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

Abstract

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 $^{172}\mathrm{Yb}$, $^{94}\mathrm{Mo}$, and $^{56}\mathrm{Fe}$. For the heavy nucleus $^{172}\mathrm{Yb}$, the heat capacities in both the SPA and the number-projected SPA (NPSPA) exhibit an $\mathcal{S}$ shape; the difference between the SPA and NPSPA heat-capacity curves is not very large and the particle-number projection thereby enhances the $\mathcal{S}$ shape already seen in the SPA. The temperature at which the $\mathcal{S}$-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 $^{94}\mathrm{Mo}$ and $^{56}\mathrm{Fe}$, the SPA does not produce an $\mathcal{S}$-shaped heat capacity on its own; only after particle-number projection the $\mathcal{S}$ shape appears in the heat-capacity curve. For $^{94}\mathrm{Mo}$, we compare the NPSPA result with thermal odd-even mass differences, which are regarded as a direct measure of the pairing gap.