Sub-barrier fusion of ${}^{40}\mathrm{Ca}+{}^{94}\mathrm{Zr}$: Interplay of phonon and transfer couplings

A precise fusion excitation function has been measured for ${}^{40}\mathrm{Ca}+{}^{94}\mathrm{Zr}$ at near- and sub-barrier energies, and the fusion barrier distribution has been extracted. Comparing with the existing data for ${}^{40,48}\mathrm{Ca}+{}^{90,96}\mathrm{Zr}$ shows that couplings to inelastic excitations determine the fusion cross sections and the shape of the barrier distributions near the barrier. At lower energies, the two systems possessing neutron-transfer channels with large positive $Q$-values (${}^{40}\mathrm{Ca}+{}^{94,96}\mathrm{Zr}$) have remarkably similar cross sections, and both show a large enhancement with respect to the other systems and to coupled-channels calculations including up to three quadrupole and octupole phonons in the Zr targets.

Figure 1

(top left) Linear plot of $\mathrm{E}\times {\sigma }_{\mathrm{fus}}$ vs energy for several Ca+Zr systems; (top right and bottom left) the same plot with adjusted energy scales (see text); (bottom right) fusion excitation functions on a logarithmic scale vs energy.

Figure 2

Fusion barrier distributions, where the ordinates for the various systems are diminished by successive 0.1 MeV${}^{-1}$ steps with respect to the case of ${}^{40}\mathrm{Ca}+{}^{90}\mathrm{Zr}$.

Figure 3

Fusion excitation function of ${}^{40}\mathrm{Ca}+{}^{94}\mathrm{Zr}$.