  Recently, we have derived a two--nucleon potential and consistent nuclear
electromagnetic currents in chiral effective field theory with pions and
nucleons as explicit degrees of freedom. The calculation of the currents has
been carried out to include N$^3$LO corrections, consisting of two--pion
exchange and contact contributions. The latter involve unknown low-energy
constants (LECs), some of which have been fixed by fitting the $np$ S- and
P-wave phase shifts up to 100 MeV lab energies. The remaining LECs entering the
current operator are determined so as to reproduce the experimental deuteron
and trinucleon magnetic moments, as well as the $np$ cross section. This
electromagnetic current operator is utilized to study the $nd$ and $n^3$He
radiative captures at thermal neutron energies. Here we discuss our results
stressing on the important role played by the LECs in reproducing the
experimental data.
