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

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.