The role of the intrinsic E2 matrix element between the first two 0 + states in their configuration mixing in 100Zr

Abstract

Shape coexistence in 100Zr is a well-known phenomenon. However, a consistent description of the configuration mixing between two shapes with very different deformation has not been made. In this work, the B(E2,2 + 2→0 + 2) value in 100Zr has been inferred from the known γ-ray branching ratios between the intraband transition and the interband transitions to members of the ground-state band. The absolute scale of the latter was established under the assumption that adjustments to the interband transitions due to the coupling between the rotation and intrinsic motions can be approximated by a perturbation expansion of angular-momentum dependence. Correction terms up to the second order, which account for the deformation difference between two 0 + bands, were considered in the description. The intrinsic E2 matrix elements for the second 0 + state at 331 keV is derived to be ≈0.53 eb from the B(E2,2 + 2→0 + 2) value assuming a rotational relationship. This suggests that the weakly deformed 0 + 2 state coexists with the strongly deformed ground state of 〈0 1|E2|0 1〉≈1.06 eb. Configuration mixing between the two 0 + states has been studied using both the known E0 and the intrinsic E2 matrix elements derived from this work. A weak mixing of ≈7.7% was found, which is nearly a factor of two lower than suggested by a previous analysis. Quantitative evidence of the energy shift for the ground state, deduced from the systematics of transition energies for the yrast states, is consistent with this weak mixing scenario. Near-spherical and well-deformed shapes with the intrinsic E2 matrix elements of ≈0.37 eb and ≈1.14 eb, respectively, are identified as the basis states before the mixing takes place. The intrinsic E2 matrix element between those two unperturbed 0 + states, ≈0.19 eb, is required to describe their configuration mixing.