We show that a correct formulation of the cold collision frequency shift fortwo photon spectroscopy of Bose-condensed and cold non-Bose-condensed hydrogenis consistent with experimental data. Our treatment includes transport andinhomogeneity into the theory of a non-condensed gas, which causes substantialchanges in the cold collision frequency shift for the ordinary thermal gas, asa result of the very high frequency (3.9kHz) of transverse trap mode. For thecondensed gas, we find substantial corrections arise from the inclusion ofquasiparticles, whose number is very large because of the very low frequency(10.2Hz) of the longitudinal trap mode. These two effects together account forthe apparent absence of a "factor of two" between the two possibilities. Our treatment considers only the Doppler-free measurements, but could beextended to Doppler-sensitive measurements. For Bose-condensed hydrogen, wepredict a characteristic "foot" extending into higher detunings than can arisefrom the condensate alone, as a result of a correct treatment of the statisticsof thermal quasiparticles.
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