The closed shell structure at $N=Z=28\mathrm{}$ is studied by a large-scale shell model calculation by the quantum Monte Carlo diagonalization method. Latest crucial improvements of the method are described. The doubly closed shell probability of ${}^{56}\mathrm{Ni}$ is shown to be only $49\%$ in a full $\mathrm{pf}$ shell calculation, in contrast to the corresponding probability of ${}^{48}\mathrm{Ca}$ which reaches $86\%$.

• Received 2 September 1997

DOI:https://doi.org/10.1103/PhysRevLett.81.1588