Symplectic ab initio no–core shell model

J.P. Draayerª, T. Dytrychª, K.D. Sviratchevaª, C. Bahriª and J.P. Vary^b

ª Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803, USA.

^b Department of Physics and Astronomy, Iowa State University, Ames, IA 50011, USA.

Recibido el 28 de febrero de 2008
Aceptado el 7 de mayo de 2008

Abstract

The present study confirm the significanc of the symplectic Sp(3,R) symmetry in nuclear dynamics as unveiled, for the firs time, by examinations of realistic nucleon–nucleon (N N) interactions as well as of eigenstates calculated in the framework of the ab initio No–Core Shell Model (NCSM). The results reveal that the NCSM wave functions for light nuclei highly overlap (at the 90% level) with only a few of the most deformed Sp(3,R)–symmetric basis states. This points to the possibility of achieving convergence of higher–lying collective modes and reaching heavier nuclei by expanding the NCSM basis space beyond its current limits through Sp(3,R) basis states. Furthermore, the symplectic symmetry is found to be favored by the JISP16 and CD–Bonn realistic nucleon–nucleon interactions, which points to a more fundamental origin of the symplectic symmetry.

Keywords: Shell model; nucleon–nucleon interactions; models based on group theory.

Resumen

En el presente trabajo se confirma la importancia de la simetría simpléctica Sp(3,R) en la dinámica nuclear a través de estudios de interacciones nucleón–nucleón realistas así como de eigenestados calculados en el marco del modelo de capas sin carozo (NCSM, por sus siglas en inglés). Los resultados demuestran para núcleos ligeros un gran traslapo entre la funciones de onda NCSM usando nada más los estados base con simetría Sp(3,R) con mayor deformación, lo cual abre la posibilidad para obtener convergencia de modos colectivos con energías altas y poder describir nucleos más pesados con una extensión del espacio de los estados base NCSM usando estados con simetría Sp(3,R). Además, las interacciones nucleón–nucleón realistas JISP16 y CD–Bonn favorecen la simetría simpléctica lo cual apunta a una explicación a nivel mas fundamental de la simetría simpléctica.

Descriptores: Modelo de capas; interacciones nucleón–nucleón; modelos con base en teoría de grupos.

PACS: 21.60.Cs; 13.75.Cs; 21.60.Fw

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Acknowledgments

Discussions with Bruce R. Barrett are gratefully acknowledged. This work was supported by the US National Science Foundation, Grants 0140300 and 0500291, and the Southeastern Universities Research Association, as well as, in part, by the US Department of Energy Grant DE–FG02–87ER40371. T.D. acknowledges supplemental support from the Graduate School of Louisiana State University.

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