The nuclear shell model with a second-order effective Hamiltonian derived within Brueckner theory from the free nucleon-nucleon interaction is shown to yield accurate binding energies of nuclei with $16<A<\mathrm{}40\mathrm{}$. This agreement is obtained by choosing the spectrum of low-lying unoccupied orbitals in a justified manner and, when necessary, by employing a statistical method to approximate the lowest eigenvalue of very large shell-model diagonalizations.

• Received 28 February 1977

DOI:https://doi.org/10.1103/PhysRevLett.38.1348