Energy Spectrum of a Dirac Particle with Position-Dependent Mass Under the Influence of the Aharonov-Casher Effect

In this paper, we investigate the influence of the Aharonov-Casher (AC) effect on the relativistic and nonrelativistic energy spectra of a neutral Dirac particle with position-dependent mass (PDM). To exactly solve our system, we use the projection operators left - handed and right - handed . Next, we explicitly determine the energy spectra for the bound states of the particle. As a result, we verify that the relativistic spectrum depends on the quantum numbers n and m l , AC quantum phase Φ AC generated by AC effect and of the parameter κ that characterize the PDM. In addition, this spectrum is a periodic function and increase in absolute values with the increase of Φ AC . We also verify that the energies of the particle are minors that of the antiparticle, and in the limit of the constant mass ( κ → 0) the rest energy is recovered. However, in the absence of the AC effect ( Φ AC → 0), the spectrum still remains quantized in terms of n and m l . Finally, we analyze the nonrelativistic limit of our work, where we obtain an energy spectrum with some characteristics similar to the relativistic case. Making an analogy with some works of the literature, in particular with the hydrogen atom, we note that our nonrelativistic spectrum provides the so-called binding energies, while that its absolute values provides the so-called ionization energies.