Improved Actions for Nuclear Effective Field Theories

TL;DR

This paper introduces an improved action method for nuclear effective field theories that uses a fake interaction range at leading order to stabilize calculations for larger nuclei, enhancing convergence and accuracy.

Contribution

It proposes a novel fake interaction range at leading order in EFTs, addressing instabilities and improving calculations for larger nuclei.

Findings

Fake range does not affect EFT convergence when comparable to experimental effective range.

The approach benefits calculations at the lowest orders.

Implications for ground-state energies of various nuclei are discussed.

Abstract

Effective field theories have been successful in describing nuclei up to the alpha particle but face significant challenges for larger nuclei due to leading-order instabilities. These issues can be addressed with the introduction of a fake interaction range at leading order, whose effects are compensated for in perturbation theory at higher orders. The calculation of two-body phase shifts and ground-state energies for up to five $^4$He atoms in a theory with only contact interactions shows that, as long as it remains smaller or comparable to the experimental effective range, the fake range does not alter the convergence of the EFT expansion but is often beneficial at the lowest orders. I discuss the implications of this improved-action approach to the ground-state energies of nuclei such as $^6$Li, $^{12}$C, and $^{16}$O.