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

In this work, we analyze the Dirac-Morse problem with spin and pseudo-spin symmetries in deformed nuclei. So, we consider the Dirac equation with the scalar U (r) and vector V (r) Morse-type potentials and tensor Hellmann-type potential in curved space-time whose line element is of type ds2 = (1 + α2 U (r))2 (dt2 − dr2 )− r2 dθ2 − r2 sin2θdφ2 . From the effective tensor potential Aeff(r) = λ/r + α2 λU(r)/r + A(r), that contain terms of spin-orbit coupling, line element and electromagnetic field, we analyze dirac’s spinor in two ways: (i) in the first, we solve the problem approximately considering A ef f (r) not null; (ii) in the second analysis, we obtain exact solutions of radial spinor and eigenenergies considering Aeff(r) = 0. In both cases, we consider two types of coupling of vector and scalar potentials, with spin symmetry for V (r) = U (r) and pseudo-spin symmetry for V (r) = −U (r). We analyzed the effect of coupling the electromagnetic field with the curvature of space in eigenenergies and radial spinor.