  The discovery of the jet quenching in central Au + Au collisions at the
Relativistic Heavy-ion Collider (RHIC) at Brookhaven National Laboratory has
provided clear evidence for the formation of strongly interacting dense matter.
It has been predicted to occur due to the energy loss of high energy partons
that propagate through the quark gluon plasma. In this paper we investigate the
dependence of the parton energy loss due to elastic scatterings in a parton
plasma on the value of the strong coupling and its running with the evolution
of the system. We analyze different prescriptions for the QCD coupling and
calculate the energy and length dependence of the fractional energy loss.
Moreover, the partonic quenching factor for light and heavy quarks is
estimated. We found that the predicted enhancement of the heavy to light
hadrons ($D/\pi$) ratio is strongly dependent on the running of the QCD
coupling constant.
