Double-folding Optical Potentials Research Articles

Initial State Interaction for the 20Ne + 130Te and 18O + 116Sn Systems at 15.3 AMeV from Elastic and Inelastic Scattering Measurements

Double charge exchange (DCE) reactions could provide experimentally driven information about nuclear matrix elements of interest in the context of neutrinoless double-β decay. To achieve this goal, a detailed description of the reaction mechanism is mandatory. This requires the full characterization of the initial and final-state interactions, which are poorly known for many of the projectile-target systems involved in future DCE studies. Among these, we intend to study the 20Ne + 130Te and 18O + 116Sn systems at 15.3 AMeV, which are particularly relevant due to their connection with the 130Te→130Xe and 116Cd→116Sn double-β decays. We measure the elastic and inelastic scattering cross-section angular distributions and compare them with theoretical calculations performed in the optical model, one-step distorted wave Born approximation, and coupled-channel approaches using the São Paulo double-folding optical potential. A good description of the experimental data in the whole explored range of transferred momenta is obtained provided that couplings with the 21+ states of the projectile and target are explicitly included within the coupled-channel approach. These results are relevant also in the analysis of other quasi-elastic reaction channels in these systems, in which the same couplings should be included.

Analysis of 6Li+16O elastic scattering using different potentials

Available experimental angular distributions for 6Li elastically scattered from 16O nucleus in the energy range 13.0–50.0 MeV are reanalyzed within the framework of optical potential, double folding optical potential as well as cluster folding potential. Special interest was paid to the cluster folding based on the well-known cluster structure of 6Li. Elastic scattering data for 6Li+16O system plotted as a function of momentum transfer showed that the real Coulomb nuclear interference region independent of the bombarding energy. This structural behavior for the data could be used to define the interaction potential with some certainty and to extract reliable values for the renormalization factors.

Elastic and Inelastic α-Scatterings from 58Ni, 116Sn, and 208Pb Targets at 288, 340, 480, and 699 MeV

Real double-folding optical potentials are calculated using the S1Y effective nucleon-nucleon (NN) interaction and the tρρ approximation in order to analyze elastic and inelastic scattering of α-particles from 58Ni, 116Sn, and 208Pb targets at 288, 340, 480, and 699 MeV. The relativistic corrections for momenta and reduced masses are performed to investigate the data at the energies 480 and 699 MeV. The second-order (double-scattering) correction to the tρρ potential is also considered. The inelastic scattering to low-lying excited states (2+) is investigated using the distorted wave born approximation (DWBA) and the coupled-channel (CC) techniques.

An investigation of α-nucleus elastic scattering

The α elastic scattering from various targets over a wide range of energy (120-400 MeV) has been analyzed in the framework of the double-folding (DF) optical model potential. The real DF optical potentials are generated based upon the M3Y and JLM effective nucleon-nucleon interactions. Density- dependent versions, DDM3Y, DDJLM, are also considered. The imaginary part of the optical potential is expressed either in a phenomenological Woods-Saxon form or microscopically using a normalization of the real DF potential. The angular distributions of the elastic scattering differential cross sections using the derived microscopic real potentials revealed successful description of nine sets of data all over the measured angular range. The extracted reaction cross sections have been also investigated.

Quantitative analysis of two-neutron correlations in the12C(18O,16O)14C reaction

The ${}^{12}$C(${}^{18}$O,${}^{16}$O)${}^{14}$C and ${}^{12,13}$C(${}^{18}$O,${}^{17}$O)${}^{13,14}$C reactions are studied at 84 MeV. Mass distributions and energy spectra of the ejectiles are measured, indicating the selectivity of these reactions to populate two- and one-neutron configurations in the states of the residual nucleus, respectively. The measured absolute cross-section angular distributions are analyzed by exact finite range coupled reaction channel calculations based on a parameter free double-folding optical potential. The form factors for the (${}^{18}$O,${}^{16}$O) reaction are extracted within an extreme cluster and independent particles scheme with shell-model-derived coupling strengths. The results show that the measured cross sections are accurately described for the first time without the need for any arbitrary scaling factor. The (${}^{18}$O,${}^{16}$O) reaction is thus found to be a powerful tool for quantitative spectroscopic studies of pair configurations in nuclear states.

