Finite size effects in the equilibrium phase space density distribution function are taken into account for alculations of the relaxation of collective motion in finite nuclei. Memory effects in the collision integral and the diffusivity and the quantum oscillations of the equilibrium distribution function in momentum space are considered. It is shown that a smooth diffuse (Fermi-type) equilibrium distribution function leads to a spurious contribution to the relaxation time. The residual quantum oscillations of the equilibrium distribution function eliminates the spurious contribution. It ensures the disappearance of the gain and loss terms in the collision integral in the ground state of the system and strongly reduces the internal collisional width of the isoscalar giant quadrupole resonances.
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