Sensitivity to multi-phonon excitations in heavy-ion fusion reactions

Measured cross sections for the fusion of ⁶⁴Ni with ⁶⁴Ni, ⁷⁴Ge, and ¹⁰⁰Mo targets are analyzed in a coupled-channels approach. The data for the ⁶⁴Ni target above 0.1 mb are reproduced by including couplings to the low-lying 2⁺ and 3^- states and the mutual and two-phonon excitations of these states. The calculations become more challenging as the fusing nuclei become softer and heavier, and excitations to multi-phonon states start to play an increasingly important role. Thus it is necessary to include up to four-phonon excitations to reproduce the data for the ⁶⁴Ni+⁷⁴Ge system. Similar calculations for ⁶⁴Ni+¹⁰⁰Mo, and also for the symmetric ⁷⁴Ge+⁷⁴Ge system, show large discrepancies with the data. Possible ways to improve the calculations are discussed.