  We apply degenerate many-body perturbation theory at high orders for the
ab-initio description of ground states and excitation spectra of open-shell
nuclei using soft realistic nucleon-nucleon interactions. We derive a recursive
formulation of standard degenerate many-body perturbation theory that enables
us to evaluate order-by-order perturbative energy and state corrections up to
the 30th order. We study 6,7-Li as test cases using a similarity
renormalization group (SRG) evolved nucleon-nucleon interaction from chiral
effective field theory. The simple perturbation series exhibits a strong, often
oscillatory divergence, as was observed previously for ground states of
closed-shell nuclei. Even for very soft interactions resulting from SRG
evolutions up to large flow parameter, i.e. low momentum scales, the
perturbation series still diverges. However, a resummation of the perturbation
series via Pad\'e approximants yields very stable and converged ground and
excited-state energies in very good agreement with exact no-core shell-model
calculations for the same model space.
