Universal correlations in pion-less EFT with the resonating group method: Three and four nucleons

Abstract

The Effective Field Theory "without pions" at next-to-leading order is used to analyze universal bound state and scattering properties of the 3-and 4-nucleon system. Results of a variety of phase shift equivalent nuclear potentials are presented for bound state properties of 3 H and 4 He, and for the singlet S-wave 3 He-neutron scattering length a0( 3 He-n). The calculations are performed with the Refined Resonating Group Method and include a full treatment of the Coulomb interaction and the leading-order 3-nucleon interaction. The results compare favorably with data and values from AV18(+UIX) model calculations. A new correlation between a0( 3 He-n) and the 3 H binding energy is found. Furthermore, we confirm at next-to-leading order the correlations, already found at leadingorder, between the 3 H binding energy and the 3 H charge radius, and the Tjon line. With the 3 H binding energy as input, we get predictions of the Effective Field Theory "without pions" at next-toleading order for the root mean square charge radius of 3 H of (1.6±0.2) fm, for the 4 He binding energy of (28 ± 2.5) MeV, and for Re{a0( 3 He-n)} of (7.5 ± 0.6) fm. Including the Coulomb interaction, the splitting in binding energy between 3 H and 3 He is found to be (0.66 ± 0.03) MeV. The discrepancy to data of (0.10 ∓ 0.03) MeV is model independently attributed to higher order charge independence breaking interactions. We also demonstrate that different results for the same observable stem from higher order effects, and carefully assess that numerical uncertainties are negligible. Our results demonstrate the convergence and usefulness of the pion-less theory at next-to-leading order in the 4 He channel. We conclude that no 4-nucleon interaction is needed to renormalize the theory at next-to-leading order in the 4-nucleon sector.

Universal correlations in pion-less EFT with the resonating group model: three and four nucleons

“…This simplification, irrelevant thanks to modern computer technology for the three-and four-body observables for which we included all possible groupings, becomes an efficient tool that makes A > 5 body calculations feasible. For instance, a single fragmentation with a 4 He core and two attached neutrons was found to yield more than 95% of the assumed converged observables calculated here for 6 He.…”

“…We presented an analysis of two universal correlations, the dependencies of the 4 He binding energy and a 3 He-neutron scattering length on the triton binding energy, with the nuclear Effective Field Theory "without pions". The calculations include a three-body force and the Coulomb interaction, and report the expected order-by-order improvement consistent with an expansion parameter p typ /Λ b ≈ 1 3 .…”

“…We attribute the quantitative discrepancy to data in part to the small model space used for the 4 He core in which it is only bound by B( 4 He) ≈ 20 MeV.…”

“…Observables of subsystems have to be monitored carefully for consistency with the predicted theoretical uncertainty at the given order. For instance, the model spaces used for the 4 He cores do not meet this criterium and have to be refined as explained above.…”

“…With the systematic and predictive power thus demonstrated, the status of our investigation in an A = 5 scattering system and the halo system 6 He is shown. Specifically, we present leading order (LO) results for the doublet Swave phase shift for 4 He-neutron scattering, in addition to binding energy, charge-and matter radii results for 6 He. Before that, we present the specific form of the next-to-leading order (NLO) EFT / π NN interaction and the few-body technique of the Refined Resonating Group Model (RRGM [5]) used to solve the many-body Schrödinger equation.…”