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

TL;DR

This paper investigates how large regularization cutoffs in chiral effective field theory affect nuclear properties in Hartree-Fock calculations, revealing issues with spurious bound states and cutoff sensitivity.

Contribution

It demonstrates that high cutoff values lead to spurious bound states in Hartree-Fock calculations with leading-order chiral potentials, limiting their reliability as reference states.

Findings

Cutoff effects cause strong sensitivity to counter-terms in attractive singular partial waves.

High cutoffs can induce spurious deeply bound states, affecting bound solutions.

Partial corrections for spurious states are possible but full correction remains challenging.

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 $^3S_1$ 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 $^3D_2$ channel, with energy shifts of the order of or somewhat larger than those recommended in Phys. Rev. C 103, 054304 (2021), is possible.