  Pairing reentrance phenomenon in the warm rotating $^{104}$Pd nucleus is
studied within the Bardeen-Cooper-Schrieffer (BCS)-based approach (the FTBCS1).
The theory takes into account the effect of quasiparticle number fluctuations
on the pairing field at finite temperature and angular momentum within the
pairing model plus noncollective rotation along the symmetry axis. The
numerical calculations for the pairing gaps and nuclear level densities (NLD),
of which an anomalous enhancement has been experimentally observed at low
excitation energy $E^*$ and high angular momentum $J$, show that the pairing
reentrance is seen in the behavior of pairing gap obtained within the FTBCS1 at
low $E$ and high $J$. This leads to the enhancement of the FTBCS1 level
densities, in good agreement with the experimental observation. This agreement
indicates that the observed enhancement of the NLD might be the first
experimental detection of the pairing reentrance in a finite nucleus.
