  The theory of quasiparticle interference (QPI) for non-centrosymmetric (NCS)
superconductors with Rashba spin-orbit coupling is developed using T-matrix
theory in Born approximation. We show that qualitatively new effects in the QPI
pattern originate from the Rashba spin-orbit coupling: The resulting spin
coherence factors lead to a distinct difference of charge- and spin- QPI and to
an induced spin anisotropy in the latter even for isotropic magnetic impurity
scattering. In particular a cross - QPI appears describing the spin oscillation
pattern due to nonmagnetic impurity scattering which is directly related to the
Rashba vector. We apply our theory to a 2D model for the NCS heavy fermion
unconventional superconductor CePt$_3$Si and discuss the new QPI features for a
gap model with accidental node lines due to its composite singlet-triplet
nature.
