Applying the exponential convergence method: Shell-model binding energies of ${0f}_{7/2}$ nuclei relative to ${}^{40}\mathrm{Ca}$

It was suggested earlier that, due to the statistical properties of complicated many-body dynamics, the energies of low-lying nuclear states in large shell model spaces converge to their exact values exponentially as a function of the dimension in progressive truncation. Applying the exponential convergence algorithm as a practical method of extrapolation we calculated ground-state energies, spins, and isospins of 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. The binding energies relative to ${}^{40}\mathrm{Ca}$ are compared with the experimental values. The deviation can be accounted by adding monopole terms to the single-particle energies and two-body matrix elements.