This paper tests how well a relatively cheap nuclear theory method can predict electromagnetic properties of light nuclei. The authors compare angular-momentum projected-after-variation Hartree–Fock (PHF) calculations to full configuration-interaction (FCI) results computed in the same shell-model spaces and with the same interaction matrix elements. They focus on two common observables: electric quadrupole (E2) moments and transitions, which probe charge shape, and magnetic dipole (M1) moments and transitions, which probe spin and orbital motion.

Hartree–Fock (HF) builds a single Slater determinant — a simple product of single-particle states — and then varies those single-particle states to lower the energy. That determinant typically breaks symmetries such as total angular momentum. The authors restore angular momentum by projecting the HF state onto states with good total angular momentum. Full configuration-interaction (FCI) is a much more expensive calculation that mixes all allowed Slater determinants in the chosen valence space and serves here as the benchmark of exact results within the model space. Both PHF and FCI results were run in the same model spaces so the comparison is fair; FCI results were obtained with the BIGSTICK code.

The study looks at selected cases in the sd and pf valence spaces. For the sd-shell examples they used a frozen 16O core with valence orbitals 1s1/2, 0d3/2 and 0d5/2 and the USDB interaction. For E2 observables they used standard effective charges (proton ep = 1.5 e, neutron en = 0.5 e) and set the oscillator parameter b ≈ 1.0 A1/6 fm. For M1 they used bare orbital g-factors gl = 1 e for protons and 0 for neutrons, and spin g-factors gs = 5.5857 µN for protons and −3.2863 µN for neutrons (µN is the nuclear magneton). The workflow computes one-body density matrices from each method and then computes moments and transition strengths from those densities.