Describing resonances in a discrete basis

The problem of describing resonances when the continuum is represented by a discrete set of normalizable states is addressed. In particular, here the description of resonances in a transformed harmonic oscillator basis is presented. A method to disentangle the resonances from the nonresonant continuum is proposed. The Ginocchio potential is used to model a case in which resonances appear in the continuum and a reference case in which only nonresonant continuum appears.Ministerio de Ciencia y Tecnología FPA2002-04181-C04-04 BFM2002-0331

Comment on “Pairing interaction and Galilei invariance”

A recent article by Dussel, Sofia, and Tonina studies the relation between Galilei invariance and dipole energy weighted sum rule (EWSR). The authors find that the pairing interaction, which is neither Galilei nor Lorentz invariant, produces big changes in the EWSR and in effective masses of the nucleons. They argue that these effects of the pairing force could be realistic. In this Comment we stress the validity of Galilei invariance to a very good approximation in this context of low-energy nuclear physics and show that the effective masses and the observed change in the EWSR for the electric dipole operator relative to its classical value are compatible with this symmetry.Dirección General de Investigación Científica y Técnica PB95-0533European Commission CI1*-CT94-007

Four-body continuum-discretized coupled-channels calculations: Application to 6He+64Zn at 13.6 MeV

The recently developed four-body continuum-discretized coupled-channels (CDCC) method, making use of the binning procedure [1], is applied to the reaction 6He+64Zn at 13.6 MeV (around the Coulomb barrier). Excellent agreement with available elastic data [2] is found.Dirección General de Investigación Científica y Técnica FIS 2008-04189, FPA 2006- 13807-C02-01U.S. Department of Energy DE-AC52-07NA27344U.K. STFC EP/D00362

Reactions induced by 9Be in a four-body continuum-discretized coupled-channels framework

We investigate the elastic scattering of 9Be on 208Pb at beam energies above (50MeV) and below (40MeV) the Coulomb barrier. The reaction is described within a four-body framework using the Continuum-Discretized Coupled-Channels (CDCC) method. The 9Be projectile states are generated using the analytical Transformed Harmonic Oscillator (THO) basis in hyperspherical coordinates. Our calculations confirm the importance of continuum effects at low energies.Ministerio de Economía y Competitividad FIS2014-53448-c2-1-P FIS2014-51941-PJunta de Andalucía FQM-160 P11-FQM-763

Three-body nuclei and their astrophysical implications: The case of 6He

The analytic THO method [1] is generalized to study three-body nuclei of astrophysical interest, and applied to 6He. Results are consistent with previous publications and experimental data [2, 3].Economía y Competitividad FPA2009-07653 FIS2011-28738-c02-01Junta de Andalucía FQM-7632Consolider-Ingenio 2010 Programme CPAN CSD2007-0004

Entropies and IPR as Markers for a Phase Transition in a Two-Level Model for Atom–Diatomic Molecule Coexistence

A quantum phase transition (QPT) in a simple model that describes the coexistence of atoms and diatomic molecules is studied. The model, which is briefly discussed, presents a second-order ground state phase transition in the thermodynamic (or large particle number) limit, changing from a molecular condensate in one phase to an equilibrium of diatomic molecules–atoms in coexistence in the other one. The usual markers for this phase transition are the ground state energy and the expected value of the number of atoms (alternatively, the number of molecules) in the ground state. In this work, other markers for the QPT, such as the inverse participation ratio (IPR), and particularly, the Rényi entropy, are analyzed and proposed as QPT markers. Both magnitudes present abrupt changes at the critical point of the QPT.Ministerio de Ciencia e Innovación PID2019-104002GB-C22, PID2020-114687GB-I00, 10.13039/501100011033Junta de Andalucía US-1380840, P20_0124

Astrophysical reaction rate for 9 Be formation within a three-body approach

The structure of the Borromean nucleus 9Be (α+α+n) is addressed within a three-body approach using the analytical transformed harmonic oscillator method. The three-body formalism provides an accurate description of the radiative capture reaction rate for the entire temperature range relevant in astrophysics. At high temperatures, results match the calculations based on two-step sequential processes. At low temperatures, where the particles have no access to intermediate two-body resonances, the three-body direct capture leads to reaction rates larger than the sequential processes. These results support the reliability of the method for systems with several charged particles.Ministerio de Economía y Competitividad (España) FPA2009-07653 FIS2011-28738-c02-0Junta de Andalucía FQM-160 P11-FQM-7632Programa Consolider-Ingenio 2010 CSD2007-0004

Probing 6He structure from proton inelastic collisions

We explore the Hyperspherical Harmonics pseudostate method to describe the 6He continuum. The method is use it within the multiple scattering of the transition amplitude (MST) approach to study inelastic scattering of p-6He at 700 MeV/u.Fundaçao para a Ciência e Tecnologia (FCT) POCTI/FNU/43421/200

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12th International Conference on Nucleus-Nucleus Collisions 2015The scattering of 9Be on 208Pb is addressed within a four-body Continuum-Discretized Coupled-Channels (CDCC) framework, considering a three-body α + α + n projectile plus a structureless target. The projectile states are generated using the analytical Transformed Harmonic Oscillator (THO) basis in hyperspherical coordinates. Both the elastic and breakup channels are described on the same footing. We find a good agreement between our calculations and the experimental data at beam energies around and below the Coulomb barrierMinisterio de Economía y Competitividad FIS2014-53448-c2-1-PMinisterio de Economía y Competitividad FIS2014-51941-PJunta de Andalucía FQM-160Junta de Andalucía P11-FQM- 763

Understanding 6He induced reactions at energies around the Coulomb barrier

Recent developments aimed to understand the observed features arising in the scattering of the Borromean nucleus 6He on heavy targets are discussed and compared with recent data for 6He+208Pb measured at the RIB facility at Louvain-la-Neuve at energies around the Coulomb barrier. The analysis of the elastic scattering data in terms of the optical model, reveals the presence of a long range absorption mechanism, that manifests in the form of a large value of the imaginary diffuseness parameter. The elastic data have been also compared with three–body CDCC calculations, based on a di-neutron model of 6He, and four–body CDCC calculations, based on a more realistic three-body model of this nucleus. Finally, the angular and energy distribution of a particles emitted at backward angles are discussed and compared with different theoretical approaches.We find that these a particles are produced mainly by a two-neutron transfer mechanism to very excited states in the residual nucleus