Exact Solution of Modified Dirac Oscillator in Curved Space-time with Spin and Pseudo-spin Symmetries

Exact and approximate solutions of Dirac-Morse problem in curved space-time

“…In the second case, we eliminating the presence of the pseudocentrifugal potential, we obtain exact solutions for the Dirac spinor and eigenergies, so even with a tensor potential non null, the symmetries were maintained, since the effective tensor potential is null and there is no degeneracy break in the doublets states. This result differs from what is already well established in the literature that tensor potentials break spin and pseudo-spin symmetries [7,[9][10][11][12][13][14][26][27][28][29][30], so we see that it is possible in some cases to obtain spin and pseudo-spin symmetries in the presence of tensor potential. We also analyzed the influence of the coupling of the space curvature with the EM field on the probability densities, as observed in the figures (3), ( 4), ( 5) and ( 6), noting that the higher the values of the coupling constants of the vector and scalar potentials, the more the particle is confined in regions where its mass is smaller, being able to approach or move away from the origin in r. denação de Aperfeiçoamento de Pessoal de Nível Superior -Brasil (CAPES) -Finance Code 001.…”

“…In summary, we obtained exactly the Dirac spinor given in (35) and eigenvalues energies given in (29) of the Dirac-Morse problem with spin symmetry in the presence of Hellmann-FIG. 3: Plots of some normalized probabilities density for values different of B, where we use n = 0, A = 1, δ = 0.5 and the positive eigenenergie.…”

“…In summary, we obtained the Dirac spinor given in (35) and eigenvalues energies given in (29) of the Morse-type scalar and vector potential and Hellmann-type tensor potential on curved space-time whose metric is…”

“…It is important to note that with the appearance of the effective tensor potential given by A ef f = (λ + A)/r, this causes the eigenenergies given in (29) to depend on the spinorbit coupling term given by λ. Thus, that for each choice of λ given in (17) we will have a different eigenenergies value, thus resulting in the break of degenerescence between the doublets states (n, l, l − 1/2) and (n, l, l + 1/2), causing the spin symmetry to be broken.…”

“…The investigation of this approach motivated the works [26][27][28][29][30] where we solved the Dirac equation in curved space-time.…”