Abstract
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 $T=4 \mathrm{MeV}$ compared to its value at $T=0.$ The effect of angular momentum on the damping of the hot GDR of this nucleus increases the GDR width by $\ensuremath{\sim}22%$ at $T=2 \mathrm{MeV}$ and $J\ensuremath{\simeq}69\ensuremath{\Elzxh}$ compared to its value at $T=2 \mathrm{MeV}$ and $J=0.$ A combined effect of temperature and angular momentum leads to a GDR energy that is nearly independent of the excitation energy.
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