The validity of the small damping approximation (SDA) for the quasi-classical description of the averaged properties of nuclei at high temperatures is studied within the framework of collisional kinetic theory. The isoscalar collective quadrupole vibrations in hot nuclei are considered. We show that the extension of the SDA, by accounting for the damping of the distribution function δ f in the collision integral, reduces the rate of variation of distortion effects of the Fermi surface with temperature. The damping of the δ f in the collision integral increases the collisional width of the giant quadrupole resonance (GQR) significantly for small enough values of the relaxation time. The temperature dependence of the eigenenergy of the GQR becomes much weaker than in the corresponding SDA case.
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