Analytical expressions for electromagnetic transition rates in the SU(3) limit of thespdfinteracting boson model

Abstract

Collective negative parity states are believed to be related to octupole degrees of freedom in the nucleus in the geometrical model @1#. In the algebraic model, their description is the interacting boson model ~IBM! including s, p, d, and f bosons @2‐7#. One advantage of the algebraic model is the availability of analytical expressions for many physical quantities. The SU~3! limit describes a rotational spectrum @3‐5#. Analytical expressions for the energy can be written explicitly in terms of the Casimir operators of the corresponding group chain. Besides the energy spectrum, electromagnetic transition properties are important in determining the structure of a nucleus. In the sd-IBM, electromagnetic transition rates are obtained analytically @6,8#. Numerical studies have shown that the low-lying positive parity states are well-described by Ns dbosons, and the low-lying negative parity states are well described by coupling one pf boson with N21 sd bosons. In this limit, the sd bosons and pf bosons interact only via the quadrupole interaction. This is the weak correlation case. In this study, we adopt this assumption. In the strong correlation, sd bosons and pf bosons interact strongly, and the pf bosons and sd bosons are mixed strongly. Lac and Morrison @9# have derived analytical expressions in the strong correlation case using the 1/ N expansion technique. It is the purpose of this paper to give analytical expressions of E1, E2, E3, M1, and M2 transition rates involving low-lying negative parity states in the SU(3) sd 3SU(3) pf limit. The paper is organized as follows. In Sec. II, we give a brief description of the method of the calculation. In Sec. III we give the results. In Sec. IV we apply the results to some deformed nuclei. In Sec. V we give a brief summary.