Universal Correlations in Pion-less EFT with the Resonating Group Model: Three, Four, and Six Nucleons

TL;DR

This paper applies pion-less effective field theory to nuclei with up to six nucleons, demonstrating its convergence and predictive power for correlations, binding energies, and scattering properties, with implications for nuclear theory.

Contribution

It provides the first systematic application of pion-less EFT to nuclei with up to six nucleons, showing convergence and renormalization without four-body forces at leading and next-to-leading order.

Findings

EFT converges rapidly with an expansion parameter of about 1/3.

Results agree with data within predicted uncertainty bands.

Proper renormalization achieved with three-body forces and Coulomb interaction.

Abstract

A systematic connection between QCD and nuclear few- and many-body properties in the form of the Effective Field Theory "without pions" is applied to $A\le 6$ nuclei to determine its range of applicability. We present results at next-to-leading order for the Tjon correlation and for a correlation between the singlet S-wave $^3$He-neutron scattering length and the triton binding energy. In the A=6 sector we performed leading order calculations for the binding energy and the charge and matter radii of the halo nucleus $^6$He. Also at leading order, the doublet S-wave 4-He-neutron phase shifts are compared with R-matrix data. These analysis provide evidence for a sufficiently fast convergence of the effective field theory, in particular, our results in $A\le 4$ predict an expansion parameter of about 1/3, and they converge to data within the predicted uncertainty band at this order. A properly adjusted three-body contact force which we include together with the Coulomb interaction in all calculations is found to correctly renormalize the pion-less theory at leading- and next-to-leading order, i.e. the power counting does not require four-body forces at the respective order.