Temperature Dependence of Pair Correlations in Nuclei in the Iron-Region

We use the shell model Monte Carlo approach to study thermal properties and pair correlations in $^{54,56,58}$Fe and in $^{56}$Cr. The calculations are performed with the modified Kuo-Brown interaction in the complete $1p0f$ model space. We find generally that the proton-proton and neutron-neutron $J=0$ pairing correlations, which dominate the ground state properties of even-even nuclei, vanish at temperatures around 1 MeV. This pairing phase transition is accompanied by a rapid increase in the moment of inertia and a partial unquenching of the M1 strength. We find that the M1 strength totally unquenches at higher temperatures, related to the vanishing of isoscalar proton-neutron correlations, which persist to higher temperatures than the pairing between like nucleons. The Gamow-Teller strength is also correlated to the isoscalar proton-neutron pairing and hence also unquenches at a temperature larger than that of the pairing phase transition.