Padé-resummed high-order perturbation theory for nuclear structure calculations

We apply high-order many-body perturbation theory for the calculation of ground-state energies of closed-shell nuclei using realistic nuclear interactions. Using a simple recursive formulation, we compute the perturbative energy contributions up to 30th order and compare to exact no-core shell model calculations for the same model space and Hamiltonian. Generally, finite partial sums of this perturbation series do not show convergence with increasing order, but tend to diverge exponentially. Nevertheless, through a simple resummation via Padé approximants it is possible to extract rapidly converging and highly accurate results for the ground-state energy once perturbative contributions beyond 5th order are included.