In this paper we consider a model of Poincare gauge theory (PGT) in which a translational gauge field and a Lorentz gauge field are actually identified with the Einsteins gravitational field and a pair of ``Yang-Mills field and its partner, respectively.In this model we re-derive some special solutions and take up one of them. The solution represents a ``Yang-Mills field without its partner field and the Reissner-Nordstrom type spacetime, which are generated by a PGT-gauge charge and its mass.It is main purpose of this paper to investigate the interaction of massless Dirac fields with those fields. As a result, we find an interesting fact that the left-handed massless Dirac fields behave in the different manner from the right-handed ones. This can be explained as to be caused by the direct interaction of Dirac fields with the ``Yang-Mills field. Accordingly, the phenomenon can not happen in the behavior of the neutrino waves in ordinary Reissner-Nordstrom geometry. The difference between left- and right-handed effects is calculated quantitatively, considering the scattering problems of the massless Dirac fields by our Reissner-Nordstrom type black-hole.
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