Approximate treatment of the Dirac equation with scalar and vector potentials of rectangular shapes - Grypeos, M. E.; Koutroulos, C. G.; Papadopoulos, G. J. (HNPS Advances in Nuclear Physics, 2020)
The Dirac equation with scalar potential Us(r) and fourth component of vector po tential Uv(r) is considered in the case of the rectangular shapes of these potentials with the same radius R and approximate analytic expressions are derived for the single-particle energy of bound states in certain cases. The results obtained with these expressions are compared with the corresponding "exact" results obtained by solving the eigenvalue equa tion numerically.It is found that very good results are obtained for the ground state and for quite a wide range of values of R with one of the proposed expressions. Even the corresponding non-relativistic version of this expession, has not been derived before, to our knowledge.