Contribution of higher-order processes to the damping of hot giant dipole resonance

A systematic study is presented for three characteristics of the giant dipole resonance (GDR): (i) its width, (ii) its shape, and (iii) the integrated yield of emitted $\gamma$ rays in ${}^{120}\mathrm{Sn}$ and ${}^{208}\mathrm{Pb}$ as a function of temperature T. The double-time Green’s function method has been used to derive a complete set of equations, which allow one to calculate explicitly the GDR width due to coupling to all forward-going processes up to two-phonon ones at most in the second order of the interaction strength. The numerical calculations have been performed using the single-particle energies defined from the Woods-Saxon potentials. An overall agreement between theory and experiment is found for all three characteristics. The results show that the total width of the GDR due to coupling of the GDR phonon to all $ph,$ $pp,$ and $\mathrm{hh}$ configurations increases sharply at low temperatures up to $T\sim$ 3 MeV and saturates at $T\sim 4–6$ MeV. The quantal width ${\Gamma }_Q$ due to coupling to $\mathrm{ph}$ configurations decreases slowly with increasing T. It becomes almost independent of T only when the contribution of two-phonon processes at $T\ne 0$ is omitted. The observed saturation of the integrated yield above $E^{*}\sim 300$ MeV is reproduced in both the GDR region and the region above it.