Pairing effect in the thermal shape-fluctuation model on the width of the giant dipole resonance

We present an approach that includes temperature-dependent shell effects and fluctuations of the pairing field in the thermal shape-fluctuation model (TSFM). We apply this approach to study the width of giant dipole resonance (GDR) in ${}^{97}\mathrm{Tc}$, ${}^{120}\mathrm{Sn}$, and ${}^{208}\mathrm{Pb}$. Our results demonstrate that the TSFM that includes pairing fluctuations can explain the recently observed quenching in the GDR width. We also show that to validate pairing prescriptions and the parameters involved, we require more and precise data.

Figure 1

(a) and (b) represent the pairing gaps as a function of temperature for ${}^{120}\mathrm{Sn}$ with $\beta =0$ calculated from the simple BCS approach and with the pairing fluctuations (without shape fluctuations). Full results for both protons and neutrons are also shown: (c) average pairing gap, (d) GDR width in the case of ${}^{120}\mathrm{Sn}$, as a function of temperature. The calculations done without pairing utilize a CE approach (CE), whereas the calculations with simple BCS pairing (BCS) and with pairing fluctuations (PF) utilize a GCE approach (GCE). The results obtained using the liquid drop model (LDM) are also presented. Experimental values for ${}^{120}\mathrm{Sn}$ are taken from Refs. [11, 38] and are shown by solid squares. For comparison, data for ${}^{119}\mathrm{Sb}$, taken from Ref. [19], are also shown with open circles.

Figure 2

The free energy surfaces for ${}^{120}\mathrm{Sn}$ at $T=0.4$ MeV plotted without pairing and with pairing where the calculations are with CE and GCE, respectively. The contour line spacing is 0.5 MeV, the most probable shape is marked by a solid (red) circle and the first two minima are shaded.

Figure 3

Similar to Figs. 1 and 1 but for the nucleus ${}^{97}\mathrm{Tc}$. Experimental values are taken from Ref. [25] are shown with solid squares.

Figure 4

Similar to Fig. 1 but for the nucleus ${}^{208}\mathrm{Pb}$. Experimental values are taken from Ref. [23] are shown with solid squares.