Discrete structures in fusion-barrier distributions for vibrational nuclei

We obtain a closed-form expression for the distribution of fusion barriers for vibrational nuclei using a generalization of Dasso, Landowne, and Winther's model, which represents the nuclear surface vibrations as a number of harmonic oscillators, and allows the excitation of an arbitrary number of phonons in the target and/or projectile. We find that this expression is in reasonable agreement with the average trends of the empirical distributions for the fusion of O-16 with Zr-92, Sm-144 and Pb-208, but fails to reproduce the double peaking of the distribution for the Sm-144 target. Only when we restrict the number of excited phonons to a limited number, we are able to reproduce such discrete structures. We show that limiting the number of coupled channels, particularly in the case of strong coupling, increases the spacings between the channel eigenvalues that determine the positions of the peaks of the barrier distribution and modifies their heights.