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Excited-state quantum phase transitions (ESQPTs) strongly influence the spectral properties of collective many-body quantum systems, changing degeneracy patterns in different quantum phases. Level degeneracies, in turn, affect the system's dynamics. We analyze the degeneracy dependence on the size of two-level boson models with a $u(n+1)$ dynamical algebra, where $n$ is the number of collective degrees of freedom. Below the ESQPT critical energy of these models, the energy gap between neighboring levels that belong to different symmetry sectors gets close to zero as the system size increases. We report and explain why this gap goes to zero exponentially for systems with one collective degree of freedom, but algebraically in models with more than one degree of freedom. As a consequence, we show that the infinite-time average of out-of-time-order correlators is an ESQPT order parameter in finite systems with $n=1$, but in systems with $n>1$, this average only works as an order parameter in the mean-field limit.

We characterize excited state quantum phase transitions in the two dimensional limit of the vibron model with the quantum fidelity susceptibility, comparing the obtained results with the information provided by the participation ratio. As an application, we perform fits using a four-body algebraic Hamiltonian to bending vibrational data for several molecular species and, using the optimized eigenvalues and eigenstates, we locate the eigenstate closest to the barrier to linearity and determine the linear or bent character of the different overtones., Comment: 31 pages, 7 figures, and 4 tables

We give an account of the main achievements of the scientific career of Andrea Vitturi so far, that have recently been discussed during the workshop "Theoretical Nuclear Physics in Padova" on the occasion of his retirement from full professor at the University of Padova. He has oftentimes been the driving force behind numerous contributions to nuclear structure and nuclear reactions that are here reviewed: giant resonances, pairing correlations, collective modes, algebraic models, inelastic excitations, electromagnetic response, break-up and transfer reactions, coupled-channel formalism, clustering, subbarrier fusion processes, etc. Among these topics several inspirational works and ideas can be found that we would like to highlight.

We propose a method to identify the order of a Quantum Phase Transition by using area measures of the ground state in phase space. We illustrate our proposal by analyzing the well known example of the Quantum Cusp, and four different paradigmatic boson models: Dicke, Lipkin-Meshkov-Glick, interacting boson model, and vibron model.

We propose a simple schematic model for two-neutron halo nuclei. In this model, the two valence neutrons move in a one-dimensional mean field, interacting with each other via a density-dependent contact interaction. We first investigate the ground state properties, and demonstrate that the dineutron correlation can be realized with this simple model due to the admixture of even- and odd-parity single-particle states. We then solve the time-dependent two-particle Schr\"odinger equation under the influence of a time-dependent one-body external field, in order to discuss the effect of dineutron correlation on nuclear breakup processes. The time evolution of two-particle density shows that the dineutron correlation enhances the total breakup probability, especially for the two-neutron breakup process, in which both the valence neutrons are promoted to continuum scattering states. We find that the interaction between the two particles definitely favours a spatial correlation of the two outgoing particles, which are mainly emitted in the same direction., Comment: 17 pages, 11 figures

This Conference is the fifth of a series of Workshops on High Energy Gamma- ray Experiments, following the Conferences held in Perugia 2003, Bari 2004, Cividale del Friuli 2005, Elba Island 2006. This year the focus was on the use of gamma-ray to study the Dark Matter component of the Universe, the origin and propagation of Cosmic Rays, Extra Large Spatial Dimensions and Tests of Lorentz Invariance., Comment: 328 pages, 7.8Mb, Proceedings of the 5th SCINEGHE Workshop, June 18-20, 2007 http://www.roma2.infn.it/SciNeGHE07/

GAW, acronym for Gamma Air Watch, is a Research and Development experiment in the TeV range, whose main goal is to explore the feasibility of large field of view Imaging Atmospheric Cherenkov Telescopes. GAW is an array of three relatively small telescopes (2.13 m diameter) which differs from the existing and presently planned projects in two main features: the adoption of a refractive optics system as light collector and the use of single photoelectron counting as detector working mode. The optics system allows to achieve a large field of view (24x24 squared degrees) suitable for surveys of large sky regions. The single photoelectron counting mode in comparison with the charge integration mode improves the sensitivity by permitting also the reconstruction of events with a small number of collected Cherenkov photons. GAW, which is a collaboration effort of Research Institutes in Italy, Portugal and Spain, will be erected in the Calar Alto Observatory (Sierra de Los Filabres - Andalucia, Spain), at 2150 m a.s.l.). The first telescope will be settled within Autumn 2007. This paper shows the main characteristics of the experiment and its expected performance., Comment: 4 pages, 2 figures, PDF format, Proceedings of 30th ICRC, International Cosmic Ray Conference 2007, Merida, Yucatan, Mexico, 3-11 July 2007

New experimental data from the scattering of 6He+208Pb at energies around and below the Coulomb barrier are presented. The yield of breakup products coming from projectile fragmentation is dominated by a strong group of $\alpha$ particles. The energy and angular distributions of this group have been analyzed and compared with theoretical calculations. This analysis indicates that the $\alpha$ particles emitted at backward angles in this reaction are mainly due to two-neutron transfer to weakly bound states of the final nucleus., Comment: 20 pages, 5 figures. Nuclear Physics A792 (2007) 2-17

The problem of Coulomb breakup in the scattering of a two-body loosely bound projectile by a heavy target is addressed. A basis of transformed harmonic oscillator (THO) wave functions is used to discretize the projectile continuum and to diagonalize the Hamiltonian of the two-body system. Results for the reaction $^{8}$B+$^{58}$Ni at subcoulomb energies are presented. Comparison of different observables with those obtained with the standard Continuum Discretized Coupled-Channels (CDCC) method shows good agreement between both approaches., Comment: 5 pages, 5 figures, submitted to Phys. Rev. C as Rapid Communication

