Spectra of Open-Shell Nuclei with Pad\'e-Resummed Degenerate Perturbation Theory

TL;DR

This paper develops a high-order degenerate perturbation theory approach with Padé resummation to accurately compute ground and excited states of open-shell nuclei, overcoming divergence issues in traditional series.

Contribution

It introduces a recursive formulation for high-order degenerate perturbation theory and demonstrates effective Padé resummation for nuclear spectra calculations.

Findings

Padé resummation stabilizes divergent perturbation series.

Accurate energies match no-core shell-model results.

Method effective for soft chiral EFT interactions.

Abstract

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.