Spectra of Open-Shell Nuclei with Padé-Resummed Degenerate Perturbation Theory

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 Padé 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.

arXiv comment8 pages, 4 figures; minor changes to match published version

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• Reduced regulator dependence of neutron-matter predictions with chiral interactions
• New applications of renormalization group methods in nuclear physics
• Hartree-Fock Many-Body Perturbation Theory for Nuclear Ground-States
• In-Medium Similarity Renormalization Group for Closed and Open-Shell Nuclei
• Improved many-body expansions from eigenvector continuation
• Open-Shell Nuclei from No-Core Shell Model with Perturbative Improvement
• Effective density functionals beyond mean field
• Normal-ordered $k$-body approximation in particle-number-breaking theories
• Pre-processing the nuclear many-body problem: Importance truncation versus tensor factorization techniques
• Importance truncation in non-perturbative many-body techniques
• Impact of correlations on nuclear binding energies
• Giant Resonances based on Unitarily Transformed Two-Nucleon plus Phenomenological Three-Nucleon Interactions
• Modewise Johnson-Lindenstrauss Embeddings for Nuclear Many-Body Theory
• Many-body perturbation theory for strongly correlated effective Hamiltonians using effective field theory methods