A. Vitturi

Analytically solvable potentials for γ-unstable nuclei

An analytical solution of the collective Bohr equation with a Coulomb-like and a Kratzer-like γ-unstable potential in quadrupole deformation space is presented. Eigenvalues and eigenfunctions are given in closed form and transition rates are calculated for the two cases. The corresponding SO(2, 1) × SO(5) algebraic structure is discussed.

Coulomb- and nuclear-induced break-up of halo nuclei at bombarding energies around the Coulomb barrier

Abstract We investigate the relative importance of the Coulomb and nuclear fields to induce the break-up of neutron-rich nuclei such as 11 Li at energies close to the Coulomb barrier. We assume that the mechanism that leads to the separation is the excitation of a low-lying dipole mode in which the weakly-bound neutron halo performs a collective oscillation against the residual nuclear core. To this end we exploit semiclassical prescriptions that are adequate to calculate not only the average break-up probabilities but also to estimate the size of fluctuations about the quantal expectation values. Possible outcomes are explored as a function of both bombarding energy and impact parameter. Consequences of the couplings for elastic scattering and fusion processes are also discussed.

New analytic solutions of the collective Bohr Hamiltonian for a β-soft, γ-soft axial rotor

New analytic solutions of the quadrupole collective Bohr Hamiltonian are proposed, exploiting an approximate separation of the β and γ variables to describe γ-soft prolate axial rotors. The model potential is a sum of two terms: a β-dependent term taken either with a Coulomb-like or a Kratzer-like form, and a γ-dependent term taken as a harmonic oscillator. In particular, it is possible to give a one-parameter paradigm for a β-soft, γ-soft axial rotor that can be applied, with considerable agreement, to the spectrum of 234U.

Low-lying component in strength distributions of weakly bound neutron-rich nuclei

Abstract We study the multipole response of nuclei for situations in which the neutron content becomes progressively rich. It is observed that the occurrence of weakly bound states towards the neutron drip line gives rise to low-lying concentrations of strength in the continuum which are not of a resonant character. These do not result from a redistribution of the expected high-lying response, but rather amount to a significant source of additional strength. The effect can be accounted for in terms of sum rules that grow — beyond a straightforward increase in the number of particles involved — because of the large spatial extent of the weakly bound orbitals.

Microscopic structure of monopole and quadrupole bosons

Abstract Within the pairing-plus-quadrupole model the wave function of the intrinsic state will be described as a product of basic fermion pairs, which are a linear combination of correlated monopole and quadrupole pairs only. The microscopic structure of these S- and D-pairs, as well as the mixture coefficient between them, are determined by minimizing the total energy within the field approximation. While the mixture between monopole and quadrupole pairs changes drastically to account for the transition from sphericity to static deformation, their internal structure remains fairly constant when varying the number of particles.

Dominance of Nuclear Processes in the Dissociation of 8B

Abstract We study the break-up of 8 B in collisions with heavy-ions. The process is described in terms of inelastic excitations leading to states in the continuum. The effects of the nuclear and Coulomb fields induced by the reaction partner are included on the same footing in the microscopic construction of the transition matrix elements. At variance with previous findings, the contribution of the nuclear component is found to be comparable to — and even larger than — that of the Coulomb one. Because of the weak binding energy of 8 B the nuclear couplings associated with inelastic excitation to low-lying states in the continuum extend to unusually large distances. As a consequence, the interplay between nuclear and Coubomb excitation processes differs significantly from the situation encountered in reactions involving systems close to the stability line. In particular, nuclear excitation is found to remain predominant at energies well below the Coulomb barrier.

Absolute cross sections of two-nucleon transfer reactions induced by heavy ions

Abstract Two-nucleon transfer reactions are calculated for a variety of reactions induced by 14 C and 16 O. The contributions due to the successive and the simultaneous transfer of nucleons and the correction connected with the non-orthogonality of the basis states are included in the calculations. They reproduce the experimental cross sections within a factor of 3. The successive transfer of nucleons alone accounts for the major fraction of the predicted cross section.

Role of high multipole pairs in the description of deformed nuclei

Abstract The intrinsic wave function associated to the ground state rotational band of axially symmetric deformed nuclei is described as a condensate of a basic collective pair which includes components with all possible angular momenta. The microscopic structure of this pair is determined by a variational procedure within the pairing plus quadrupole model. The effect of the truncation to the components with angular momentum Λ =0,2 only, as suggested by the Interacting Boson Model, is tested. It is found that this truncation emphasizes the pairing effects with respect to the shape distortion, with major consequences on different physical observables.

Test of the validity of the SD truncation for deformed systems

Abstract We have tested the basic assumption of the interacting boson model stating that only pairs of particles coupled to angular momentum 0 and 2 are important to the description of low-lying nuclear spectra, even for deformed systems. Variational solutions of the pairing plus quadrupole hamiltonian are obtained for a system of particles moving in a realistic set of single-particle orbitais. Two calculations are carried out based on the field approximation. The first corresponds to the quasiparticle Nilsson model, in which pairs of particles can couple to all values of Λ allowed by the angular momentum selection rule. In the second, pairs of particles are restricted to couple to angular momentum Λ = 0 and Λ = 2. Although most of the predicted values of the different observables are qualitatively similar in the two models, the underlying many-body pictures are very different. Restricting pairs of particles to couple to angular momentum Λ = 0 and Λ = 2 leads to a system in which pairing correlations are as strong as quadrupole correlations. On the other hand, quadrupole correlations are dominant in the Nilsson plus BCS model. Pairs of particles coupled to angular momentum Λ > 2 thus seem to play a decisive role in obtaining the many-body correlations appropriate to strongly deformed systems.

The electron screening puzzle and nuclear clustering

Abstract Accurate measurements of nuclear reactions of astrophysical interest within, or close to, the Gamow peak show evidence of an unexpected effect attributed to the presence of atomic electrons in the target. The experiments need to include an effective “screening” potential to explain the enhancement of the cross sections at the lowest measurable energies. Despite various theoretical studies conducted over the past 20 years and numerous experimental measurements, a theory has not yet been found that can explain the cause of the exceedingly high values of the screening potential needed to explain the data. In this letter we show that instead of an atomic physics solution of the “electron screening puzzle”, the reason for the large screening potential values is in fact due to clusterization effects in nuclear reactions, in particular for reaction involving light nuclei.