Electromagnetic two-body currents of one- and two-pion range

Abstract

Nuclear electromagnetic currents are derived in time-ordered perturbation theory within an effective-field-theory framework including explicit nucleons, \ensuremath{\Delta} 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 Schr\"odinger 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 \ensuremath{\Delta}-excitation currents occurring at ${\mathrm{N}}^{2}$LO determined to reproduce the $n\text{\ensuremath{-}}p$ cross section and isovector combination of the trinucleon magnetic moments, we find that the cross section and photon circular polarization parameter, measured in $n\text{\ensuremath{-}}d$ and $\stackrel{\ensuremath{\rightarrow}}{n}\text{\ensuremath{-}}d$ 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.