Particle-number conservation in static-path approximation for thermal superfluid systems

By applying particle-number projection to the static-path approximation (SPA), the heat capacity and the breakdown of pairing correlations are investigated in the thermally excited, superfluid systems ¹⁷²Yb, ⁹⁴Mo, and ⁵⁶Fe. For the heavy nucleus ¹⁷²Yb, the heat capacities in both the SPA and the number-projected SPA (NPSPA) exhibit an S shape; the difference between the SPA and NPSPA heat-capacity curves is not very large and the particle-number projection thereby enhances the S shape already seen in the SPA. The temperature at which the S-shape of heat capacity curve occurs parallels the temperature of the breakdown of pairing correlations as indicated by the effective pairing gap. However, for the comparatively lighter nuclei ⁹⁴Mo and ⁵⁶Fe, the SPA does not produce an S-shaped heat capacity on its own; only after particle-number projection the S shape appears in the heat-capacity curve. For ⁹⁴Mo, we compare the NPSPA result with thermal odd-even mass differences, which are regarded as a direct measure of the pairing gap.