Coupled-Channel Effects in Sub-Barrier Heavy-Ion Fusion Reactions: Barrier Distributions, Deformation, and Deep Sub-Barrier Hindrance

Abstract

The fusion of two heavy ions at energies near and below the Coulomb barrier is one of the most sensitive probes of quantum tunnelling in a many-body environment. Measured fusion cross sections at sub-barrier energies exceed the predictions of a one-dimensional barrier-penetration model by several orders of magnitude, an enhancement that cannot be removed by any reasonable adjustment of the bare potential. This article reviews and develops the coupled-channels description of this phenomenon, in which the relative motion of the colliding nuclei is coupled to their collective and single-particle intrinsic degrees of freedom. It is shown that the coupling replaces the single fusion barrier by a distribution of eigenbarriers, the lowest of which dominates sub-barrier tunnelling and accounts naturally for the enhancement. The fusion barrier distribution, defined as the second energy derivative of the energy-weighted cross section, is introduced as a model-independent fingerprint of the underlying channel structure, and its shape is related to vibrational, rotational, and nucleon-transfer couplings. Using an eigenchannel decomposition together with the iso-centrifugal approximation, the excitation functions and barrier distributions of a representative set of reactions on vibrational and statically deformed targets are reproduced, the enhancement is quantified, and the onset of deep sub-barrier hindrance is discussed. Coupled-channel analysis thus turns precise fusion measurements into a spectroscopic tool for nuclear structure and reaction dynamics