  We formulate the Einstein-Cartan-Dirac equations in the Newman-Penrose (NP)
formalism, thereby presenting a more accurate and explicit analysis of previous
such studies. The equations show in a transparent way how the Einstein-Dirac
equations are modified by the inclusion of torsion. In particular, the
Hehl-Datta equation is presented in NP notation. We then describe a few
solutions of the Hehl-Datta equation on Minkowski space-time, and in particular
report a solitonic solution which removes the unphysical behavioiur of the
corresponding Dirac solution. The present work serves as a prelude to similar
studies for non-degenerate Poincare gauge gravity.
