Hartree-Fock calculations in the s-d shell with realistic and semi-realistic interactions

doi:10.1016/0375-9474(69)90112-2

Nuclear Physics A

Volume 137, Issue 2, 10 November 1969, Pages 318-330

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Abstract

HF calculations with configurations restricted to the s-d shell have been performed for axially symmetric nuclei with renormalized matrix elements derived from various realistic and semi-realistic interactions. The results for binding energies and projected spectra compare favourably with those obtained so far with completely phenomenological effective interactions.

References (17)

T.T.S. Kuo et al.
Nucl. Phys.
(1966)
T.T.S. Kuo
Nucl. Phys.
(1967)
F. Tabakin
Ann. of Phys
(1964)
C.W. Nestor et al.
Nucl. Phys.
(1968)
G. Saunier and J. M. Pearson, to be...
R. Dreizler et al.
Nucl. Phys.
(1968)
S.K.M. Wong et al.
Phys. Rev. Lett.
(1968)
C.A. Levinson
Phys. Rev.
(1963)
G. Ripka

There are more references available in the full text version of this article.

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A basis of two particle intrinsic states for ²²Ne and ²⁶Mg is defined in terms of the Hartree-Fock solutions for ²⁰Ne and ²⁴Mg. Mixing between the different intrinsic states is estimated from a deformed shell model. The model proceeds to describe the lowest 12 positive parity states in ²²Ne and the lowest 15 in ²⁶Mg. Spin, parity and K-quantum number assignments are proposed. These results are also compared with the existing shell model and projection model interpretations of ²²Ne and ²⁶Mg.
Pairing correlations and simultaneous projection of particle number and angular momentum in light nuclei
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The Hartree-Bogolubov theory with simultaneous projection on sharp angular momentum quantum number and sharp particle number is presented as a description of the ground state rotational bands of doubly even nuclei. Calculations with effective G-matrix elements of the Hamada-Johnston potential and also of the Yale potential have been performed within this framework for the nuclei ²⁰Ne, ²²Ne, ²⁴Ne, ²⁴Mg, ²⁶Mg, ²⁸Si, ³⁰Si, ³²S and ³⁴S. Rotational energies, moments of inertia, pairing correlations, quadrupole moments and B(E2) values are discussed and compared with available experimental data. The effect of particle number fluctuation on the ground state rotational spectrum and on the intrinsic wave function is investigated. The particle number projection turns out to be important for the description of the rotational levels, whereas it has only a negligible effect on the properties of the intrinsic wave function. Comparison with Hartree-Fock results and with experimental data shows that the inclusion of pairing correlations provides a significant improvement on the excitation energies, their relative ratios and the angular momentum dependence of the moments of inertia. All solutions show an antistretching effect in the quadrupole moments and especially in the B(E2) values. The rotational bands in ²⁰Ne, ²²Ne, ²⁴Ne and ²⁸Si turn out to be well described in the framework presented.
Antipairing effect in the rotational states of light nuclei
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Properties of rotational levels of sd shell nuclei are studied in the self-consistent deformed Hartree-Bogoliubov model with a variation performed approximately after angular momentum projection. This formalism, which consists of a constrained Hartree-Bogoliubov theory with an additional pairing potential, is explained in detail. Excitation energies, moments of inertia, pairing correlations and quadrupole moments of the ground state rotational bands of ²²Ne, ²⁴Ne and ³⁰Si are investigated and compared with experimental data. In the calculation all particles are treated alike without the assumption of an inert core, using the effective G-matrix elements of Barrett et al., the Yale-Shakin interaction and the B1 force of Brink and Boeker. It turns out to be important to perform the projection before the variation and not afterwards, since the pairing correlations change drastically in going to higher J-states. In the nuclei ²⁴Ne and ³⁰Si the calculations indicate a phase transition into the unpaired states at J = 4⁺ and 8⁺ respectively. The agreement with experiment is satisfactory and the experimental deviation from the J(J+1) law is quite well reproduced. In each case the Barrett G-matrix gives the best results, which are, in the case of ²²Ne, in good agreement with experimental values.
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^†: Work supported by the National Research Council of Canada.

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Nuclear Physics A

Abstract

References (17)

Nucl. Phys.

Nucl. Phys.

Ann. of Phys

Nucl. Phys.

Nucl. Phys.

Phys. Rev. Lett.

Phys. Rev.

Cited by (12)

A new method for calculating rotational spectra for complex nuclei

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Pairing correlations and simultaneous projection of particle number and angular momentum in light nuclei

Antipairing effect in the rotational states of light nuclei

The effect of particle number fluctuation on the rotational states of paired light nuclei

Structure of <sup>28</sup>Si, some answers and their problems