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Title: Nucleus-nucleus scattering in the high-energy approximation and optical folding potential

Abstract

A microscopic complex folding-model potential that reproduces the scattering amplitude of Glauber-Sitenko theory in its optical limit is obtained. The real and imaginary parts of this potential are dependent on energy and are determined by known data on the nuclear-density distributions and on the nucleon-nucleon scattering amplitude. For the real part, use is also made of a folding potential involving effective nucleon-nucleon forces and allowing for the nucleon-exchange term. Three forms of semimicroscopic optical potentials where the contributions of the template potentials-that is, the real and the imaginary folding-model potential-are controlled by adjusting two parameters are constructed on this basis. The efficiency of these microscopic and semimicroscopic potentials is tested by means of a comparison with the experimental differential cross sections for the elastic scattering of heavy ions {sup 16}O on nuclei at an energy of E {approx} 100 MeV per nucleon.

Authors:
; ;  [1]
  1. Joint Institute for Nuclear Research (Russian Federation)
Publication Date:
OSTI Identifier:
21076119
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Atomic Nuclei; Journal Volume: 69; Journal Issue: 2; Other Information: DOI: 10.1134/S1063778806020086; Copyright (c) 2006 Nauka/Interperiodica; Article Copyright (c) 2006 Pleiades Publishing, Inc; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; APPROXIMATIONS; COMPARATIVE EVALUATIONS; DIFFERENTIAL CROSS SECTIONS; DISTRIBUTION; EFFICIENCY; ELASTIC SCATTERING; FOLDING MODEL; HEAVY IONS; MEV RANGE 100-1000; NUCLEAR MATTER; NUCLEON-NUCLEON INTERACTIONS; NUCLEONS; OXYGEN 16; POTENTIALS; SCATTERING AMPLITUDES

Citation Formats

Lukyanov, V. K., E-mail: lukyanov@thsuni.jinr.ru, Zemlyanaya, E. V., and Lukyanov, K. V.. Nucleus-nucleus scattering in the high-energy approximation and optical folding potential. United States: N. p., 2006. Web. doi:10.1134/S1063778806020086.
Lukyanov, V. K., E-mail: lukyanov@thsuni.jinr.ru, Zemlyanaya, E. V., & Lukyanov, K. V.. Nucleus-nucleus scattering in the high-energy approximation and optical folding potential. United States. doi:10.1134/S1063778806020086.
Lukyanov, V. K., E-mail: lukyanov@thsuni.jinr.ru, Zemlyanaya, E. V., and Lukyanov, K. V.. Wed . "Nucleus-nucleus scattering in the high-energy approximation and optical folding potential". United States. doi:10.1134/S1063778806020086.
@article{osti_21076119,
title = {Nucleus-nucleus scattering in the high-energy approximation and optical folding potential},
author = {Lukyanov, V. K., E-mail: lukyanov@thsuni.jinr.ru and Zemlyanaya, E. V. and Lukyanov, K. V.},
abstractNote = {A microscopic complex folding-model potential that reproduces the scattering amplitude of Glauber-Sitenko theory in its optical limit is obtained. The real and imaginary parts of this potential are dependent on energy and are determined by known data on the nuclear-density distributions and on the nucleon-nucleon scattering amplitude. For the real part, use is also made of a folding potential involving effective nucleon-nucleon forces and allowing for the nucleon-exchange term. Three forms of semimicroscopic optical potentials where the contributions of the template potentials-that is, the real and the imaginary folding-model potential-are controlled by adjusting two parameters are constructed on this basis. The efficiency of these microscopic and semimicroscopic potentials is tested by means of a comparison with the experimental differential cross sections for the elastic scattering of heavy ions {sup 16}O on nuclei at an energy of E {approx} 100 MeV per nucleon.},
doi = {10.1134/S1063778806020086},
journal = {Physics of Atomic Nuclei},
number = 2,
volume = 69,
place = {United States},
year = {Wed Feb 15 00:00:00 EST 2006},
month = {Wed Feb 15 00:00:00 EST 2006}
}
  • Microscopic optical model potentials, based on density-dependent effective interactions, involve multidimensional integrals to account for the full Fermi motion of the target struck nucleon throughout the nucleus. If a spherical matter distribution is assumed, then each matrix element of the optical potential requires the evaluation of seven-dimensional integrals. In this work we provide a full account of these integrals, retaining the genuine off-shell structure of the nucleon-nucleon effective interaction. The evaluation is based on the asymptotic separation of the optical model potential for nucleon-nucleus scattering in momentum space, where the potential is split into a free t-matrix contribution and anothermore » which depends exclusively on the gradient of the density-dependent g matrix. The calculated potentials, based on the Paris nucleon-nucleon (NN) potential, are applied to proton elastic scattering from {sup 16}O and {sup 90}Zr at beam energies between 30 and 65 MeV. The results were compared with two approximations to the unabridged expression, revealing moderate differences among their scattering observables. When comparing with results based on the Argonne v{sub 18} NNpotential, these differences appear smaller than those attainable by the choice of the internucleon potential.« less
  • The folding-model optical potential is generalized in such a way as to apply it to calculating the cross sections for inelastic scattering of π{sup ±}-mesons on {sup 28}Si, {sup 40}Ca, {sup 58}Ni, and {sup 208}Pb nuclei at the energies of 162, 180, 226, and 291 MeV leading to the excitation of the 2{sup +} and 3{sup −} collective states. In doing this, use is made of known nucleon-density distributions in nuclei and the pion–nucleon scattering amplitude whose parameters were obtained previously by fitting the elastic scattering cross sections for the same nuclei. Thus, the values of quadrupole (β{sub 2}) andmore » octupole (β{sub 3}) deformations of nuclei appear here as the only adjustable parameters. The scattering cross section is calculated by solving the relativistic wave equation, whereby effects of relativization and distortion in the entrance and exit scattering channels are taken exactly into account. The cross sections calculated in this way for inelastic scattering are in good agreement with respective experimental data. The importance of the inclusion of in-medium effects in choosing parameters of the pion–nucleon amplitude is emphasized.« less
  • The surface peaked modification to the conventional six-parameter representation of an ..cap alpha.. particle-nucleus interaction potential has been studied further. In particular we have used a nucleon-nucleus optical potential folded over the ..cap alpha.. particle to derive the central well depth, and it is found that constant geometry parameters can be used to fit the A dependence and energy dependence of the optical model for /sup 9/0Zr from 40--140 MeV. It is further found that good quality fits to elastic scattering can be obtained for the entire energy range for /sup 9/0Zr with constant geometry for the Woods-Saxon imaginary wellmore » depth, resulting in a five search parameter potential. The energy dependence can be incorporated in the strengths of the real and imaginary components of the potential and the geometrical parameters of the modification.« less