  A strong effort will be dedicated in the coming years to extend the reach of
ab initio nuclear-structure calculations to heavy doubly open-shell nuclei. In
order to do so, the most efficient strategies to incorporate dominant many-body
correlations at play in such nuclei must be identified. With this motivation in
mind, the present work pedagogically analyses the inclusion of many-body
correlations and their impact on binding energies of Calcium and Chromium
isotopes. Employing an empirically-optimal Hamiltonian built from chiral
effective field theory, binding energies along both isotopic chains are studied
via a hierarchy of approximations based on polynomially-scaling expansion
many-body methods. The corresponding results are compared to experimental data
and to those obtained via valence-space in-medium similarity renormalization
group calculations at the normal-ordered two-body level that act as a reference
in the present study. The spherical mean-field approximation is shown to
display specific shortcomings in Ca isotopes that can be understood
analytically and that are efficiently corrected via the consistent addition of
low-order dynamical correlations on top of it. While the same setting cannot
appropriately reproduce binding energies in doubly open-shell Cr isotopes,
allowing the unperturbed mean-field state to break rotational symmetry permits
to efficiently capture the static correlations responsible for the
phenomenological differences observed between the two isotopic chains.
Eventually, the present work demonstrates in a pedagogical way that
polynomially-scaling expansion methods based on unperturbed states that
possibly break (and restore) symmetries constitute an optimal route to extend
ab initio calculations to heavy closed- and open-shell nuclei.
