All Order Coupled Channels Calculations for Sub Barrier Fusion: Multi Phonon Effects and Barrier Distribution Asymmetry in 58Ni+58Ni

Abstract

The enhancement of heavy-ion fusion cross sections at sub-barrier energies is now understood as a consequence of the coupling of the relative motion to the collective excitations of the colliding nuclei. Quantitatively reproducing the enhancement, and the structure of the experimentally extracted barrier distribution, requires that these couplings be treated to all orders rather than in the linear (first-order) approximation. This article presents all-order coupled-channels calculations of sub-barrier fusion, in which the full, non-linearized nuclear coupling form factor and the complete multi-phonon channel space are retained. Taking the ^58Ni+^58Ni reaction as a benchmark, it is shown that the linear-coupling approximation reproduces the gross enhancement but fails to account for the asymmetry of the barrier distribution, which the all-order treatment recovers. The sub-barrier cross section is found to converge only when two or more phonons are included, the converged enhancement exceeding the single-phonon result by about a factor of two and a half, while the first moment of the barrier distribution is preserved. The all-order coupled-channels method is thus confirmed as the quantitative standard for sub-barrier fusion, and the present calculation provides a controlled benchmark of its multi-phonon convergence..