Giant dipole resonance in $^{88}$Mo from phonon damping model's strength functions averaged over temperature and angular momentum distributions

The line shapes of giant dipole resonance (GDR) in the decay of the compound nucleus $^{88}$Mo, which is formed after the fusion-evaporation reaction $^{48}$Ti + $^{40}$Ca at various excitation energies $E^{*}$ from 58 to 308 MeV, are generated by averaging the GDR strength functions predicted within the phonon damping model (PDM) using the empirical probabilities for temperature and angular momentum. The average strength functions are compared with the PDM strength functions calculated at the mean temperature and mean angular momentum, which are obtained by averaging the values of temperature and angular momentum using the same temperature and angular-momentum probability distributions, respectively. It is seen that these two ways of generating the GDR linear line shape yield very similar results. It is also shown that the GDR width approaches a saturation at angular momentum $J\geq$ 50$\hbar$ at $T=$ 4 MeV and at $J\geq$ 70$\hbar$ at any $T$.