Hot giant dipole resonance with thermal shape fluctuation corrections in the static path approximation

The giant dipole resonances (GDR) of ${}^{120}\mathrm{Sn}$ are calculated in linear response theory incorporating the thermal shape fluctuations within the static path approximation (SPA). This is the first application of such an approach to the GDR in a realistic nucleus at finite temperature and angular momentum using a model Hamiltonian with a quadrupole-quadrupole interaction. The results obtained show that thermal fluctuations of quadrupole shapes increase the GDR width only by about $15\%$ at $T=4\mathrm{}\hspace{0.5em}\mathrm{MeV}$ compared to its value at $T=0.\mathrm{}$ The effect of angular momentum on the damping of the hot GDR of this nucleus increases the GDR width by $\sim 22\%$ at $T=2\mathrm{}\hspace{0.5em}\mathrm{MeV}$ and $J\simeq 69ħ$ compared to its value at $T=2\mathrm{}\hspace{0.5em}\mathrm{MeV}$ and $J=0.\mathrm{}$ A combined effect of temperature and angular momentum leads to a GDR energy that is nearly independent of the excitation energy.