Effect of cold collisions on spin coherence and resonance shifts in a magnetically trapped ultracold gas

We have performed precision microwave spectroscopy on ultracold ⁸⁷Rb confined in a magnetic trap, both above and below the Bose-condensation transition. The cold collision frequency shifts for both normal and condensed clouds were measured, which allowed the intrastate and interstate density correlations (characterized by sometimes controversial ``factors of 2'') to be determined. Additionally, temporal coherence of the normal cloud was studied, and the importance of mean-field and velocity-changing collisions in preserving coherence is discussed.