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Spin-isospin SU(4) symmetry in sd- and fp-shell nuclei

Vogel, P. and Ormand, W. E. (1993) Spin-isospin SU(4) symmetry in sd- and fp-shell nuclei. Physical Review C, 47 (2). pp. 623-628. ISSN 0556-2813. doi:10.1103/PhysRevC.47.623.

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For all even-A nuclei in the sd shell we evaluate the overlap between several low-lying states, obtained by diagonalizing the realistic Wildenthal interaction, and the eigenstates of the SU(4) Casimir operator. We find that the J=0+ ground states of even-even nuclei near the middle of the shell have rather small overlaps (less than 0.5) with the lowest SU(4) Young tableaux, while the J=0+ and 1+ lowest states of odd-odd nuclei have noticeably larger overlaps (0.6–0.7). We also find that the expansion in the SU(4) Young tableaux converges quite rapidly, and that the two or three lowest tableaux usually account for more than 90% of the nuclear wave function. We then extend the calculation to the fp shell and evaluate the overlaps between the J=0+ ground states obtained by diagonalizing a realistic interaction and the SU(4) eigenstates for even-even nuclei with maximum isospin. For the fp shell the overlaps are even smaller than in the sd shell. Since we observe such sizable SU(4) symmetry breaking effects in the relatively simple sd and pf nuclei, we are rather pessimistic about the prospects of using conclusions based on SU(4) in heavier, more complex nuclei.

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Vogel, P.0000-0003-0587-5466
Additional Information:©1993 The American Physical Society Received 27 August 1992 We would like to thank Prof. Jiři Patera for generous help with evaluation of the decomposition of the SU(6) group representations. W.E.O. acknowledges the Weingart Foundation for financial support. This work was supported in part by the U.S. Department of Energy under Contract No. DE-F603-88ER-40397 and by National Science Foundation Grant No. PHY91-15574.
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Deposited On:25 May 2006
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