Free energy and criticality in the nucleon pair breaking process

Experimental level densities for ${}^{171,172}\mathrm{Yb},$ ${}^{166,167}\mathrm{Er},$ ${}^{161,162}\mathrm{Dy},$ and ${}^{148,149}\mathrm{Sm}$ are analyzed within the microcanonical ensemble. In the even isotopes at excitation energies $E<\mathrm{}2\mathrm{}\mathrm{MeV},$ the Helmholtz free energy F signals the transition from zero to two quasiparticles. For $E>\mathrm{}2\mathrm{}\mathrm{MeV},$ the odd and even isotopes reveal a surprisingly constant F at a critical temperature $T_c\sim 0.5\mathrm{MeV},$ indicating the continuous melting of nucleon Cooper pairs as function of excitation energy.