Proton and neutron exchange as a prelude to fusion at near-barrier energies

Systematic examination of fusion for ${}^{39,41,45,47}\mathrm{K}+{}^{28}\mathrm{Si}$ and ${}^{36,44}\mathrm{Ar}+{}^{28}\mathrm{Si}$ provides insight into the impact of neutron and proton exchange on fusion for nuclei at and near the $N=20$ and $N=28$ shells. Comparison of the reduced excitation functions reveals a marked difference between the behavior of open-shell and closed-shell systems. While coupled channels calculations provide a good description for the closed-shell nuclei, they significantly underpredict the fusion cross section for open-shell nuclei. The observed trends are examined in the context of a potential energy surface, including shell effects, and multinucleon exchange with consideration of Pauli blocking.

Figure 1

Comparison of the reduced fusion excitation functions.

Figure 2

Reduced excitation functions for the measured systems. The upper panel shows the systems closest to the $N=20$ shell closure. The lower panel shows the systems closest to the $N=28$ shell closure.

Figure 3

Comparison of the experimental cross sections with the predictions of the São Paulo model using DHB densities for both the ground state and coupled channel calculations.

Figure 4

Potential energy surfaces (in MeV) for binary fragmentation of each of the K $+ {}^{28}\mathrm{Si}$ systems. The arrows indicate the gradient of the liquid drop surface calculated with shell and proximity corrections for impact parameter zero. The initial projectile-target combination is indicated by the solid (red) symbol.