Description of light nuclei in pionless effective field theory using the stochastic variational method

TL;DR

This paper develops a pionless effective field theory with a Gaussian regulator and uses the stochastic variational method to accurately describe light nuclei up to helium-4, including charge-symmetry breaking effects.

Contribution

It introduces a coordinate-space potential based on pionless EFT and demonstrates its effectiveness in modeling light nuclei using the stochastic variational method.

Findings

Good agreement with empirical data within estimated uncertainty

Successful fitting of three-body parameters to binding energies

Effective description of charge radii for helium isotopes

Abstract

We construct a coordinate-space potential based on pionless effective field theory with a Gaussian regulator. Charge-symmetry breaking is included through the Coulomb potential and through two- and three-body contact interactions. Starting with the effective field theory potential, we apply the stochastic variational method to determine the ground states of nuclei with mass number $A\leq 4$. At next-to-next-to-leading order, two out of three independent three-body parameters can be fitted to the three-body binding energies. To fix the remaining one, we look for a simultaneous description of the binding energy of $^4$He and the charge radii of $^3$He and $^4$He. We show that at the order considered we can find an acceptable solution, within the uncertainty of the expansion. We find that the EFT expansion shows good agreement with empirical data within the estimated uncertainty, even for a system as dense as $^4$He.