Symmetric and antisymmetric states: A general feature of two-component systems.

Abstract

It is shown that in both the nuclear shell model, considering explicitly proton and neutron degrees of freedom (seniority scheme), and in particle-core coupling model calculations, ${2}^{+}$ levels with symmetric and antisymmetric character in the constituent unperturbed basis result. Besides the excitation energy for such ${2}^{+}$ levels, the E2 decay properties also are studied. Constructive and destructive interference between the two distinct E2 matrix elements results for the ${2}_{1}^{+}$ (symmetric) and ${2}_{2}^{+}$ (antisymmetric) levels, respectively. Applications are shown for the Cd (Z=48) and the N=84 nuclei.