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Symplectic group structure of the 48Cr, 88Ru, and 92Pd ground states

The ground states of 48Cr, 88Ru, and 92Pd are studied in the 1f7/2 or 1g9/2 shell model with effective interactions from the literature. They are found to be composed, quite independently of the shell and the interaction, roughly of 75% of (s,t)=(0,0) and 25% of (s,t)=(4,0), where s is the seniority and t the reduced isospin. Other irreps of the symplectic group Sp(2j+1), where j is the single-nucleon angular momentum, make only very small contributions. The state chi obtained by antisymmetriziation and normalization of the ground state in the stretch scheme of Danos and Gillet [M. Danos and V. Gillet, Phys. Rev. 161, 1034 (1967)] has a very different structure where the Sp(2j+1) irreps other than (s,t)=(0,0) and (4,0) contribute 20% and 41% for j=7/2 and 9/2, respectively. The contributions of chi and the s=0 state to the calculated ground states state are about equal for 48Cr. For 88Ru and 92Pd the s=0 state is unambiguously a better approximation to the calculated states than chi. A state chi' obtained by antisymmetrization and normalization of the product of two stretch-scheme ground states of the system with two valence nucleons or nucleon holes of each type has much larger overlaps with the calculated ground states than chi but a deviating Sp(2j+1) decomposition.