FERMI-EDGE SINGULARITIES AND BACKSCATTERING IN A WEAKLY INTERACTING ONE-DIMENSIONAL ELECTRON-GAS

The photon-absorption edge in a weakly interacting one-dimensional electron gas is studied, treating backscattering of conduction electrons from the core hole exactly. Close to threshold, there is a power-law singularity in the absorption, I(epsilon) proportional to epsilon(-alpha), with alpha = 3/8 + delta(+)/pi - delta(+)(2)/2 pi(2), where delta(+) is the forward-scattering phase shift of the core hole. In contrast to previous theories, cu is finite (and universal) in the limit of weak core-hole potential. In the case of weak backscattering U(2k(F)), the exponent in the power-law dependence of absorption on energy crosses over to and value alpha = delta(+)/pi - delta(+)(2)/2 pi(2) above an energy scale epsilon* similar to [U(2k(F))](1/gamma), where gamma is a dimensionless measure of the electron-electron interactions.