Population of dipole states via isoscalar probes: the splitting of pygmy dipole resonance in 124^{124}Sn}

Inelastic $\alpha$-scattering excitation cross sections are calculated for electric dipole excitations in $^{124}$Sn based on the transition densities obtained from the relativistic quasiparticle time-blocking approximation (RQTBA) in the framework of a semiclassical model. The calculation provides the missing link to directly compare the results from the microscopic RQTBA calculations to recent experimental data measured via the $(\alpha ,\alpha '\gamma)$ reaction, which show a structural splitting of the low-lying E1 strength often denoted as pygmy dipole resonance (PDR). The experimentally observed splitting is reproduced by the cross section calculations, which allows to draw conclusion on the structure of the PDR.Comment: 6 pages, 7 figures; accepted in Phys. Rev C as Rapid Communicatio

TFF (v.4.1): A Mathematica Notebook for the Calculation of One- and Two-Neutron Stripping and Pick-Up Nuclear Reactions

The program TFF calculates stripping single-particle form factors for one-neutron transfer in prior representation with appropriate perturbative treatment of recoil. Coupled equations are then integrated along a semiclassical trajectory to obtain one- and two-neutron transfer amplitudes and probabilities within first- and second-order perturbation theory. Total and differential cross-sections are then calculated by folding with a transmission function (obtained from a phenomenological imaginary absorption potential). The program description, user instructions and examples are discussed

Role of the continuum in reactions with weakly bound systems: A comparative study between the time evolution of a break-up wave function and its coupled-channel approximation

We exploit a model describing the breakup of weakly bound nuclei that can be used as a laboratory for testing different prescriptions that have been advanced in the literature to take into account the nearby presence of continuum states. In the model, we follow the evolution of a single-particle wave function in one dimension, initially bound by a Woods-Saxon type potential and then perturbed by a time- and position-dependent external field. Proper choices of this potential can simulate the effect of the interaction between reaction partners in a nuclear collision. These processes generate inelastic excitation probabilities that-distributed over the bound and continuum states of the system-lead to either a partial or a total fragmentation of the final wave function.Ministerio de Educación y Ciencia (España) y FEDER FIS2008-04189 FPA2006-13807-C02-01Programa Consolider Ingenio CSD2007-0042INFNJunta de Andalucía P07-FQM-02894 FQM16

New analytic solutions of the collective Bohr hamiltonian for a beta-soft, gamma-soft axial rotor

New analytic solutions of the quadrupole collective Bohr hamiltonian are proposed, exploiting an approximate separation of the beta and gamma variables to describe gamma-soft prolate axial rotors. The model potential is a sum of two terms: a beta-dependent term taken either with a Coulomb-like or a Kratzer-like form, and a gamma-dependent term taken as an harmonic oscillator. In particular it is possible to give a one parameter paradigm for a beta-soft, gamma-soft axial rotor that can be applied, with a considerable agreement, to the spectrum of 234U.Comment: (Dipartimento di Fisica ``G.Galilei'' and INFN, via Marzolo 8, I-35131 Padova, Italy) 10 pages, 3 figure

Quantum phase transitions in odd-A nuclei: The effect of the odd particle from spherical to oblate shapes

Quantum shape-phase transitions in odd-nuclei are investigated within the framework of the interacting boson-fermion model (IBFM). We consider the case of a single-j fermion coupled to an even-even boson core that performs a transition from spherical to oblate shapes varying a control parameter in the boson Hamiltonian. The aim of this work is to see the effect of the coupling of the unpaired fermion on the transition, to understand how the coupled single particle modifies the geometric shape of the system and how each of the odd states behaves when the boson core shifts along the transitional path.Scientific and Technical Research Council of Turkey BIDEB-2224AMinisterio de Economía y Competitividad FIS2011-28738- c02-01, CSD2007-00042Junta de Andalucía FQM160, P11-FQM-763

Role of continuum in nuclear direct reactions with one-neutron halo nuclei: a one-dimensional model

