Radiative energy loss of high energy quarks and gluons in a finite volume quark-gluon plasma

The medium induced energy loss spectrum of a high energy quark or gluon traversing a hot QCD medium of finite volume is studied. We model the interaction by a simple picture of static scattering centres. The total induced energy loss is found to grow as $L^2$, where $L$ is the extent of the medium. The solution of the energy loss problem is reduced to the solution of a Schr\"odinger-like equation whose ``potential'' is given by the single-scattering cross section of the high energy parton in the medium. These resuls should be directly applicable to a quark-gluon plasma.