Beyond-mean-field-model analysis of low-spin normal-deformed and superdeformed collective states of^{32} S,^{36} Ar,^{38} Ar, and^{40} Ca

Vrije Universiteit Brussel, Bruxelles, Brussels Capital, Belgium
Physical Review C (Impact Factor: 3.73). 10/2003; 68(4). DOI: 10.1103/PhysRevC.68.044321
Source: arXiv


We investigate the coexistence of spherical, deformed, and superdeformed states at low spin in 32S, 36Ar, 38Ar, and 40Ca. The microscopic states are constructed by configuration mixing of BCS states projected on good particle number and angular momentum. The BCS states are themselves obtained from Hartree-Fock BCS calculations using the Skyrme interaction SLy6 for the particle-hole channel and a density-dependent contact force in the pairing channel. The same interaction is used within the generator coordinate method to determine the configuration mixing and calculate the properties of even-spin states with positive parity. Our calculations underestimate moments of inertia. Nevertheless, for the four nuclei, the global structural properties of the states of normal deformation as well as the recently discovered superdeformed bands up to spin 6 are correctly reproduced with regard to both the energies and the transition rates.

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    ABSTRACT: We investigate truncation schemes to reduce the computational cost of calculating correlations by the generator coordinate method based on mean-field wave functions. As our test nuclei, we take examples for which accurate calculations are available. These include a strongly deformed nucleus, 156Sm, a nucleus with strong pairing, 120Sn, the krypton isotope chain which contains examples of soft deformations, and the lead isotope chain which includes the doubly magic 208Pb. We find that the Gaussian overlap approximation for angular momentum projection is effective and reduces the computational cost by an order of magnitude. Cost savings in the deformation degrees of freedom are harder to realize. A straightforward Gaussian overlap approximation can be applied rather reliably to angular-momentum projected states based on configuration sets having the same sign deformation (prolate or oblate), but matrix elements between prolate and oblate deformations must be treated with more care. We propose a two-dimensional GOA using a triangulation procedure to treat the general case with both kinds of deformation. With the computational gains from these approximations, it should be feasible to carry out a systematic calculation of correlation energies for the nuclear mass table. Comment: 11 pages revtex, 9 eps figures
    Physical Review C 11/2003; 69(3). DOI:10.1103/PhysRevC.69.034340 · 3.73 Impact Factor
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    ABSTRACT: We study the low-lying collective excitation spectra of the neutron-deficient lead isotopes Pb182-Pb194 by performing a configuration mixing of angular-momentum and particle-number projected self-consistent mean-field states. The same Skyrme interaction SLy6 is used supplemented by a density-dependent zero-range pairing force. This study supports the interpretation of spectra made on the grounds of more schematic models in terms of coexisting spherical, oblate, prolate and superdeformed prolate structures. The model qualitatively reproduces the variation of the spectra with neutron number. Our results for E0 and E2 transition probabilities are compared with the few existing experimental data. Finally, we predict the presence of superdeformed bands at low excitation energy in the most neutron-deficient isotopes. Comment: 14 pages, 14 figures. submitted to Phys. Rev. C
    Physical Review C 11/2003; 69(6). DOI:10.1103/PhysRevC.69.064303 · 3.73 Impact Factor
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    ABSTRACT: The superdeformed band of $^{36}$Ar is studied with the Gogny force D1S and the angular momentum projected generator coordinate method for the quadrupole moment. The band head excitation energy, moments of inertia, $B(E2)$ transition probabilities and stability against quadrupole fluctuations at low spin are studied. The Self Consistent Cranking method is also used to describe the superdeformed rotational band. In addition, properties of some normal deformed states are discussed. Comment: 8 pages, 3 figures, Talk given at 10th Nuclear Physics Workshop Marie and Pierre Curie, September 24-28, 2003, Kazimierz Dolny, Poland. To be published in IJMPE
    International Journal of Modern Physics E 11/2003; DOI:10.1142/S0218301304001862 · 1.34 Impact Factor
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