Once the Hartree-Fock equations are solved, the Fock matrix (4) becomes diagonal, and its diagonal elements can be viewed as single-particle energies. Hopefully, there is a clear gap in the single-particle spectrum at the Fermi surface, i.e. after \( N \) orbitals are filled.
If symmetry-restricted Hartree-Fock is used, one is limited to compute systems with closed subshells for neutrons and for protons. On a first view, this might seem as a severe limitation. But is it?