Antisymmetrization effects in heavy ion potentials

doi:10.1016/0375-9474(77)90268-8

Nuclear Physics A

Volume 277, Issue 1, 7 February 1977, Pages 170-188

https://doi.org/10.1016/0375-9474(77)90268-8 Get rights and content

Abstract

The effects of antisymmetrization on heavy ion potentials are investigated. To this purpose we derive for the Skyrme force an energy-density functional that neglects all effects of antisymmetrization between the nuclei. Starting from this potential we then include step by step the antisymmetrization in the interaction matrix element, the Pauli distortion of the densities and the change of the intrinsic kinetic energies due to the Pauli principle and discuss their relative magnitude. It is found that the sum of these corrections most of which are not included in the folding model is repulsive and changes the not antisymmetrized potential by about 70 % at the strong absorption radius. The effects of nuclear polarization on the potential are discussed by comparison with the results of a two-center self-consistent calculation and are found to deepen the potential considerably. Finally a detailed comparison of the not antisymmetrized potential that can be easily evaluated from the densities with experimental results shows good agreement over large mass regions.

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But the situation for the nuclear part is much more complicated. At present, different models have been used for its approximation [1–4,7–24] and the heights of the barrier in the nucleus-nucleus interaction potential, which influences the mechanism of nuclear reactions, within these models can differ significantly. For this reason, information about the potential of nucleus-nucleus interaction and barrier heights is fundamentally important to describe the reaction process.
The nucleon density distributions and nucleus-nucleus interaction potentials for the reactions ¹⁶O+⁹²Zr and ¹⁶O+¹¹⁶Sn were calculated using the modified Thomas-Fermi method, taking into account all terms up to members of the second order by ħ in the quasiclassical decomposition of the kinetic energy. As a nucleon-nucleon interaction, density depended Skyrme forces were used. Based on the obtained potentials, the cross-sections of subbarrier fusion and elastic scattering were calculated. It is shown that the obtained cross-sections of the reactions agree well with the latest experimental data.
The nucleus-nucleus potential within the extended Thomas-Fermi method and the cross-sections of subbarrier fusion and elastic scattering for the systems 16O + 58,60,62,64Ni
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In this work, we use a semi-microscopic approach to determine the potential of nuclear interaction. In the framework of this approach, the nucleon density distributions in interacting nuclei as well as the potential interaction energy of the nuclei are calculated within the extended Thomas-Fermi approach with the Skyrme force [4,7,8,10,11,13–24]. For Skyrme force in both cases, we use the parameterization SkM* [29,31].
The nucleus-nucleus interaction potentials for the ${}^{16}O +^{58, 60, 62, 64} Ni$ systems are calculated within the extended Thomas-Fermi method by taking into account all terms up to terms of the second order in ħ of the quasiclassical decomposition of kinetic energy. The density-dependent Skyrme force is used as the nucleon-nucleon interactions. Using the obtained potentials, the cross sections of subbarrier fusion and elastic scattering are found, which are in good agreement with the experimental data.
Comparison of the nucleus-nucleus potential evaluated in the double-folding and energy density approximations and the cross-sections of elastic scattering and fusion of heavy ions
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The Coulomb and centrifugal interactions between nuclei are well-known, whereas the nuclear interaction is less known. As a result, there are many different approximations for evaluation of the nuclear interaction part [1–54]. For example, the Woods-Saxon potential is often applied in the analysis of experimental data [1–4,39–47].
The nucleus-nucleus potentials evaluated in the double-folding and energy density approximations with and without the contributions of the kinetic energy of the nucleons are discussed in detail. The nuclear part of nucleus-nucleus potentials obtained in the double-folding approach is close to the one calculated in the energy density approximation without the contributions of the kinetic energy. The cross-sections of fusion around the barrier and elastic scattering are calculated for the systems ¹⁶O + ²⁰⁸Pb, ⁴⁰Ca + ⁴⁰Ca, ¹⁶O + ⁵⁶Fe, ¹⁶O + ⁹²Zr using the total nucleus-nucleus interaction. It is shown that taking into account the contribution of kinetic energy to the potential allows simultaneously describes the experimental cross sections of the fusion and elastic scattering.
Pauli exchange effects in the elastic scattering of 16O + 16O
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The real optical potential for ¹⁶O+¹⁶O system is calculated within a generalized version of the double-folding model with the Pauli knock-on exchange effects between the projectile nucleons and the target nucleons taken into account from first principle. The elastic scattering data at E_lab=350 MeV supplemented by the new measurement at larger angles seem to be the first case in heavy-ion scattering where one can test the reliability of different theoretical heavy-ion optical potentials. Predictions are made for the elastic scattering of ¹⁶O+¹⁶O at laboratory energies of 240–480 MeV to illustrare the energy dependence of the rainbow structure which has been clearly observed in experiment at 350 MeV.
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A simple theory of the heavy-ion optical potential oV, based on the local density approximation, is presented. The colliding ions are described locally as two slabs of nuclear matter. The real part of the energy density of the two slabs is derived from the properties of nuclear matter, and for the imaginary part the “frivolous model” is applied. Results for oV in the case of two slabs are presented and compared with results of other calculations. Arguments are given in favour of using the frivolous model in the optical potential and the VUU calculations for heavy-ion collisions.

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^☆: Work supported by Bundesministerium für Forschung und Technologie (BMFT), Gesellschaft für Schwerionenforschung (GSI) and the US Energy Research and Development Administration.

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Nuclear Physics A

Abstract

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Classical and quantum mechanical aspects of heavy ion collisions

Cited by (59)

Subbarrier fusion and elastic scattering cross-sections based on modified Thomas-Fermi method potentials

The nucleus-nucleus potential within the extended Thomas-Fermi method and the cross-sections of subbarrier fusion and elastic scattering for the systems <sup>16</sup>O + <sup>58,60,62,64</sup>Ni

Comparison of the nucleus-nucleus potential evaluated in the double-folding and energy density approximations and the cross-sections of elastic scattering and fusion of heavy ions

Pauli exchange effects in the elastic scattering of <sup>16</sup>O + <sup>16</sup>O

Diabatic shifts and fluctuations of heavy-ion fusion barriers

On the nuclear matter approach to the heavy-ion optical potential

Antisymmetrization effects in heavy ion potentials☆

Abstract

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Phys. Lett.

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Phys. Lett.

Classical and quantum mechanical aspects of heavy ion collisions