Direct reaction description of sub- and above-barrier fusion of heavy ions

TLDR

The study explores a possible link between the direct‑reaction fusion model, especially at sub‑barrier energies, and spontaneous fission. The authors propose a new direct‑reaction method for calculating fusion cross sections σ_F. They define a fusion potential W_F as part of the optical model’s imaginary potential and compute σ_F from the absorption due solely to W_F, optionally adding coupled‑channel contributions for special cases. With r_F = 1.40–1.50 fm, the method reproduces experimental σ_F across sub‑ and above‑barrier energies for many nuclear pairs, and including coupled‑channel effects improves fits when structure effects are significant.

Abstract

A new approach to calculation of the fusion cross section ${\ensuremath{\sigma}}_{F}$, based on the direct reaction concept, is presented. The method is to define a fusion potential ${W}_{F}$ [with r\ensuremath{\le}${R}_{F}$=${r}_{F}$(${A}_{1}^{1/3}$+${A}_{2}^{1/}$ 3)] as a part of the imaginary potential of the usual optical model. The ${\ensuremath{\sigma}}_{F}$ is then obtained as that part, due to only ${W}_{F}$, of the total absorption cross section. It is seen that, if ${r}_{F}$ is chosen as 1.40--1.50 fm, the value of ${\ensuremath{\sigma}}_{F}$ computed as described fits the experimental ${\ensuremath{\sigma}}_{F}$ very well, in both sub- and above-barrier regions, and for a variety of fusing nuclear pairs ${A}_{1}$ and ${A}_{2}$. In most cases, it is sufficient to consider only the incident (elastic scattering) channel. In a few cases, in which some specific nuclear structure effects are involved, it is found necessary to perform coupled-channel calculations. Then absorption due to other channels is also taken into account explicitly. It is shown that adding these contributions is the key to getting good fits to data, under the above-mentioned special circumstances. A possible relation of what the present approach describes, particularly when it is used in the sub-barrier region, to (spontaneous) fission is also discussed.