Effective field theory calculation of nd radiative capture at thermal energies

Abstract

The cross section for the thermal neutron capture by the deuteron is calculated with pionless Effective Field Theory(EFT). No new Three-Nucleon forces are needed up to next-to-next-to-leading order in order to achieve cut-off independent results, besides those fixed by the triton binding energy and Nd scattering length in the triton channel. The cross-section is accurately determined to be $\sigma_{tot}=[0.503\pm 0.003]mb$. At zero energies, the magnetic $M1$-transition gives the dominant contribution and is calculated up to next-to-next-to-leading order (N$^2$LO). Close agreement between the available experimental data and the calculated cross section is reached. We demonstrate convergence and cutoff independence order by order in the low-energy expansion.