Search

The molecular algebraic model based on three and four alpha clusters is used to describe the inelastic scattering of alpha particles populating low-lying states in $^{12}$C and $^{16}$O. Optical potentials and inelastic formfactors are obtained by folding densities and transition densities obtained within the molecular model. One-step and multi-step processes can be included in the reaction mechanism calculation. In spite of the simplicity of the approach the molecular model with rotations and vibrations provides a reliable description of reactions where $\alpha$-cluster degrees of freedom are involved and good results are obtained for the excitation of several low-lying states. Within the same model we briefly discuss the expected selection rules for the $\alpha$-transfer reactions from $^{12}$C and $^{16}$O., Comment: 8 pages, 8 figures; submitted to EPJA special issue Cluster Structure and Dynamics of Nuclei - A Tribute to Mahir Hussein

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.

Densities and transition densities are computed in an equilateral triangular alpha-cluster model for $^{12}$C, in which each $\alpha$ particle is taken as a gaussian density distribution. The ground-state, the symmetric vibration (Hoyle state) and the asymmetric bend vibration are analyzed in a molecular approach and dissected into their components in a series of harmonic functions, revealing their intrinsic structures. The transition densities in the laboratory frame are then used to construct form-factors and to compute DWBA inelastic cross-sections for the $^{12}$C$(\alpha, \alpha')$ reaction. The comparison with experimental data indicates that the simple geometrical model with rotations and vibrations gives a reliable description of reactions where $\alpha$-cluster degrees of freedom are involved.

Form factors for $\alpha+{^{12}}$C inelastic scattering are obtained within two theoretical ($\alpha+\alpha+\alpha$) approaches: The hyperspherical framework for three identical bosons, and the algebraic cluster model assuming the $D_{3h}$ symmetry of an equilateral triangle subject to rotations and vibrations. Results show a good agreement, with form factors involving the Hoyle state having a slightly larger extension within the hyperspherical approach. Coupled-channel calculations using these form factors are ongoing., Comment: Proceedings of the NSD2019 conference

The algebraic molecular model is used in $^{12}$C to construct densities and transition densities connecting low-lying states of the rotovibrational spectrum, first and foremost those belonging to the rotational bands based on the ground and the Hoyle states. These densities are then used as basic ingredients to calculate, besides electromagnetic transition probabilities, nuclear potentials and formfactors to describe elastic and inelastic $\alpha$+$^{12}$C scattering processes. The calculated densities and transition densities are also compared with those obtained by directly solving the problem of three interacting alpha's within a three-body approach where continuum effects, relevant in particular for the Hoyle state, are properly taken into account., Comment: Contribution to "Symmetries and Order: Algebraic Methods in Many Body Systems", in honor of F. Iachello

Isospin properties of dipole excitations in 74 Ge are investigated using the ({\alpha},{\alpha}'{\gamma}) reaction and compared to ({\gamma},{\gamma}) data. The results indicate that the dipole excitations in the energy region of 6 to 9 MeV adhere to the scenario of the recently found splitting of the region of dipole excitations into two separated parts: one at low energy, being populated by both isoscalar and isovector probes, and the other at high energy, excited only by the electromagnetic probe. Relativistic quasiparticle time blocking approximation (RQTBA) calculations show a reduction in the isoscalar E1 strength with an increase in excitation energy, which is consistent with the measurement., Comment: 7 pages, 7 figures

We present an extension of the random--phase approximation (RPA) where the RPA phonons are used as building blocks to construct the excited states. In our model, that we call double RPA (DRPA), we include up to two RPA phonons. This is an approximate and simplified way, with respect to the full second random--phase approximation (SRPA), to extend the RPA by including two particle--two hole configurations. Some limitations of the standard SRPA model, related to the violation of the stability condition, are not encountered in the DRPA. We also verify in this work that the energy--weighted sum rules are satisfied. The DRPA is applied to low--energy modes and giant resonances in the nucleus $^{16}$O. We show that the model (i) produces a global downwards shift of the energies with respect to the RPA spectra; (ii) provides a shift that is however strongly reduced compared to that generated by the standard SRPA. This model represents an alternative way of correcting for the SRPA anomalous energy shift, compared to a recently developed extension of the SRPA, where a subtraction procedure is applied. The DRPA provides results in good agreeement with the experimental energies, with the exception of those low--lying states that have a dominant two particle--two hole nature. For describing such states, higher--order calculations are needed., Comment: 9 pages, 13 figures

The construction of differential cross sections as a function of excitation energy for systems with a collection of low- and high-lying intrinsic vibrational modes has been attempted in the past. A prescription is proposed that simplifies the implementation of such calculation schemes with a remarkable reduction in computational time., Comment: 6 pages, 3 figures, to be published in Phys. Rev. C

We study the nature of the low-lying dipole strength in neutron-rich nuclei, often associated to the Pygmy Dipole Resonance. The states are described within the Hartree-Fock plus RPA formalism, using different parametrizations of the Skyrme interaction. We show how the information from combined reactions processes involving the Coulomb and different mixtures of isoscalar and isovector nuclear interactions can provide a clue to reveal the characteristic features of these states., Comment: 9 Pages, 8 figures, contribution to International Symposium On Nuclear Physics, December 8-12, 2009,Bhabha Atomic Research Centre, Mumbai, India

