Effects of Impurity Scattering on Excitons in Superconductor

Effects of impurity scattering on excitons, or transverse collective excitations, in a superconductor are discussed with the help of the Green's function formalism. The binding energy of the excitons with zero total momentum is obtained explicitly in tLe limit of both low and high impurity concentration. Some discussions are given also on the ex citons with a finite momentum. It is shown that tl:e primary effect of the scattering is to shift the energy of the excitons while their damping is not appreciable. Since the shift is rather drastic it seems unlikely that the subsidiary absorption maximum of i~frared radiatiCn observed in some superconductors is due to the excitons.