Exponential convergence method: Nonyrast states, occupation numbers, and a shell-model description of the superdeformed band in ⁵⁶Ni

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 |Δ(N-Z)| nuclides from ⁴²Ca to ⁵⁶Ni using the 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 ⁵⁶Ni. We also show that a similar algorithm can be used to calculate expectation values of observables, such as single-particle occupation probabilities.