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Effects of thermal shape fluctuations and pairing fluctuations on the giant dipole resonance in warm nuclei

Apart from the higher limits of isospin and temperature, the properties of atomic nuclei are intriguing and less explored at the limits of lowest but finite temperatures. At very low temperatures there is a strong interplay between the shell (quantal fluctuations), statistical (thermal fluctuations), and residual pairing effects as evidenced from the studies on giant dipole resonance (GDR). In our recent work [Phys. Rev. C \textbf{90}, 044308 (2014)], we have outlined some of our results from a theoretical approach for such warm nuclei where all these effects are incorporated along within the thermal shape fluctuation model (TSFM) extended to include the fluctuations in the pairing field. In this article, we present the complete formalism based on the microscopic-macroscopic approach for determining the deformation energies and a macroscopic approach which links the deformation to GDR observables. We discuss our results for the nuclei $^{97}$Tc, $^{120}$Sn, $^{179}$Au, and $^{208}$Pb, and corroborate with the experimental data available. The TSFM could explain the data successfully at low temperature only with a proper treatment of pairing and its fluctuations. More measurements with better precision could yield rich information about several phase transitions that can happen in warm nuclei.