Superfluid-normal phase transition in finite systems and its effect on damping of hot giant resonances

Thermal fluctuations of quasiparticle number are included making use of the secondary Bogolyubov's transformation, which turns quasiparticles operators into modified-quasiparticle ones. This restores the unitarity relation for the generalized single-particle density operator, which is violated within the Hartree-Fock-Bogolyubov (HFB) theory at finite temperature. The resulting theory is called the modified HFB (MHFB) theory, whose limit of a constant pairing interaction yields the modified BCS (MBCS) theory. Within the MBCS theory, the pairing gap never collapses at finite temperature T as it does within the BCS theory, but decreases monotonously with increasing T. It is demonstrated that this non-vanishing thermal pairing is the reason why the width of the giant dipole resonance (GDR) does not increase with T up to T around 1 MeV. At higher T, when the thermal pairing is small, the GDR width starts to increase with T. The calculations within the phonon-damping model yield the results in good agreement with the most recent experimental systematic for the GDR width as a function of T. A similar effect, which causes a small GDR width at low T, is also seen after thermal pairing is included in the thermal fluctuation model