Pair-truncated shell-model approach to the mass $A\sim 130$ region

There exist two prominent features in even-even nuclei in the mass $A\sim 130$ region. First, low-lying states of these nuclei exhibit the $\gamma$ instability, which manifests in the energy staggering of even-odd spin states in the quasi-$\gamma$ bands and also in some forbidden $E2$ interband transition rates. Second, at high-spins yrast bands of these nuclei show anomalous behavior, the so-called backbending phenomenon. It arises due to band crossing between the ground-state band and s band originating from the alignment of two neutrons in the $0h_{11/2}$ orbital. For a description of both the low-lying states and backbending phenomena, we proposed a new version of the pair-truncated shell model, where the even-even nuclear states were constructed from angular momenta zero ($S$), two ($D$) and four ($G$) collective pairs, and non-collective $H$ pairs, which were made by two nucleons in the $0h_{11/2}$ orbitals. The model was applied to the even-even nuclei in this mass region, and reproduced well experimental energy spectra and electromagnetic properties.