  We use precision microwave spectroscopy of magnetically trapped, ultra-cold
87Rb to characterize intra- and inter-state density correlations. The cold
collision shifts for both normal and condensed clouds are measured. The results
verify the presence of the sometimes controversial "factors of two", in
normal-cloud mean-field energies, both within a particular state and between
two distinct spin species. One might expect that as two spin species decohere,
the inter-state factor of two would revert to unity, but the associated
frequency chirp one naively expects from such a trend is not observed in our
data.
