M. N. A. Abdullah

Non-monotonic potentials for 6Li elastic scattering at 88 MeV

This work compares the performance of the traditional phenomenological Woods–Saxon (WS) and squared WS (SWS) potentials with that of a non-monotonic (NM) potential, for 6Li elastic scattering by targets of a wide range, namely 24,25,26Mg, 27Al, 40,44Ca, 59Co, 60Ni, 197Au and 206,208Pb at an incident energy of 88 MeV. The real part of this NM potential is derived microscopically using the energy-density functional (EDF) formalism, from a realistic two-nucleon potential, that includes the Pauli principle. The experimental differential cross sections (DCSs) for the 6Li elastic scattering are well accounted for using this raw EDF-generated real part along with an empirical imaginary part, referred to as the NM-1 potential, which needs no renormalization. To make this potential more consistent in terms of the variations of the volume integrals per nucleon pair of its real part with the target mass numbers, a completely empirical NM potential, referred to as the NM-2 potential, is derived that fits the data more satisfactorily. The DCS data are also well described by the SWS and WS potentials. However, the SWS potential is found to be inconsistent in terms of the above-mentioned criterion and the NM-2 potential has an edge over all the potentials.

Microscopic 6Li-28Si potential from the energy-density functional theory

The experimental differential cross-sections for the 6Li elastic scattering by 28Si over the incident energies ELi=7.5–99.0 MeV and vector analyzing power data at 22.8 MeV have been analyzed in terms of a non-monotonic potential, microscopically derived from the energy-density functional (EDF) theory using a realistic two-nucleon potential that incorporates effects of the Pauli principle. The data are accounted for well without any need for renormalization of the potential or adjustment of its parameters. Inclusion of a static spin-orbit potential with the EDF-generated central real one is found to describe satisfactorily the features of the vector analyzing power data.

Non-monotonic potentials and vector analyzing powers of 6,7Li scattering by 12C, 26Mg, 58Ni, and 120Sn

The data on the elastic scattering cross-section (CS) and vector analyzing power (VAP) of 6,7Li incident on 12C , 26Mg, 58Ni and 120Sn nuclei are analyzed in terms of an optical model (OM) potential, the real part of which is generated from a realistic two-nucleon interaction using the energy-density functional (EDF) formalism. The EDF-generated real part of the potential is non-monotonic (NM) in nature. This NM real potential part, without any renormalization, along with an empirically determined imaginary part and spin-orbit potential, embodying the underlying physics of projectile excitation, can successfully account for both CS and VAP data in all four cases. This investigation, for the first time, using the simple OM analysis accounts well for the opposite signs of the VAP data of elastically scattered 6,7Li by 58Ni at Elab≈20 MeV and by 120Sn at Elab=44 MeV. The ramification of successfully describing the data by the EDF-generated potential to the equation of state of nuclear matter is discussed.

Molecular versus squared Woods–Saxon α-nucleus potentials in the 27Al(α, t)28Si reaction

The differential cross-section of the 27Al(α, t)28Si reaction for 64.5 MeV incident energy has been reanalysed in DWBA with full finite range using a squared Woods–Saxon (Michel) α-nucleus potential with the modified value of the depth parameter α = 2.0 as reported in a comment article by Michel and Reidemeister. This new value produces significant improvement in fitting the data of the reaction with its overall performance, in some cases, close to that previously observed for the molecular potential. Although the non-monotonic shallow molecular potential with a soft repulsive core and the Michel potentials produce the same quality fits to the elastic scattering and non-elastic processes, they are not phase equivalent. The two types of potential produce altogether different cross-sections, particularly at large reaction angles. The importance of the experimental cross-sections at large angles for both elastic scattering and non-elastic processes is elucidated.

Non-monotonic potential description of alpha–Zr refractive elastic scattering

Experimental differential cross sections of α elastic scattering by 90Zr in the 15.0–141.7 MeV range of the bombarding energies have been analysed within the framework of an optical model using non-monotonic (NM) potentials. These potentials are generated from the energy-density functional theory using a realistic two-nucleon potential coupled with an appropriate consideration of the Pauli principle. The NM nature of the real part of the potential seems to be gradually diminishing at energies beyond 118.0 MeV. The Airy structure of the nuclear rainbow scattering data in the energy range of 79.5–141.7 MeV is for the first time well accounted for by the shallow NM potential. Two potential families, which are located in the real part, bear a linear variation of a volume integral in the energy range 25.0–141.7 MeV with a threshold anomaly at the lower energies. The potential contains an interior repulsive part that, with energy, shifts towards the surface and gradually weakens until it is almost lost in the nuclear surface. The requirement of a deep attractive real part of the nuclear potential seems to be generally non-stringent for describing the nuclear rainbow oscillations. Some discrete ambiguities in the potentials seem to persist even when the ‘exponential falloff’ in the angular distribution following the ‘rainbow angle’ is well reproduced in this investigation using the NM real part of the optical potentials.

NON-MONOTONIC ALPHA- AND 6Li-POTENTIALS FROM ENERGY DENSITY FUNCTIONAL FORMALISM

The present status of the α-nucleus potential, generated from the energy density functional (EDF) formalism using a realistic two-nucleon potential, which incorporates the Pauli principle, is discussed. The EDF potentials, calculated using a density distribution of α-particle that yields a binding energy of 20 MeV with a reasonable root-mean-squared radius and observed density distributions of 6Li and various target nuclei, are found to be shallow and non-monotonic in character. This non-monotonic EDF potential reproduces satisfactorily the experimental elastic scattering data, particularly at energies above the Coulomb barrier. Since the elastic scattering data and the binding energies of all nuclei considered herein are well reproduced using the mean field generated from a realistic two-nucleon potential for nuclear and nucleonic matter, one may conclude to have reasonable information on the equation of states of nuclear and nucleonic matter from a very low to the saturation density from the present investigation.

ALPHA-ALPHA AND ALPHA-NUCLEUS POTENTIALS: AN ENERGY-DENSITY FUNCTIONAL APPROACH

The real parts of the alpha-alpha and alpha-nucleus potential, particularly for 40,44,48Ca and 58Ni targets are determined from a realistic two-nucleon potential using an energy-density functional approach and are found to be non-monotonic with a short range repulsion in their functional forms that are similar to those needed in accounting for elastic scattering data. The deduced alpha-alpha potential has no bound states and the calculated decay width of 8Be of about 6.4 eV at about 200 keV energy is in agreement with the measurement.

Band mixing in 29Si and 29P

The experimental data of the 28Si(α, t)29P and 28Si(α, 3He)29Si reactions at 45 MeV have been analysed in terms of full finite-range coupled-channels calculations. In the calculations, the reaction paths, direct and two step via the inelastic states of the initial and final nuclei have been treated in terms of the finite-range transfer theory. The spectroscopic amplitudes connecting the deformed initial and final nuclei in both the reactions are obtained from Nilssons model. The data of both the reactions, populating the 1/2+, 3/2+ and 5/2+ states in the Kπ = 1/2+ band and the 3/2+ and 5/2+ states in the Kπ = 3/2+ band, are best described by about 20% mixing of between the two bands. The effects of normal Woods–Saxon (WS), squared WS and molecular type of α-nucleus potentials are also discussed.