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Title: Nucleon direct-semidirect radiative capture with Skyrme-Hartree-Fock-BCS bound states

Abstract

The nucleon direct-semidirect (DSD) capture cross sections are obtained by calculating a transition amplitude to the Hartree-Fock-BCS bound states. The radial matrix elements in the DSD amplitudes are calculated from the radial part of the single-particle wave functions. For deformed nuclei the single-particle states are expanded in the cylindrical harmonic-oscillator basis and then projected on the spherical harmonic-oscillator basis. The pairing correlations are treated in the BCS approach and the calculated spectroscopic factors are in fairly good agreement with experimental data in the even tin isotopes from {sup 116}Sn to {sup 124}Sn. The resulting DSD cross sections for the neutron capture by {sup 208}Pb and {sup 238}U are found to be in good agreement with the available experimental data. The calculations are also performed for the neutron capture on {sup 122}Sn and {sup 132}Sn isotopes that are important for the r-process in astrophysics.

Authors:
;  [1];  [1];  [2];  [3]
  1. Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
  2. (Japan)
  3. Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195 (Japan)
Publication Date:
OSTI Identifier:
20995304
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. C, Nuclear Physics; Journal Volume: 75; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevC.75.054618; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; BOUND STATE; CAPTURE; CROSS SECTIONS; CYLINDRICAL CONFIGURATION; DEFORMED NUCLEI; HARMONIC OSCILLATORS; HARTREE-FOCK METHOD; LEAD 208; MATRIX ELEMENTS; NEUTRON REACTIONS; NUCLEONS; R PROCESS; SKYRME POTENTIAL; SPECTROSCOPIC FACTORS; TIN 116; TIN 122; TIN 124; TIN 132; TRANSITION AMPLITUDES; URANIUM 238

Citation Formats

Bonneau, L., Kawano, T., Watanabe, T., Department of Applied Quantum Physics and Nuclear Engineering, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, and Chiba, S.. Nucleon direct-semidirect radiative capture with Skyrme-Hartree-Fock-BCS bound states. United States: N. p., 2007. Web. doi:10.1103/PHYSREVC.75.054618.
Bonneau, L., Kawano, T., Watanabe, T., Department of Applied Quantum Physics and Nuclear Engineering, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, & Chiba, S.. Nucleon direct-semidirect radiative capture with Skyrme-Hartree-Fock-BCS bound states. United States. doi:10.1103/PHYSREVC.75.054618.
Bonneau, L., Kawano, T., Watanabe, T., Department of Applied Quantum Physics and Nuclear Engineering, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, and Chiba, S.. Tue . "Nucleon direct-semidirect radiative capture with Skyrme-Hartree-Fock-BCS bound states". United States. doi:10.1103/PHYSREVC.75.054618.
@article{osti_20995304,
title = {Nucleon direct-semidirect radiative capture with Skyrme-Hartree-Fock-BCS bound states},
author = {Bonneau, L. and Kawano, T. and Watanabe, T. and Department of Applied Quantum Physics and Nuclear Engineering, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395 and Chiba, S.},
abstractNote = {The nucleon direct-semidirect (DSD) capture cross sections are obtained by calculating a transition amplitude to the Hartree-Fock-BCS bound states. The radial matrix elements in the DSD amplitudes are calculated from the radial part of the single-particle wave functions. For deformed nuclei the single-particle states are expanded in the cylindrical harmonic-oscillator basis and then projected on the spherical harmonic-oscillator basis. The pairing correlations are treated in the BCS approach and the calculated spectroscopic factors are in fairly good agreement with experimental data in the even tin isotopes from {sup 116}Sn to {sup 124}Sn. The resulting DSD cross sections for the neutron capture by {sup 208}Pb and {sup 238}U are found to be in good agreement with the available experimental data. The calculations are also performed for the neutron capture on {sup 122}Sn and {sup 132}Sn isotopes that are important for the r-process in astrophysics.},
doi = {10.1103/PHYSREVC.75.054618},
journal = {Physical Review. C, Nuclear Physics},
number = 5,
volume = 75,
place = {United States},
year = {Tue May 15 00:00:00 EDT 2007},
month = {Tue May 15 00:00:00 EDT 2007}
}
  • Self-consistent Skyrme-Hartree-Fock plus BCS calculations are performed to generate potential energy curves (PECs) in various chains of Pd, Xe, Ba, Nd, Sm, Gd, and Dy isotopes. The evolution of shapes with the number of nucleons is studied in a search for signatures of E(5) and X(5) critical point symmetries. It is shown that the energy barriers in the PECs are determined to a large extent by the treatment of the pairing correlations.
  • Self-consistent axially symmetric Skyrme Hartree-Fock plus BCS calculations are performed to study the evolution of shapes with the number of nucleons in various chains of Yb, Hf, W, Os, and Pt isotopes from neutron number N=110 up to N=122. Potential energy curves are analyzed in a search for signatures of oblate-prolate phase shape transitions, and results from various Skyrme and pairing forces are considered. Comparisons with results obtained with the Gogny interaction as well as with relativistic mean field calculations are presented. The role of the {gamma} degree of freedom is also discussed.
  • An exact treatment of the Coulomb interaction is performed within the Skyrme-Hartree-Fock/Bardeen-Cooper-Schrieffer approach for even-even nuclei ranging from light to superheavy nuclei. A test of the usual Slater approximation for the exchange part is carried out. The error made on the exchange term of the Coulomb interaction when using this approximation follows two schematic patterns. Beyond a decreasing behavior when increasing the mass number A, a more important structural effect has been found. The relative error ranges roughly from 0 to 8% being maximal for light closed proton (sub-)shell nuclei and minimal for open proton (sub-)shell nuclei.
  • A recent study of (..gamma..,n/sub 0/) reactions on /sup 207/Pb and /sup 208/Pb produced a direct-semidirect model calculation of the angular distribution (the a/sub 2/ coefficient) which was vastly different for these two cases. In this paper we offer the formal proof that this is incorrect. It is shown that the angular distribution involving a target with spin is exactly equal to that obtained if the target is treated as spin zero with the residual spin being the single particle total angular momentum in the final state. A corrected calculation for a/sub 2/ is presented for the case of /supmore » 208/Pb(..gamma..,n/sub 0/) /sup 207/Pb and /sup 207/Pb(..gamma..,n/sub 0/) /sup 206/Pb.« less