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

¹ Center for Nuclear Studies, Department of Physics, The George Washington University, Washington, DC 20052, USA
² Department of Physics and Astronomy, University of North Carolina, Chapel Hill, NC 27599-3255, USA
³ Institut für Theoretische Physik III, Department für Physik, Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany

^a e-mail: kirscher@gwmail.gwu.edu

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 ≤ 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 ⁶He. 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 ≤ 4 predict 1 an expansion parameter of about , 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.