Experimental barrier distributions for the fusion of ${}^{12}\mathrm{C},$ ${}^{16}\mathrm{O},$ ${}^{28}\mathrm{Si},$ and ${}^{35}\mathrm{Cl}$ with ${}^{92}\mathbf{Zr}$ and coupled-channels analyses

Precise excitation functions for the fusion of ${}^{12}\mathrm{C},$ ${}^{16}\mathrm{O},$ ${}^{28}\mathrm{Si},$ and ${}^{35}\mathrm{Cl}$ on ${}^{92}\mathrm{Zr}$ were measured for bombarding energies spanning the Coulomb barrier regions. Experimental fusion barrier distributions were derived from these data and compared with the results of realistic coupled-channels calculations, which included couplings to all orders and treated excitation energies correctly. To gain reasonable agreement for the heavier projectiles it was necessary to include double-phonon excitations of the first $2^{+}$ and $3^{-}$ vibrational states in ${}^{92}\mathrm{Zr}.$ The diffuseness parameter required to fit the high-energy cross sections increases with increasing charge of the projectile and, as found in earlier work, is higher than that required to fit elastic-scattering data. It is suggested that a potential which falls more rapidly at large distance than the Woods-Saxon form might help explain the anomaly.