Mixed Symmetry Nuclear Shell Model

A mixed-symmetry nuclear shell-model scheme for carrying out calculations in regimes where there is a competition between two or more modes is proposed. A one-dimensional toy model is used to demonstrate the concept. The theory is then applied to 24Mg and 44T i. For lower pf -shell nuclei such as 44−48T i and 48Cr there is strong SU(3) symmetry breaking due to the spin-orbit interaction. However, the quadrupole collectivity as measured by B(E2) transition strengths in the yrast band remain high even though SU(3) appears to be broken. Some results for the so-called X(5) symmetry that falls along the U(5) ↔ SU(3) leg of the Interacting Boson Model are also considered. The results show that the mixed-symmetry concept is effective, even when strong symmetry breaking occurs. 1 The Mixed-Mode Concept Two dominant and often competing modes characterize the structure of atomic nuclei. One is the single-particle structure that is demonstrated by the ∗On leave of absence from Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia 1784, Bulgaria.