The nuclear level densities of $^{194-196}$Pt and $^{197,198}$Au below the neutron separation energy have been measured using transfer and scattering reactions. All the level density distributions follow the constant-temperature description. Each gro
up of isotopes is characterized by the same temperature above the energy threshold corresponding to the breaking of the first Cooper pair. A constant entropy excess $Delta S=1.9$ and $1.1$ $k_B$ is observed in $^{195}$Pt and $^{198}$Au with respect to $^{196}$Pt and $^{197}$Au, respectively, giving information on the available single-particle level space for the last unpaired valence neutron. The breaking of nucleon Cooper pairs is revealed by sequential peaks in the microcanonical caloric curve.
Experimental nuclear level densities at excitation energies below the neutron threshold follow closely a constant-temperature shape. This dependence is unexpected and poorly understood. In this work, a fundamental explanation of the observed constant
-temperature behavior in atomic nuclei is presented for the first time. It is shown that the experimental data portray a first-order phase transition from a superfluid to an ideal gas of non-interacting quasiparticles. Even-even, odd-$A$, and odd-odd level densities show in detail the behavior of gap- and gapless superconductors also observed in solid-state physics. These results and analysis should find a direct application to mesoscopic systems such as superconducting clusters.
