Cutoff effects in Hartree-Fock calculations at leading order of chiral effective field theory

Abstract

We explore the effects on nuclear bulk properties of using regularization cutoffs larger than the nucleon mass within the chiral effective field theory with a power counting that ensures order-by-order renormalization in the two-nucleon system. To do so we calculate ground-state properties of the ${}^{16}$O nucleus in the Hartree--Fock approach in a basis made up of plane waves confined in a cube. We find that regularization cutoff effects manifest themselves in two distinct ways: a strong sensitivity to the the counter-terms in attractive singular partial waves (related to the sign of the corresponding low-energy constant) and to the correction for spurious deeply bound states (for high enough cutoffs). In fact the latter happens to deprive the Hartree--Fock approximation of yielding bound solutions in nuclei. We conclude that, when using a leading-order chiral potential in the Nogga--Timmermans--van Kolck's power counting (with a regularization cutoff higher than the nucleon mass), one cannot produce a selfconsistent mean field free of spurious bound-state effects that can serve as a reference state for beyond-mean-field methods. For high regularization cutoffs which yield an attractive ${}^3{S}_1$ contact potential, one can at best incorporate in the mean-field solution a partial correction for spurious bound states. Then the remaining correction has to be added to the residual interaction in a treatment beyond the Hartree--Fock approximation. In fact a ``full'' correction in the ${}^3{D}_2$ channel, with energy shifts of the order of or somewhat larger than those recommended in Phys. Rev. C 103, 054304 (2021), is possible.

arXiv commentResubmitted to Physical Review C. Thoroughly revised version

References in corpus (31)

• Chiral effective field theory and nuclear forces
• Coupled-cluster computations of atomic nuclei
• The In-Medium Similarity Renormalization Group: A Novel Ab Initio Method for Nuclei
• Renormalization of One-Pion Exchange and Power Counting
• Discrepancy between experimental and theoretical $\beta$-decay rates resolved from first principles
• A nucleus-dependent valence-space approach to nuclear structure
• A Guided Tour of Ab Initio Nuclear Many-Body Theory
• In-Medium Similarity Renormalization Group for Nuclei
• Power counting with one-pion exchange
• Novel chiral Hamiltonian and observables in light and medium-mass nuclei
• Ab-initio self-consistent Gorkov-Green's function calculations of semi-magic nuclei - I. Formalism at second order with a two-nucleon interaction
• Light nuclei with semilocal momentum-space regularized chiral interactions up to third order
• Bogoliubov Many-Body Perturbation Theory for Open-Shell Nuclei
• On the renormalization of the one-pion exchange potential and the consistency of Weinberg's power counting
• Multi-reference many-body perturbation theory for nuclei III -- Ab initio calculations at second order in PGCM-PT
• Projection on particle number and angular momentum: Example of triaxial Bogoliubov quasiparticle states
• How (not) to renormalize integral equations with singular potentials in effective field theory
• A New Look into the Partial Wave Decomposition of Three-Nucleon Forces
• Power Counting in Peripheral Partial Waves: The Singlet Channels
• The Two-Nucleon 1S0 Amplitude Zero in Chiral Effective Field Theory
• Power counting in chiral effective field theory and nuclear binding
• Perturbative $NN$ scattering in chiral effective field theory
• Renormalization of the leading-order chiral nucleon-nucleon interaction and bulk properties of nuclear matter
• Moving away from singly-magic nuclei with Gorkov Green's function theory
• Decoupling of Spurious Deep Bound States with the Similarity Renormalization Group
• Power counting for nuclear forces in chiral effective field theory
• Comment on "How (not) to renormalize integral equations with singular potentials in effective field theory"
• Reply to "Comment on "How (not) to renormalize integral equations with singular potentials in effective field theory"
• Improved description of light nuclei through chiral effective field theory at leading order
• Tri-axial deformation in nuclei with realistic NN interactions
• How to renormalize coupled cluster theory