Neutron interactions with electromagnetic fields and single-neutron solitons

We address the bound-state dynamics of a neutron with anomalous magnetic dipole moment in the presence of electromagnetic (EM) fields described by a generalized Dirac-Pauli equation. This generalization consists of including appropriate couplings between Lorentz scalar and pseudoscalar fields with EM fields in the Lagrangian of the system. We exactly solve two single-particle problems: first, a Hydrogen-like system; second, a relativistic Schrödinger-like equation for a linear confining potential. We comment on the relevance of this approach to explore fermion (e.g. neutron) self-interactions as solitonic models of the neutron.