An algebraic method especially suited to describe strongly anharmonic vibrational spectra in molecules may be an appropriate framework to study vibrational spectra of Na$^+_n$ clusters, where nearly flat potential energy surfaces and the appearance of close lying isomers have been reported. As an illustration we describe the model and apply it to the Be$_4$, H$_3^+$, Be$_3$ and Na$_3^+$ clusters., Comment: 8 pages with 2 tables, invited talk at `Atomic Nuclei & Metallic Clusters: Finite Many-Fermion Systems', Prague, Czech Republic, September 1-5, 1997

We discuss a symmetry-adapted algebraic (or vibron) model for molecular spectroscopy. The model is formulated in terms of tensor operators under the molecular point group. In this way, we have identified interactions that are absent in previous versions of the vibron model, in which the Hamiltonian is expressed in terms of Casimir operators and their products. The inclusion of these new interactions leads to reliable spectroscopic predictions. As an example we study the vibrational excitations of the methane molecule, and compare our results with those obtained in other algebraic models., Comment: 11 pages, invited talk at `Symmetries in Science X', July 13-18, 1997, Bregenz, Austria

An algebraic model in terms of a local harmonic boson realization was recently proposed to study molecular vibrational spectra [Zhong-Qi Ma et al., Phys. Rev. A 53, 2173 (1996)]. Because of the local nature of the bosons the model has to deal with spurious degrees of freedom. An approach to eliminate the latter from both the Hamiltonian and the basis was suggested. We show that this procedure does not remove all spurious components from the Hamiltonian and leads to a restricted set of interactions. We then propose a scheme in which the physical Hamiltonian can be systematically constructed up to any order without the need of imposing conditions on its matrix elements. In addition, we show that this scheme corresponds to the harmonic limit of a symmetry adapted algebraic approach based on U(2) algebras., Comment: 9 pages Revtex, submitted February 1997

We present a symmetry-adapted version of the vibron model and discuss an application to D_{3h} triatomic molecules: H_3^+, Be_3 and Na_3^+., Comment: 3 pages, invited talk at `21st International Colloquium on Group Theoretical Methods in Physics', Goslar, Germany, July 15-20, 1996

We apply a symmetry-adapted algebraic model to the vibrational excitations in D_3h and T_d molecules. A systematic procedure is used to establish the relation between the algebraic and configuration space formulations. In this way we have identified interaction terms that were absent in previous formulations of the vibron model. The inclusion of these new interactions leads to reliable spectroscopic predictions. We illustrate the method for the D_3h triatomic molecules, H_3^+, Be_3 and Na_3, and the T_d molecules, Be_4 and CH_4., Comment: 16 pages with 4 tables, invited talk at `Symmetries in Science IX', August 6-10, 1996

The stretching and bending vibrations of methane are studied in the framework of a symmetry-adapted algebraic model. The model is based on the realization of the one-dimensional Morse potential in terms of a $U(2)$ algebra. For the 44 observed energies we obtain a fit with a r.m.s. deviation of 1.16 cm$^{-1}$ which is an order of magnitude more accurate than previous algebraic calculations., Comment: 5 pages, invited talk at ``21st International Colloquium on Group Theoretical Methods in Physics'', Goslar, Germany, July 15-20, 1996

The stretching and bending vibrations of methane are studied in a local anharmonic model of molecular vibrations. The use of symmetry-adapted operators reduces the eigenvalue problem to block diagonal form. For the 44 observed energies we obtain a fit with a standard deviation of 0.81 cm$^{-1}$ (and a r.m.s. deviation of 1.16 cm$^{-1}$)., Comment: revised and updated version: 13 pages, 3 tables, Revista Mexicana de Fisica, in press

The vibrational excitations of ozone, including both bending and stretching vibrations, are studied in the framework of a symmetry-adapted algebraic approach. This method is based on the isomorphism between the U(2) algebra and the one-dimensional Morse oscillator, and the introduction of point group symmetry techniques. The use of symmetry-adapted interactions, which in the harmonic limit have a clear physical interpretation, makes it possible to systematically include higher order terms and anharmonicities. A least-square fit to all published experimental levels (up to ten quanta) of 16 O_3 and 18 O_3 yields a r.m.s. deviation of 2.5 and 1.0 1/cm, respectively., Comment: 28 pages with 6 tables and 4 figures, revised version, Journal of Molecular Spectroscopy, in press

We introduce the Anharmonic Oscillator Symmetry Model to describe vibrational excitations in molecular systems exhibiting high degree of symmetry. A systematic procedure is proposed to establish the relation between the algebraic and configuration space formulations, leading to new interactions in the algebraic model. This approach incorporates the full power of group theoretical techniques and provides reliable spectroscopic predictions. We illustrate the method for the case of ${\cal D}_{3h}$-triatomic molecules., Comment: 35 pages TEX, submitted to Annals of Physics (N.Y.)

We apply the Anharmonic Oscillator Symmetry Model to the description of vibrational excitations in ${\cal D}_{3h}$ and ${\cal T}_d$ molecules. A systematic procedure can be used to establish the relation between the algebraic and configuration space formulations, by means of which new interactions are found in the algebraic model, leading to reliable spectroscopic predictions. We illustrate the method for the case of ${\cal D}_{3h}$-triatomic molecules and the ${\cal T}_d$ Be-cluster., Comment: 12 pages, invited talk at XIX Oaxtepec Symposium on Nuclear Physics, January 1996

The relation between algebraic and traditional calculations of molecular vibrations is investigated. An explicit connection between interactions in configuration space and the corresponding algebraic interactions is established., Comment: 9 pages, March 1996, submitted