Nucleon interaction with electromagnetic fields in cylindrical coordinates

In relativistic quantum mechanics (RQM), we investigate the dynamics of (Fermi) nucleons with anomalous magnetic moment in the presence of certain electromagnetic (EM) fields. In a cylindrical coordinate reference frame, we compare five models within the theory of the Dirac equation supplemented with an incremental Pauli term: (i) neutron and proton harmonic oscillators; (ii) axial (neutron) harmonic oscillator; and (iii) neutron and proton hydrogen atom-like systems. We show that, in some instances, the upper and lower components of the energy eigenstates in noncentral potentials can be separable and analytically solvable. Cylindrical coordinates could be useful to improve some descriptions of known quantum systems that have been treated so far in other flat space-time dimensions. Thus, we introduce novel RQM models which can be further explored.