  We describe a blind uniform search for thermonuclear burst oscillations
(TBOs) in the majority of Type-I bursts observed by RXTE (2118 bursts from 57
neutron stars). We examined 2-2002 Hz power spectra from the Fourier transform
in sliding 0.5-2 s windows, using fine-binned light curves in 2-60 keV energy
range. The significance of the oscillation candidates was assessed by
simulations which took into account light curve variations, dead time and
sliding time windows. Some of our sources exhibited multi-frequency variability
below approximately 15 Hz that cannot be readily removed with light-curve
modeling and may have an astrophysical (non-TBO) nature. Overall, we found that
the number and strength of potential candidates depends strongly on the
parameters of the search. We found candidates from all previously known RXTE
TBO sources, with pulsations that had been detected at similar frequencies in
multiple independent time windows, and discovered TBOs from SAX J1810.8-2658.
We could not confirm most previously-reported tentative TBO detections or
identify any obvious candidates just below the detection threshold at similar
frequencies in multiple bursts. We computed fractional amplitudes of all TBO
candidates and placed upper limits on non-detections. Finally, for a few
sources we noted small excess of candidates with powers comparable to fainter
TBOs, but appearing in single independent time bins at random frequencies. At
least some of these candidates may be noise spikes that appear interesting due
to selection effects. The potential presence of such candidates calls for extra
caution if claiming single-bin TBO detections.
