Isospin dependence of electric-transition probabilities B (E2) in the unitary scheme
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CLEI Theory
Isospin Dependence of Electric-Transition Probabilities B(Е2) in the Unitary Scheme K. I. Yankauskas*, L. A. Vasiljeva, and A. K. Petrauskas Klaipeda University, Herkaus Manto g. 84, LT-92294 Klaipeda, Lithuania Received December 11, 2008
Abstract—In a physical basis of the unitary scheme, analytic formulas for the probabilities B(E2κL → κ L ) and their isospin factors for the (λ0) and (λ2) representations of the SU (3) group were obtained for even–even nuclei. It was shown that the isospin correction must be taken into account at low L and in the case of off-diagonal transitions in κ. The results obtained in the unitary scheme are compared with the results of other models and with experimental data. At high L, the transition probabilities B(E2κL → κ L ) are markedly smaller in the unitary scheme than in the rotational model, while, for L λ, these probabilities in the unitary scheme and in the rotational model are close. PACS numbers: 21.10.Ky, 21.60.Cs, 21.60.Fw, 23.20.Lv DOI: 10.1134/S106377880909004X
1. INTRODUCTION In [1], a formula for calculating electric moments of nuclei in the basis of the SU (3) model was obtained for T = 0 states. It was also shown there that the operator of the quadrupole moment of a nucleus for T = 0 states featuring a minimum number of quanta, Emin , can be replaced by an SU (3) generator. For that part of the electric-quadrupole-moment operator which is symmetric under permutations of orbital coordinates (mass moment), an expansion in irreducible SU (3) components was obtained in [2], and expressions for transition probabilities B(E2) were given there for the (λ0) representation at T = 0. In [3], the probabilities B(E2) for T = 0 states were studied in the case of the (λ2) representation by using the results reported in [1, 4, 5]. However, the mass tensor operator was actually used in all of the aforementioned studies instead of the quadrupolemoment operator—that is, the isospin dependence of this operator was disregarded. An explicit expression for the matrix element of the electric quadrupole moment with allowance for the isospin dependence was given in [6, 7]. By using the results obtained in [7], the calculation of B(E2) in the orthogonal scheme [the case of symmetric representations of the O(A − 1) group] was considered in [8]. The present study is a continuation of those that were reported in [6–8]. Its objective is to derive analytic formulas for the transition probabilities B(E2) in the physical basis of the unitary scheme for states *
characterized by the (λ0) and (λ2) representations with allowance for isospin corrections, to study the dependence of the isospin factor on the quantum numbers of the unitary scheme, and to perform a comparison with other models. {We define a physical basis as that which is characterized by the most symmetric Young diagram of the S(A) group and by the quantum numbers of the SU (3) group that correspond to the largest eigenvalues of the Casimir operator [6].} 2. DEFINITIONS AND BASIC FORMULAS According to formulas (1.160) and (
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