  We analyse the non-relativistic approximation of the Dirac equation for slow
fermions moving in spacetimes with a static metric, caused by the weak
gravitational field of the Earth and a chameleon field, and derive the most
general effective gravitational potential, induced by a static metric of
spacetime. The derivation of the non-relativistic Hamilton operator of the
Dirac equation is carried out by using a standard Foldy-Wouthuysen (SFW)
transformation. We discuss the chameleon field as source of a torsion field and
torsion-matter interactions.