Microscopic analysis of the energy dependence of the 6He, 6Li + 28Si total reaction cross sections in the energy range E = 5−50 A MeV

The experimental data on the total cross sections of the 4, 6He, 6, 7Li + 28Si reactions at energies E=5−50 A MeV are reported. The data for the 6Li, 6He + 28Si reactions have been analyzed within the microscopic model of double-folding optical potential, in which the real and imaginary parts are calculated at different densities of the projectile nucleus. The cross sections calculated with the microscopic double-folding Coulomb potential and the standard Coulomb potential for uniform charge distribution are compared with each other. Semimicroscopic potentials providing agreement with experimental data have been constructed on the basis of renormalized microscopic potentials and their derivatives, added to take into account collective effects.

Inelastic scattering of heavy ions at intermediate energies with excitations of nuclear collective states

Excitation of low-lying nuclear collective states upon scattering of heavy ions with energies of several tens of MeV/nucleon has been studied. The interaction potential leading to excitation is chosen in the form of a derivative of the microscopic (or semimicroscopic) nucleus-nucleus double-folding optical potential. Elastic and inelastic scattering cross sections have been calculated within the high-energy approximation; the inelastic scattering amplitude was obtained in the first order in the deformation parameter. The cross sections are compared with the experimental data on scattering of 17O from a series of nuclei with excitation of the 2+ level.

Folding model and coupled-channels analysis of 6,7 Li elastic and inelastic scattering

The double-folding optical potentials of 6,7Li nuclei have been constructed using the S1Y effective nucleon-nucleon interaction. Angular distributions of the differential cross-section of 6,7Li elastic and inelastic scattering from 12 C, 28 Si and 58 Ni targets in the energy range 12-35 MeV/u were analyzed using the derived potentials through the coupled-channels mechanism. Successful descriptions of the data were obtained using the derived potentials.

Folding model analysis of 6,7Li elastic scattering at 12.5–53 MeV/u

6,7Li-nucleus double-folding optical potentials have been constructed using the JLM and a gaussian shape of the effective nucleon–nucleon interaction. Angular distributions of the differential cross sections of 6,7Li elastic scattering from 12C, 28Si, 40Ca, 58Ni, 90Zr and 208Pb targets at 12.5–53 MeV/u were analyzed using the derived potentials. An energy-dependent reducing renormalization coefficient was required for the real component of the JLM optical potential in order to obtain successful predictions of the observed cross sections even when the projectile density-dependence was considered. A similar behavior was found for calculations based on the density-independent gaussian version of the effective nucleon–nucleon interaction. However, no renormalization was needed when a density-dependence approximation was involved. The energy- and target mass number-dependence in the renormalization factor, real volume integrals and total reaction cross sections are investigated.

Analysis of heavy ions elastic scattering using the double folding cluster model

The nucleus–nucleus double folding optical potentials were constructed using the α-cluster structure of nuclei. We derived these potentials by folding an α– α interaction with density distributions of α-clusters inside projectile and target nuclei. Twenty sets of elastic scattering data in the energy range 2–22 MeV /u were analyzed using the resulted potentials. Successful descriptions of the angular distribution cross sections were obtained, particularly at energies less than 15 MeV /u. Double folded optical potentials were also calculated based upon the α-cluster structure of the projectile nucleus and an α-nucleon effective interaction. The behavior of the required renormalization factors to obtain the potential depths at the strong absorption radii for 14 reactions is quite consistent with that found for the M3Y double folded optical potentials.

