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
Abstract
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 ds2=(1+α2U(r))2(dt2−dr2)−r2d𝜃2−r2sin2𝜃dϕ2 with electromagnetic field Aμ=(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.
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