Nuclear electromagnetic currents are derived in time-ordered perturbation theory within an effective-field-theory framework including explicit nucleons, Δ isobars, and pions up to one loop, or next-to-next-to-next-to-leading order (${\mathrm{N}}^3$LO). The currents obtained at next-to-next-to-leading order (${\mathrm{N}}^2$LO), i.e., ignoring loop corrections, are used in a study of neutron radiative captures on protons and deuterons at thermal energies, and of $A=2$ and 3 nuclei magnetic moments. The wave functions for $A=2$ are derived from solutions of the Schrödinger equation with the Argonne $v_{18}$ (AV18) or CD-Bonn (CDB) potentials, while those for $A=3$ are obtained with the hyperspherical-harmonics-expansion method from a realistic Hamiltonian including, in addition to the AV18 or CDB two-nucleon, a three-nucleon potential. With the strengths of the Δ-excitation currents occurring at ${\mathrm{N}}^2$LO determined to reproduce the $n\text{−}p$ cross section and isovector combination of the trinucleon magnetic moments, we find that the cross section and photon circular polarization parameter, measured in $n\text{−}d$ and $\overrightarrow{n}\text{−}d$ processes, are underpredicted by theory; for example, the cross section is underpredicted by 11–38% as the cutoff is increased from 500 to 800 MeV. A complete analysis of the results, in particular their large cutoff dependence, is presented.

• Received 10 October 2008

DOI:https://doi.org/10.1103/PhysRevC.78.064002