EXACT CALCULATION OF SPECTRAL PROPERTIES OF A PARTICLE INTERACTING WITH A ONE-DIMENSIONAL FERMIONIC SYSTEM

Using the Bethe-analysis as reformulated by Edwards, we calculate the spectral properties of a particle interacting with a bath of fermions in one dimension for the case of equal particle-fermion masses. These are directly related to singularities apparent in optical experiments in one-dimensional systems. The orthogonality catastrophe for the case of an infinite particle mass survives in the limit of equal masses. We find that the exponent beta of the quasiparticle weight Z congruent-to N(-beta) is different for the two cases and proportional to their respective phase shifts at the Fermi surface; we present a simple physical argument for this difference. We also show that these exponents describe the low-energy behavior of the spectral function for repulsive as well as attractive interactions.