We study the evolution of a single-particle wave function during the collision of a one dimensional potential well by another well, which can be regarded as a simple model for the problem of the scattering of a one-neutron halo nucleus by another nucleus. This constitutes an effective three-body problem, whose solution in three dimensions can be extremely complicated, particularly when breakup and rearrangement channels are to be considered. Our one-dimensional model provides the essential three-body nature of this problem, and allows for a much simpler application and assessment of different methods of solution. To simplify further the problem, we assume that the potential well representing the projectile moves according to a predetermined classical trajectory, although the internal motion of the "valence" particle is treated fully quantum-mechanically. This corresponds to a semiclassical approach of the scattering problem. Different approaches are investigated to understand the dynamics involving one-body halo-like systems: the "exact" time-dependent solution of the Schr\"odinger equation is compared to a numerical continuum-discretized coupled-channels (CC) calculation presenting various model cases including different reaction channels. This framework allows us to discuss the reaction mechanism and the role of continuum, whose inclusion in the CC calculation results to be crucial to reproduce the "exact" solution, even when the initial and final states are well bound. We also link each dynamical situation with analogous problem solved in a three dimensional (3D) CC framework, discussing the main challenges experienced in the usual 3D models

Role of continuum in nuclear direct reactions with one-neutron halo nuclei: A one-dimensional model

Background: The problem of the scattering of a one-neutron halo nucleus by another nucleus might involve an extremely complicated solution, particularly when breakup and rearrangement channels are to be considered. Purpose: We construct a simple model to study the evolution of a single-particle wave function during the collision of a one-dimensional potential well by another well. Method: Our one-dimensional model provides the essential three-body nature of this problem, and allows for a much simpler application and assessment of different methods of solution. To simplify further the problem, we assume that the potential well representing the projectile moves according to a predetermined classical trajectory, although the internal motion of the “valence” particle is treated fully quantum mechanically. This corresponds to a semiclassical approach of the scattering problem, applicable in the case of heavy projectile and target. Different approaches are investigated to understand the dynamics involving one-body halo-like systems: the “exact” time-dependent solution of the Schrödinger equation is compared to a numerical continuum-discretized coupled-channels (CC) calculation presenting various model cases including different reaction channels. Results: This framework allows us to discuss the reaction mechanism and the role of the continuum, the inclusion of which in the CC calculation results to be crucial to reproduce the exact solution, even when the initial and final states are well bound. Conclusions: The dynamical situations under study can be linked to analogous problems solved in a threedimensional (3D) CC framework, so the present model provides a simple tool to understand the main challenges experienced in the usual 3D models with the treatment of the continuumUnited Kingdom Science and Technology Facilities Council (STFC) ST/L005743/1

Direct reactions of weakly-bound nuclei within a one dimensional model

TNPI2016 : XV Conference on Theoretical Nuclear Physics in ItalyA line of research has been developed to describe structure and dynamics of weakly-bound systems with one or more valence particles. To simplify the problem we are assuming particles moving in one dimension and, despite the drastic assumption, the model encompasses many characteristics observed in experiments. Within this model we can describe, for example, one- and two-particle breakup and one- and two-particle transfer processes. We concentrate here in models involving weakly-bound nuclei with just one valence particle. Exact solutions obtained by directly solving the time-dependent Schroedinger equation can be compared with the results obtained with different approximation schemes (coupled-channels formalism, continuum discretization, etc). Our goal is to investigate the limitations of the models based on approximations, and in particular to understand the role of continuum in the reaction mechanism

Shape phase transition in odd nuclei in a multi- j model: The UB(6) ⊗ UF(12) case

The phase transition in odd nuclei when the underlying even-even core nuclei experience a transition from spherical to deformed γ-unstable shapes is investigated. The odd particle is assumed to be moving in the three single-particle orbitals j=1/2,3/2, and 5/2. At the critical point in the phase transition, an analytic solution to the corresponding Bohr Hamiltonian, called E(5/12), is worked out. Energy spectra and electromagnetic transitions and moments are presented. The same problem is also attacked in the framework of the interacting boson-fermion model (IBFM). Two different Hamiltonians are used. The first one is constructed ad hoc so as to mimic the situation in the E(5/12) model. The second one leads to the occurrence of the OB(6) ⊗ UF(12) symmetry when the boson part approaches the O(6) condition. The entire transition line is studied with this Hamiltonian and, in particular, the critical point. Both IBFM calculations at the critical point are consistent with the E(5/12) results.Ministerio de Educación y Ciencia (España)FEDER FIS2005-0110