  The S shape of the canonical heat capacity is known as a signature of the
pairing transition and along an isotopic chain it is significantly more
pronounced for nuclei with an even number of neutrons than with an odd number.
Although the heat capacities extracted from experimental level densities in
93-98Mo exhibit a clear S shape, they do not show such an odd-even staggering.
To understand the underlying physics, we analyze thermal quantities evaluated
from the partition function calculated using the static-path plus random-phase
approximation (SPA+RPA) in a monopole pairing model with number-parity
projection. The calculated level densities reproduce very well the experimental
data and they also agree with estimates using the back-shifted Fermi-gas model.
We clarify the reason why the heat capacities for Mo isotopes do not show
odd-even staggering of the S shape. We also discuss thermal odd-even mass
differences in 94-97Mo using the three-, four-, and five-point formula. These
thermal mass differences are regarded as indicators of pairing correlations at
finite temperature.
