Comparative Study of Wong’s Formula and Coupled-Channel Models in Heavy-Ion Fusion: The ^16O+^144Sm Benchmark

Abstract

Wong’s analytical formula and the coupled-channels method represent the two ends of the spectrum of models used to describe heavy-ion fusion near the Coulomb barrier: the former reduces the problem to penetration of a single parabolic barrier, while the latter treats the coupling of the relative motion to the intrinsic excitations of the colliding nuclei to all orders. This article presents a systematic comparison of the two approaches, using the ^16O+^144Sm reaction as a benchmark. It is shown that the coupled-channels result can be cast, in the eigenbarrier representation, as a weighted sum of Wong-type cross sections over a distribution of barriers, which reduces exactly to Wong’s formula when the couplings are switched off. The two models agree above the barrier, where both approach the classical geometric limit, but diverge by up to two orders of magnitude below it, where channel coupling generates the sub-barrier enhancement that the single-barrier formula cannot reproduce. The fusion barrier distribution sharply distinguishes the two: a single narrow peak for Wong’s formula against a broad, structured profile for the coupled-channels calculation. The regime in which the simple formula remains adequate, and that in which the full treatment is indispensable, are delineated quantitatively