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., Comment: Revtex4, to be published in PRC

The interplay of nuclear and Coulomb processes in the inelastic excitation of single- and double-phonon giant resonances in heavy ion collisions is studied within a simple reaction model. Predominance of the Coulomb excitation mechanism on the population of the single-phonon and, on the contrary, predominance of the nuclear excitation for the double-phonon is evidenced. The effect of the spreading of the strength distribution of the giant resonances on the excitation process is analyzed, showing sizeable modifications in the case of Coulomb dominated processes., Comment: Accepten in Nuclear Physics A. 10 eps figures and source file in an uncompressed tar package

In this letter, we show that the non-linearitites of large amplitude motions in atomic nuclei induce giant quadrupole and monopole vibrations. As a consequence, the main source of anharmonicity is the coupling with configurations including one of these two giant resonances on top of any state. Two-phonon energies are often lowered by one or two MeV because of the large matrix elements with such three phonon configurations. These effects are studied in two nuclei, 40Ca and 208Pb., Comment: 4 pages, 4 tables

We calculate the inelastic scattering cross sections to populate one- and two-phonon states in heavy ion collisions with both Coulomb and nuclear excitations. Starting from a microscopic approach based on RPA, we go beyond it in order to treat anharmonicities and non-linear terms in the exciting field. These anharmonicities and non-linearities are shown to have important effects on the cross sections both in the low energy part of the spectrum and in the energy region of the Double Giant Quadrupole Resonance. By properly introducing an optical potential the inelastic cross section is calculated semiclassically by integrating the excitation probability over all impact parameters. A satisfactory agreement with the experimental results is obtained., Comment: 20 pages, 2 figures, revtex, to be published in Phys. Rev. C

The coupling of the high-lying dipole mode to the low-lying quadrupole modes for the case of deformed gamma-unstable nuclei is studied. Results from the geometrical model are compared to those obtained within the dipole boson model. Consistent results are obtained in both models. The dipole boson model is treated within the intrinsic frame, with subsequent projection onto the laboratory frame. As an application, calculations of photonuclear cross-sections in gamma-unstable nuclei are presented., Comment: 23 pages, 6 figures, Nucl. Phys. A (in press)

The effect of deformation on the excitation of multiple giant dipole resonances is studied. Analytical expressions are derived in the framework of the interacting boson model for the energies and E1 properties of giant dipole resonances in spherical and deformed nuclei, and a numerical treatment of transitional nuclei is proposed. Coulomb-excitation cross sections are calculated in $^{238}$U and in the samarium isotopes., Comment: 12 pages, LateX (elsart); accepted for publication on Phys. Lett. B

The excitation of the isovector giant dipole resonance (GDR) by alpha scattering is investigated as a method of probing the neutron excess in exotic nuclei. DWBA calculations are presented for 28O and 70Ca and the interplay of Coulomb and nuclear excitation is discussed. Since the magnitude of the Coulomb excitation amplitude is strongly influenced by the Q-value, the neutron excess plays an important role, as it tends to lower the energy of the GDR. The excitation of the compressional isoscalar dipole state in 70Ca by alpha scattering is also investigated. It is shown that the population of this latter state may be an even more sensitive probe of the neutron skin than the isovector GDR., Comment: 7 pages, 5 figures, Latex2e

We apply boson expansion methods to an extended Lipkin-Meshkov-Glick model including anharmonicities in analogy with previous microscopic calculations. We study the effects of different approximations present in these calculations, among which the truncation of the hamiltonian and of the space, in connection with the study of the properties of two-phonon and three-phonon states. By comparing the approximate results on the spectrum with the exact ones we conclude that the approximations made in the microscopic calculations on two-phonon states are well justified. We find also that a good agreement with the exact results for the three-phonon state is obtained by using a bosonic hamiltonian truncated at the fourth order. This result makes us confident that such approximation can be used in realistic calculations, thus allowing a theoretical study of triple excitations of giant resonances., Comment: 12 pages, 2 figures, Latex with epsfig.sty

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., Comment: 11 pages 8 figures, use elsart.sty and graphics package

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., Comment: 10 pages 7 figures

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., Comment: 33 pages, 9 figures, uses epsfig.sty and espart.sty

An analysis of the real and imaginary part of the polarization potential in terms of the relative contributions of the single collective states for the $ ^{208}Pb + ^{208}Pb $ system has been done. The polarization potential has been calculated within the Feshbach formalism taking into account the collective states calculated with the Wigner function moments method. The contribution of the isoscalar giant dipole resonance states has been estimated being of the order of 10 - 20 \% of the total at relatively low incident energy., Comment: Latex, 16 pages + 4 figures (available upon request: LANZA@CT.INFN.IT)

We discuss the relevance of chaotic scattering in heavy--ion reactions at energies around the Coulomb barrier. A model in two and three dimensions which takes into account rotational degrees of freedom is discussed both classically and quantum-mechanically. The typical chaotic features found in this description of heavy-ion collisions are connected with the anomalous behaviour of several experimental data., Comment: 35 pages in RevTex (version 3.0) plus 27 PostScript figures obtainable by anonymous ftp from VAXFCT.CT.INFN.IT in directory kaos. Fig. 1 upon request to the authors. To be published in the October Focus issue on chaotic scattering of CHAOS