  We discuss the two-dimensional dilaton gravity with a scalar field as the
source matter where the coupling with the gravity is given, besides the minimal
one, through an external field. This coupling generalizes the conformal anomaly
in the same way as those found in recent literature, but with a diferent
motivation. The modification to the Hawking radiation is calculated explicity
and shows an additional term that introduces a dependence on the (effective)
mass of the black-hole.