Density-independent folding analysis of the [formula omitted] Li elastic scattering at intermediate energies

The differential cross sections of 6,7 Li elastic scattering from 12 C, 28 S, 40 Ca, 58 Ni, 90 Zr and 208 Pb targets at E/A P =12.5 –53 MeV / u have been analyzed using density-independent double folding optical potentials. The calculations are built upon a very simple phenomenological nucleon–nucleon effective interaction, which is represented by a single Yukawa term with a complex strength. The complex microscopic potentials have successfully reproduced the elastic scattering data for most of the analyzed sets. However, more success has been obtained when the single Yukawa term was considered for the real part only while the imaginary part was formulated in a phenomenological Woods–Saxon form. The predictions of the calculated potentials are compared with those obtained by the phenomenological and the M3Y double folded optical potentials. The effects of the knock-on exchange contribution, the variation of the range of the interaction and the target density uncertainty have been investigated. Also, the target mass number dependence in the real volume integrals and the total reaction cross sections has been studied.

Quasielastic scattering of light exotic nuclei. A semi-microscopic folding analysis

Angular distributions and total reaction cross sections for the quasielastic scattering of (i) 8B and 7Be on 12C at E lab = 40 MeV/nucleon, (ii) 11Li on 28Si at E lab = 29 MeV/nucleon, and (iii) 11C and 11Li on 12C at lab = 60 MeV/nucleon are studied with coupled-channels calculations using double-folding optical potential based on the M3Y effective interaction and densities obtained within the energy-density functional approach with a fixed parameter set for all colliding nuclei. An imaginary part of the optical potential is constructed from folding the real one with two free parameters for volume and surface absorption. It is shown that a fairly good description of the experimental data can be achieved within a rather restricted range of these free parameters without renormalization of the real part of the optical potential. The analysis confirms the long neutron tail (halo) in 11Li and supports a rather thick proton skin in 8B and, to a lesser extent, in 7Be.

Elastic scattering of a secondary 11Li beam on 28Si at 29 MeV/nucleon

The elastic scattering of a secondary 11Li beam (29 MeV/nucleon) on a 28Si target has been measured for the first time. To compensate for the low intensity of the secondary beam, an efficient detecting system permitting one to obtain reliable experimental data has been used. An attempt has been made to reproduce the data in a phenomenological analysis and with coupled-channel calculations with a double-folding optical potential, with energy- and density-dependent effective interaction and realistic densities. In coupled-channel calculations with the folding optical potential a better description is achieved if a neutron halo of 11Li is taken into account.

Microscopic optical potential analyses of carbon–carbon elastic scattering

Utilizing eikonal phase shifts determined from a microscopic double-folding optical potential, marked improvement in the agreement between theory and experiment, for elastic carbon–carbon scattering between 200 and 300 MeV, is obtained when only those values for the nucleon–nucleon slope parameter, appropriate for diffractive scattering, are used. The appropriateness of the perturbative eikonal expansion is discussed by comparison with recent results, obtained for the same potentials, using a more exact complex Wentzell–Kramers–Brillouin (WKB) formalism.

B11+Ca40single-nucleon transfer reactionsElab=51.5MeV

Angular distributions for the single-nucleon transfer reactions /sup 40/Ca(/sup 11/B,/sup 12/C)/sup 39/K(J/sup ..pi../=3/2/sup +/ and 1/2/sup +/) and /sup 40/Ca(/sup 11/B,/sup 10/B(J/sup ..pi../=3/sup +/ and 1/sup +/))/sup 41/Ca have been measured at 51.5 MeV. The distorted-wave Born approximation was used to analyze the data. The distorted waves used in the distorted-wave Born-approximation calculations were generated from both Woods-Saxon and double-folding optical potentials which describe elastic scattering data. The standard distorted-wave Born-approximation calculations reproduced the forward angle data, including the l=1 pickup reaction, but overpredicted the back-angle data. Distorted-wave Born-approximation calculations carried out with distorted waves obtained from double-folded potentials were in much better agreement with the data. The extracted spectroscopic factors for the proton pickup reaction are much larger than those obtained from light-ion data while for the neutron stripping case they agree, even for the case where /sup 10/B was in its first excited state.