We consider the effect of interactions on the line shape of the two-photon1s-2s transition in a (doubly) spin-polarized atomic hydrogen gas in terms ofthe interatomic interaction potentials. We show that the frequency-weighted sumrule for the intensity of the line is not given simply in terms of thepseudopotentials that describe the interactions between low-energy atoms. Theorigin of the departures from the simple pseudopotential result for thefrequency-weighted sum rule is traced to what we refer to as incoherentcontributions to the spectral weight. These arise from more complicated finalstates 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 similarto the density-density response function for Fermi liquids, and express it as acoherent part coming from single particle-hole pairs, and an incoherent partcoming from other excitations. We argue that in experiments only the coherentpart of the response of the system is observed, and its contribution to thefrequency-weighted sum rule is shown to be given correctly by thepseudopotential approximation. Finally we calculate the width of the coherentpart of the line due to collisional damping.
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