Relative positions of the peaks in Raman and tunneling spectra of d-wave superconductors

We study (Formula presented) Raman intensity (Formula presented) and the density of states (Formula presented) in isotropic two-dimensional d-wave superconductors. For an ideal gas, (Formula presented) and (Formula presented) have sharp peaks at (Formula presented) and (Formula presented) respectively, where (Formula presented) is the maximum value of the gap. We study how the peak positions are affected by the fermionic damping due to impurity scattering. We show that while the damping generally shifts the peak positions to larger frequencies, the peak in (Formula presented) still occurs at almost twice the peak position in (Formula presented) and therefore cannot account for the experimentally observed downturn shift of the peak frequency in (Formula presented) in underdoped cuprates compared to twice that in (Formula presented) We also discuss how the fermionic damping affects the dynamical spin susceptibility.