Collisional frequency shifts of absorption lines in an atomic hydrogen gas

Abstract

We consider the effect of interactions on the line shape of the two-photon 1s-2s transition in a (doubly) spin-polarized atomic hydrogen gas in terms of the interatomic interaction potentials. We show that the frequency-weigted pseudopotentials that describe the interactions between low-energy atoms. The origin of the departures from the simple pseudopotential result for the frequency-weigted sum rule is traced to what we refer to as incoherent contributions to the special weight. These arise from more complicated final states of the many-body system than the ones usually considered. In particular, we show how the relevant response function may be treated in a manner similar to the density-density response function for Fermi liquids, and express it as a coherent part comming from single particle-hole pairs, and an incoherent part comming from other excitations. We argue that in experiments only the coherent part of the response of the system is observed, and its contribution to the frequence-weighted sum rule is shown to be given correctly by the pseudopotential approximation. Finally we calculate the width of the coherent part of the line due to collisional damping.