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- Title
Exact and Approximate Solutions of Dirac–Morse Problem in Curved Space-Time.
- Authors
de Oliveira, M. D.; Schmidt, Alexandre G. M.
- Abstract
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 d s 2 = (1 + α 2 U (r)) 2 (d t 2 - d r 2) - r 2 d θ 2 - r 2 sin 2 θ d ϕ 2 . From the effective tensor potential A eff (r) = λ / r + α 2 λ U (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 eff (r) not null; (ii) in the second analysis, we obtain exact solutions of radial spinor and eigenenergies considering A eff (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.
- Subjects
DIRAC equation; SPACETIME; ELECTROMAGNETIC fields; SPIN-orbit interactions; PSEUDOPOTENTIAL method; ELECTROMAGNETIC coupling
- Publication
Few-Body Systems, 2023, Vol 64, Issue 3, p1
- ISSN
0177-7963
- Publication type
Article
- DOI
10.1007/s00601-023-01840-x