  Evidence for an anomalous annual periodicity in certain nuclear decay data
has led to speculation concerning a possible solar influence on nuclear
processes. As a test of this hypothesis, we here search for evidence in decay
data that might be indicative of a process involving solar rotation, focusing
on data for 32Si and 36Cl decay rates acquired at the Brookhaven National
Laboratory. Examination of the power spectrum over a range of frequencies (10 -
15 year^-1) appropriate for solar synodic rotation rates reveals several
periodicities, the most prominent being one at 11.18 year^-1 with power 20.76.
We evaluate the significance of this peak in terms of the false-alarm
probability, by means of the shuffle test, and also by means of a new test (the
"shake" test) that involves small random time displacements. The last two tests
indicate that the peak at 11.18 year^-1 would arise by chance only once out of
about 10^7 trials. Since there are several peaks in the search band, we also
investigate the running mean of the power spectrum, and identify a major peak
at 11.93 year^-1 with peak running-mean power 4.08. Application of the shuffle
test and the shake test indicates that there is less than one chance in 10^11,
and one chance in 10^15, respectively, finding by chance a value as large as
4.08.
