Abstract
We analyze the nonrelativistic approximation of the Dirac equation for slow fermions, having small kinetic energies compared to their rest energy $m$ and 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 to order $1/m$, induced by a static metric of spacetime excluding possible rotations of the coordinate frame. The derivation of the nonrelativistic Hamilton operator of the Dirac equation is carried out by using a standard Foldy--Wouthuysen transformation. We discuss the chameleon field as source of a torsion field and torsion--matter interactions.
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