Fermi-edge singularity with backscattering in the Luttinger-liquid model.

We study the response of the interacting electron gas in one dimension on the local external potential. In the low frequency limit the power-law singularities are essentially modifyed by backscattering effects which, in the case of zero forward scattering, result in the universal critical exponent depending only on the Luttingerliquid interactions. The results obtained may be used to describe singular responses of the 1D boson chains.