  We obtain exact solution of the Dirac equation for a charged particle with
position-dependent mass in the Coulomb field. The effective mass of the spinor
has a relativistic component which is proportional to the square of the Compton
wavelength and varies as 1/r. It is suggested that this model could be used as
a tool in the renormalization of ultraviolet divergences in field theory. The
discrete energy spectrum and spinor wave-function are obtained explicitly.
