The noncommutative Dirac oscillator with a permanent electric dipole moment in the presence of an electromagnetic field

In this work, we investigate the noncommutative Dirac oscillator (NCDO) with a permanent electric dipole moment (EDM) in the presence of an electromagnetic field. We consider a radial magnetic field generated by anti-Helmholtz coils and the uniform electric field of the Stark effect. Next, we determine the exact solutions of the system, given by the Dirac spinor and by the relativistic energy spectrum. We note that such a spinor is written in terms of the generalized Laguerre polynomials, and such a spectrum is a linear function on the potential energy U and depends on the quantum numbers n and m, spin parameter s, and of four angular frequencies: omega, omega over bar , omega theta , and omega eta , where omega is the frequency of the DO, omega over bar is a type of 'cyclotron frequency', and omega theta and omega eta are the NC frequencies of position and momentum. We graphically analyze the behavior of the spectrum as a function of these frequencies for three different values of n, with and without the influence of U. Besides, as an interesting result, another interpretation can be given for the origin of the nonminimal coupling of the DO, which would be through a neutral fermion with EDM in a radial magnetic field. Finally, we also analyze the nonrelativistic limit of our results, and comparing our problem with other works, we verified that our results generalize some particular cases in the literature.