O(36) Symmetry Limit of IBM-4 with Good s, d, and sd Boson Spin–Isospin Wigner's SU(4)∼O(6) Symmetries for N≈Z Odd–Odd Nuclei

Abstract

Led by the current interest in nuclear structure experiments at the N=Z line and the problem of competing isospin T=0 and T=1 pairing modes in such nuclei, it has become important to investigate the properties of the spin–isospin invariant interacting boson model (IBM-4) of Elliott and White. Following this, in the present work the IBM-4 OsdST(36)⊃OSsTs(6)⊕OdST(30)⊃OL(3)⊕OST(6) symmetry limit with not only good sd boson spin–isospin O(6) symmetry but also good s and d boson space O(6) symmetries (i.e., Wigner's spin–isospin SU(4)'s) is identified and analyzed. This symmetry limit is expected to carry signatures typical of some heavy (proton-rich) N≈Z odd–odd nuclei. For this symmetry limit group chain, irrep labels, group generators, quadratic Casimir operators, and energy formula are given. Both in the symmetry limit and allowing for mixing, the number of T=0 pairs in the ground states as a function of boson number and isospin is studied for N=Z nuclei and the results are consistent with known shell model predictions. For N=Z odd–odd nuclei, in the symmetry limit analytical formulas are derived for B(E2)'s in low-lying levels (with O(36) quantum number ω=N, where N is boson number) and also for the yrast band with (ST)=(01) (say as in 74Rb). It is seen that the pattern of B(E2)'s in low-lying levels depend sensitively on the structure of the E2 operator with respect to OST(6) and the symmetry limit generates a isospin dictated ΔJ=4 staggering in (ST)=(01) yrast B(E2)'s. Finally, it is shown that two-nucleon transfer strengths from even–even to odd–odd N=Z nuclei give information about high-lying states with O(36) quantum number ω=N−2.