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

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.