We study extrapolation approaches to evaluate energies of low-lying states for nuclei in the $\mathit{sd}$ and $\mathit{pf}$ shells, by sorting the diagonal matrix elements of the nuclear shell-model Hamiltonian. We introduce an extrapolation method with perturbation and apply our new method to predict both low-lying state energies and $E2$ transition rates between low-lying states. Our predicted results arrive at an accuracy of the root-mean-squared deviations $~40$–60 keV for low-lying states of these nuclei.

• Received 22 February 2011

DOI:https://doi.org/10.1103/PhysRevC.83.044322