Exponential convergence method: Nonyrast states, occupation numbers, and a shell-model description of the superdeformed band in ${}^{56}\mathrm{Ni}$

We suggested earlier that the energies of low-lying states in large shell-model spaces converge to their exact values exponentially as a function of the dimension in progressive truncation. An algorithm based on this exponential convergence method was proposed and successfully used for describing the ground state energies in the lowest $|\Delta \left(N-Z\right)|$ nuclides from ${}^{42}\mathrm{Ca}$ to ${}^{56}\mathrm{Ni}$ using the $\mathrm{fp}$-shell model and the FPD6 interaction. We extend this algorithm to describe nonyrast states, especially those that exhibit a large collectivity, such as the superdeformed band in ${}^{56}\mathrm{Ni}.$ We also show that a similar algorithm can be used to calculate expectation values of observables, such as single-particle occupation probabilities.