  We formulate a theory for the polarization-dependence of the electronic
(pair-breaking) Raman response for the recently discovered non-centrosymmetric
superconductors in the clean limit at zero temperature. Possible applications
include the systems CePt$_3$Si and Li$_2$Pd$_x$Pt$_{3-x}$B which reflect the
two important classes of the involved spin-orbit coupling. We provide
analytical expressions for the Raman vertices for these two classes and
calculate the polarization dependence of the electronic spectra. We predict a
two-peak structure and different power laws with respect to the unknown
relative magnitude of the singlet and triplet contributions to the
superconducting order parameter, revealing a large variety of characteristic
fingerprints of the underlying condensate.
