  We investigate the order-by-order convergence behavior of many-body
perturbation theory (MBPT) as a simple and efficient tool to approximate the
ground-state energy of closed-shell nuclei. To address the convergence
properties directly, we explore perturbative corrections up to 30th order and
highlight the role of the partitioning for convergence. The use of a simple
Hartree-Fock solution to construct the unperturbed basis leads to a convergent
MBPT series for soft interactions, in contrast to, e.g., a harmonic oscillator
basis. For larger model spaces and heavier nuclei, where a direct high-order
MBPT calculation in not feasible, we perform third-order calculation and
compare to advanced ab initio coupled-cluster calculations for the same
interactions and model spaces. We demonstrate that third-order MBPT provides
ground-state energies for nuclei up into tin isotopic chain that are in
excellent agreement with the best available coupled-cluster results at a
fraction of the computational cost.
