the compound nucleus.

Microscopic calculations of the fine structure of single and double giant dipole resonances (GDR) in 136Xe are presented. The single GDR is treated by a wave function that takes into account a coupling of one-phonon with two-phonon configurations while for the double GDR we mix two-phonon and three-phonon configurations.

The emission of high-energyγ-rays in the deexcitation of hot40Ca and39K nuclei formed in heavy-ion fusion reactions at excitation energyEx ∼ 90 MeV has been studied. The high energyγ-rays were measured in coincidence with evaporation residues or light charged particles. Theγ spectrum from the self-conjugated compound nucleus40Ca shows an appreciable yield suppression in the Giant Dipole Resonance (GDR) energy region with respect to the39K, due to isospin selection rules in the dipoleγ-decay. The spectral line shapes of theγ spectra are well reproduced by using a statistical code which treats explicitly the isospin quantum number in evaluating level densities and transmission coefficients. The GDR parameters determined from the present coincidence measurements are in good agreement with the systematic in theA ∼ 40 mass region at lower bombarding energy based on the analysis of inclusive spectra.

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.

This work was supported by the Italian Istituto Nazionale di Fisica Nucleare and partially by the Spanish MICINN (AIC10-D-000568 bilateral action and FPA2008-06419) and Generalitat Valenciana (Grant PROMETEO/2010/101). The work has also been partially supported by the Polish Ministry of Science and Higher Education (Grant No. N N202 309135)

We review some of the recent progress made in the particle-vibration coupling calculations based on microscopic effective interactions. In particular, we focus on the s.p. states and we also briefly discuss the spreading width and decay modes of the giant resonances within the same framework.

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.

The results of a theoretical investigation on the stopping power of a heavy-ion pair in a dense plasma are presented, with particular emphasis on the two-ion correlation effects. The power deposition profile and the range are also computed and compared for different values of beam/plasma parameters.

The reaction [sup 144]Sm([ital p],[ital p][prime]) has been studied with an energy resolution of 4--5 keV using 22 MeV protons. Angular distributions for states up to 4 MeV excitation energies are compared with distorted-wave and coupled-channels calculations including one-step and two-step excitations to study direct and sequential strength distributions. The results are compared with calculations in the nuclear field theory approach where quasiparticle-random-phase-approximation-like states and their mixing with two-phonon (quadrupole and octupole) states is taken into account. Reasonable agreement is obtained for both the positive and the negative parity states.

A formulation of the pairing phase transition is presented which takes into account both thermal and quantal fluctuations, within the framework of the static path approximation with quadratic corrections. The theory is applied to the study of small superconducting particles, where it provides an overall account of the experimental findings. It is shown that the phase transition is well accounted for in the static path approximation, while the quadratic corrections are significant only for very small particles.

Information on nuclear structure at finite temperature is obtained from the physics of the level density, of the rotational damping, and of the giant dipole resonance thermally excited on a compound nucleus at very large excitation energy (and angular momentum). The current understanding in terms of mean-field theories and beyond is reviewed. The coupling to doorway states and the coupling to many-particle-many-hole states in the random-matrix-theory limit are discussed. Emph asis will be on the close relation between the single-particle damping and the damping of collective vibrations. The coherence between the particle and the hole strongly suppresses the vibrational damping, in particular, the temperature dependence.

We discuss calculations of the single-particle states in magic nuclei, performed within the particle-vibration coupling (PVC) approach by using consistently the Skyrme effective interaction. The vibrations are calculated within fully self-consistent random-phase approximation and the whole interaction is also used in the PVC vertex. Our main emphasis is therefore the discussion of our results in comparison with those in which some approximation is made. The perspectives for improving current density functional theory (DFT) calculations are also addressed.

The temperature dependence of the self-energy of a particle is studied in semiinfinite nuclear matter. Based on the finite temperature Green's function Matsubara formalism and applying it to the single particle-states in 208Pb, the calculated results show that the characteristic enhancement of the effective mass at near the Fermi energy disappears at temperature T=3 MeV, and correspondingly, as a consequence the level-density parameter should decrease in agreement with recent empirical data.

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.

Experimental evidence testifying to the existence of a limiting temperature for the observation of gamma decay from the giant dipole resonance in hot nuclei is interpreted as indicating a remarkable constancy with temperature of the width with which the giant resonance couples to the compound nucleus.

The stability of nuclei is a balance between the kinetic energy of the nucleons, the Coulomb repulsion and the nuclear attraction, resulting in the fact that no compound nucleus seems to exist at temperatures above 6–8 MeV. Even at lower temperatures, the competition between single-particle and collective channels through which the compound nucleus cools down is such that the variety of collective modes may not exist at all temperatures. Furthermore, even if the coupling of a collective mode to the compound nucleus is adequate to secure its excitation at a given temperature, the width associated from mechanisms different from compound-nucleus decay may be so large that the mode is overdamped and consequently, not directly observable as a independent mode. In the present paper, information about these temperatures for the case of the giant dipole resonance will be discussed. It will be suggested that the first temperature is controlled by the times it takes the vibration and the neutron motion to couple to the compound nucleus, while the second temperature reflects the relaxation time associated with quadrupole surface deformations.

A model accounting for the time dependence of thermal shape fluctuations in hot nuclei and their effects on the giant-dipole resonance (GDR) is presented. The thermal fluctuations are assumed to be governed by a Kubo-Anderson process, while the GDR is modeled by a classical rotating harmonic oscillator, where the photon cross section is obtained by examining the average power absorbed by a harmonic external driving force. Experimental data for Er and Sn isotopes are compared with theoretical calculations, and evidence for the motional narrowing of the GDR is investigated.

The nuclear level density for solvable model Hamiltonians is calculated as a function of the excitation energy, taking into account both large-amplitude thermal and small-amplitude quantal fluctuations. The formalism, which is applied to simple systems displaying a phase transition (deformed to spherical, superfluid to normal) as a function of the temperature, accurately reproduces the exact solutions. The contribution of thermal fluctuations changes the level density by an order of magnitude. Quantal fluctuations are essential to reproduce the absolute energies of the system and thus to relate the excitation energy to temperature.

Charged particles and high energy \ensuremath{\gamma} rays from the decay of the $^{156}\mathrm{Er}$ compound nucleus populated at ${\mathit{E}}_{\mathit{x}}$=47 MeV excitation energy by the $^{12}\mathrm{C}$${+}^{144}$Sm and $^{64}\mathrm{Ni}$${+}^{92}$Zr reactions have been measured to study possible nonstatistical or entrance channel effects. The experimental spectra and published evaporation residue and neutron data are compared with statistical model calculations. The comparison shows that the statistical model with standard parametrization of level density and yrast lines describes reasonably well the bulk of experimental observables but not the shape of neutron spectra if account is taken of the enhancement factor for E2 transitions. The discrepancies between experimental data and model calculations are discussed.