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We report the discovery with the proportional counter array (PCA) onboard theRossi X-ray Timing Explorer (RXTE) of a decrease in the frequency of X-raybrightness oscillations in the cooling tail of an X-ray burst from 4U 1636-53.This is the first direct evidence for a spin down of the pulsations seen duringthermonuclear bursts. We find that the spin down episode is correlated with theappearance in this burst of an extended tail of emission. We present both timeresolved energy and variability spectra during this burst and compare them withresults from a second burst which shows neither a spin down episode nor anextended tail. A spectral evolution study of the ``spin down'' burst reveals asecondary signature of weak radius expansion, not seen in other bursts, andcorrelated with the spin down episode, which may indicate a secondarythermonuclear energy release. We interpret the spin down episode in the contextof an angular momentum conserving shell, which is reexpanded and therefore spundown by an additional thermonuclear energy release which could also explain theextended X-ray tail.Comment: 16 pages, AASTEX preprint with 7 embedded figures. To be published in  the Astrophysical Journal Letter

Spin-down of Pulsations in the Cooling Tail of an X-Ray Burst from 4U 1636−53