The Dirac equation is written for the special case of a spinor in a relativistic potential with the even and odd components related by a constraint, and solved exactly with the even component chosen to be the Woods-Saxon potential. The corresponding radial wave functions for the two-component spinor are obtained in terms of the hypergeometric function, and the energy spectrum of the bound states is obtained as a solution to a given equation with boundary constraints in which the nonrelativistic limit reproduces the usual Woods-Saxon potential.

• Received 12 July 2002

DOI:https://doi.org/10.1103/PhysRevA.66.062105