Pionless effective field theory and the 4-nucleon scattering system

The effective field theory without pions at next-to-leading-order is used to analyse universal bound-state and scattering properties of the 4-nucleon system. Results of five phase shift equivalent nucleon-nucleon potentials for the singlet S-wave $^3$He neutron scattering length, $a_0(^3\textrm{He-n})$, the phase shifts of the $^4$He system, and bound state properties for $^3$H, $^3$He, and $^4$He, are presented. The calculations are performed within the refined resonating group model and include a full treatment of the coulomb interaction. All results are compared with experimental data and values from AV18/UIX model calculations. A correlation between $a_0(^3\textrm{He-n})$ and the $^4$He binding energy is found. Furthermore, we confirm the linear correlations, already investigated at leading-order, between the $^3$H binding energy and the $^3$H charge radius, and the Tjon line. Our results demonstrate the usefulness of the pionless theory at next-to-leading-order in the $^4$He system, and confirm that no 4-nucleon force is needed to renormalize the theory at this order.