Hawking radiation in the dilaton gravity with a nonminimally coupled scalar field

We discuss the two-dimensional dilaton gravity with a scalar field as the s ource matter where the coupling with gravity is given, besides the minimal one, trough an external field. This coupling generalizes the conformal anom aly in the same way as those found in recent literature, but with a differe nt motivation. The modification to the Hawking radiation is calculated expl icitly and show an additional term that introduces a dependence on the (eff ective) mass of the black-hole.