The $\mathcal{S}$ shape of the canonical heat-capacity curve 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 for those with an odd number. Although the heat capacities extracted from experimental level densities in ${}^{93-98}\mathrm{Mo}$ exhibit a clear $\mathcal{S}$ 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 made 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 $\mathcal{S}$ shape. We also discuss thermal odd-even mass differences in ${}^{94-97}\mathrm{Mo}$ that were calculated using the three-, four-, and five-point formulas. These thermal mass differences are regarded as indicators of pairing correlations at finite temperature.

• Received 18 May 2006

DOI:https://doi.org/10.1103/PhysRevC.74.024325