Quasi-exact solution of the anharmonic oscillator in curved space-time with tensor potential of type Ar + B/r3 and spin and pseudo-spin symmetries

In this work, we analyzed the anharmonic oscillator with spin and pseudo-spin symmetries in deformed nuclei. For that, we consider the Dirac equation in curved space-time which has a line element given by ds(2) = (1 + alpha U-2(r))(2)(dt(2) - dr(2)) - r(2)d theta(2) - r(2)sin(2)theta d phi(2) with electromagnetic field A(mu) = (V (r),cA(r), 0, 0). We consider two forms of coupling of the spin 1/2 particle with the electromagnetic field and curved space-time: V (r) = U(r) and V (r) = -U(r), where the spin and pseudo-spin symmetries were manifested, respectively. We calculate the spinorial wave function and the energy spectrum of the anharmonic oscillator quasi-exactly, and from this result it is obtained that the symmetries are broken due to the coupling of the electromagnetic field with the curvature of space-time. We analyzed the densities of radial probabilities and energy spectra in both symmetries.