  The empirical heat capacities of $^{93-98}$Mo nuclei are re-investigated by
using the latest updated and recommended nuclear level density (NLD) data below
the neutron binding energy $B_n$ combined with the back-shifted Fermi-gas
(BSFG) model for the energy region above $B_n$. For the latter, the BSFG
formula with energy-dependent level density parameter is used and the new
parameterization has been carried out in order to obtain the best fit to the
new NLD data in the whole data range. The results obtained show that the
S-shaped heat capacity, a fingerprint of the pairing phase transition, is more
pronounced in even $^{94,96,98}$Mo nuclei than that in odd $^{93,95,97}$Mo
isotopes. This result is different with those obtained in two previous studies
by R. Chankova et al., [Phys. Rev. C {\bf 73}, 034311 (2006)] and K. Kaneko et
al., [Phys. Rev. C {\bf 74}, 024325 (2006)], in which the old NLD data and the
BSFG model with energy-independent level density parameter were used. Moreover,
the present work suggests that the very strong S-shape observed in the heat
capacities of both even and odd Molybdenum isotopes by K. Kaneko et al., [Phys.
Rev. C {\bf 74}, 024325 (2006)] should be re-investigated. The present work
also suggests that obtain the correct heat capacity and associated pairing
phase transition in excited nuclei, one should use the correct NLD data and the
best fitted BSFG NLD in the entire region where the experimental data are
available.
