Hartree-Fock Many-Body Perturbation Theory for Nuclear Ground-States

Abstract

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.

arXiv comment6 pages, 5 figures, 1 table

References in corpus (27)

• Accurate Charge-Dependent Nucleon-Nucleon Potential at Fourth Order of Chiral Perturbation Theory
• Similarity Renormalization Group for Nucleon-Nucleon Interactions
• Ab Initio Calculations of Medium-Mass Nuclei with Normal-Ordered Chiral NN+3N Interactions
• Local three-nucleon interaction from chiral effective field theory
• In-Medium Similarity Renormalization Group for Nuclei
• Similarity-Transformed Chiral NN+3N Interactions for the Ab Initio Description of 12-C and 16-O
• Ab initio coupled-cluster approach to nuclear structure with modern nucleon-nucleon interactions
• In-Medium Similarity Renormalization Group with Chiral Two- Plus Three-Nucleon Interactions
• Ab Initio Path to Heavy Nuclei
• Leading chiral three-nucleon forces along isotope chains in the calcium region
• Isotopic chains around oxygen from evolved chiral two- and three-nucleon interactions
• Ab-initio Gorkov-Green's function calculations of open-shell nuclei
• Coupled cluster calculations of ground and excited states of nuclei
• The Magnus expansion and the in-medium similarity renormalization group
• Coupled cluster approach to nuclear physics
• Ab Initio Multi-Reference In-Medium Similarity Renormalization Group Calculations of Even Calcium and Nickel Isotopes
• Hartree-Fock and Many-Body Perturbation Theory with Correlated Realistic NN-Interactions
• Evolved Chiral NN+3N Hamiltonians for Ab Initio Nuclear Structure Calculations
• P-shell nuclei using Similarity Renormalization Group evolved three-nucleon interactions
• Ab Initio Calculations of Medium-Mass Nuclei with Explicit Chiral 3N Interactions
• Unitary Correlation Operator Method and Similarity Renormalization Group: Connections and Differences
• Convergence of the Born Series with Low-Momentum Interactions
• The Unitary Correlation Operator Method from a Similarity Renormalization Group Perspective
• Pade-resummed high-order perturbation theory for nuclear structure calculations
• On the Divergence of Perturbation Theory. Steps Towards a Convergent Series
• Spectra of Open-Shell Nuclei with Padé-Resummed Degenerate Perturbation Theory
• Weinberg Eigenvalues and Pairing with Low-Momentum Potentials

Cited by in corpus (46)

• A Guided Tour of Ab Initio Nuclear Many-Body Theory
• Non-Empirical Interactions for the Nuclear Shell Model: An Update
• Three-Nucleon Forces: Implementation and Applications to Atomic Nuclei and Dense Matter
• Converged ab initio calculations of heavy nuclei
• Bogoliubov Many-Body Perturbation Theory for Open-Shell Nuclei
• Ab initio electromagnetic observables with the in-medium similarity renormalization group
• Self-consistent Green's function theory for atomic nuclei
• Towards grounding nuclear physics in QCD
• In-Medium Similarity Renormalization Group for Closed and Open-Shell Nuclei
• Angular-momentum projection in coupled-cluster theory: structure of ${}^{34}$Mg
• In-medium similarity renormalization group with three-body operators
• Natural orbitals for ab initio no-core shell model calculations
• Probing chiral interactions up to next-to-next-to-next-to-leading order in medium-mass nuclei
• Improved many-body expansions from eigenvector continuation
• Neutron matter at finite temperature based on chiral effective field theory interactions
• $Ab$ $initio$ nuclear many-body perturbation calculations in the Hartree-Fock basis
• ADG: Automated generation and evaluation of many-body diagrams I. Bogoliubov many-body perturbation theory
• Accessing ground state and excited states energies in many-body system after symmetry restoration using quantum computers
• Weinberg eigenvalues for chiral nucleon-nucleon interactions
• Eigenvector Continuation and Projection-Based Emulators
• Open-Shell Nuclei from No-Core Shell Model with Perturbative Improvement
• Effective density functionals beyond mean field
• Natural orbitals for many-body expansion methods
• Bogoliubov many-body perturbation theory under constraint
• Towards heavy-mass ab initio nuclear structure: Open-shell Ca, Ni and Sn isotopes from Bogoliubov coupled-cluster theory
• In-Medium Similarity Renormalization Group Approach to the Nuclear Many-Body Problem
• Symmetry-projected variational calculations with the numerical suite TAURUS I. Variation after particle-number projection
• Pre-processing the nuclear many-body problem: Importance truncation versus tensor factorization techniques
• Excited states from eigenvector continuation: the anharmonic oscillator
• Deformed in-medium similarity renormalization group
• Tensor-decomposition techniques for ab initio nuclear structure calculations. From chiral nuclear potentials to ground-state energies
• Nuclear Structure from the In-Medium Similarity Renormalization Group
• Second-Order Perturbation Theory in Continuum Quantum Monte Carlo Calculations
• Ground-state properties of doubly magic nuclei from the unitary-model-operator approach with the chiral two- and three-nucleon forces
• Importance truncation in non-perturbative many-body techniques
• From the liquid drop model to lattice QCD
• Impact of correlations on nuclear binding energies
• Least-square approach for singular value decompositions of scattering problems
• Renormalization of pionless effective field theory in the A-body sector
• Estimates and power counting in uniform matter with softened interactions
• Bayesian approach for many-body uncertainties in nuclear structure: Many-body perturbation theory for finite nuclei
• Importance truncation for the in-medium similarity renormalization group
• Modewise Johnson-Lindenstrauss Embeddings for Nuclear Many-Body Theory
• Randomized Low-Rank Decompositions of Nuclear Three-Body Interactions
• Ab initio Bogoliubov many-body perturbation theory: closed-form constraint on the average particle number
• Many-body perturbation theory for strongly correlated effective Hamiltonians using effective field theory methods