Abstract
We study the validity of pair truncation of the nuclear shell model by using the semimagic nucleus $^{46}\mathrm{Ca}$. We present low-lying states and their $E2$ transition rates based on both nucleon pair approximation (NPA) and exact shell-model (SM) calculations. We also calculate overlaps between wave functions of low-lying states calculated by using the NPA and those calculated by using the SM. Our calculated results show a remarkable agreement between the NPA results and the SM results, although the NPA is a drastic truncation of the SM.
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