  We analysed all archival data of the low-mass X-ray binary 4U 1636--53 with
the Rossi X-ray Timing Explorer (1490 observations). We found a total of 336
type-I X-ray bursts from this source. In the time-resolved spectra of 69 of
these bursts, close to the peak of the burst, the best-fitting blackbody radius
shows the sharp increase and decrease that is typical of photospheric
radius-expansion (PRE) bursts. We found that in 17 of these 69 PRE bursts,
after the touchdown point, the blackbody radius increases again quickly after
about 1 second, and from then on the radius decreases slightly or it remains
more or less constant. In the other 52 PRE bursts, after touchdown, the radius
of the blackbody stays more or less constant for $\sim 2 - 8$ seconds, and
after that it increases slowly. Interestingly, those PRE bursts in which the
blackbody radius remains more or less constant for $\simmore 2$ seconds show
coherent oscillations in the tail of the burst, whereas those PRE bursts in
which the blackbody radius changes rapidly after touchdown show no coherent
oscillations in the tail of the burst. We found that the distribution of
durations of the post touchdown phase between these two groups of PRE bursts is
significantly different; the Kolmogorov-Smirnov probability that the two groups
of PRE bursts come from the same parent populations is only $3.5 \times
10^{-7}$. This is the first time that the presence of burst oscillations in the
tail of X-ray bursts is associated with a systematic behaviour of the spectral
parameters in that phase of the bursts. This result is consistent with
predictions of models that associate the oscillations in the tail of X-ray
bursts with the propagation of a cooling wake in the material on the
neutron-star surface during the decay of the bursts.
