  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-weighted sum
rule for the intensity of the line is not given simply in terms of the
pseudopotentials that describe the interactions between low-energy atoms. The
origin of the departures from the simple pseudopotential result for the
frequency-weighted sum rule is traced to what we refer to as incoherent
contributions to the spectral 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 coming from single particle-hole pairs, and an incoherent part
coming 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
frequency-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.
