Theoretical considerations about heavy-ion fusion in potential scattering

TL;DR

This paper compares two theoretical models for heavy-ion fusion, highlighting the importance of the nuclear potential at short distances and its influence on fusion predictions, supported by data consistency.

Contribution

It provides a detailed analysis of the differences between WKB and optical potential models near the critical energy, emphasizing the role of the inner nuclear potential.

Findings

Major differences occur around the critical energy.

Critical energy depends on the short-range nuclear potential.

Fusion data supports the importance of the inner potential region.

Abstract

We carefully compare the one-dimensional WKB barrier tunneling model, and the one-channel Sch\"odinger equation with a complex optical potential calculation of heavy-ion fusion, for a light and a heavy system. It is found that the major difference between the two approaches occurs around the critical energy, above which the effective potential for the grazing angular momentum ceases to exhibit a pocket. The value of this critical energy is shown to be strongly dependent on the nuclear potential at short distances, on the inside region of the Coulomb barrier, and this dependence is much more important for heavy systems. Therefore the nuclear fusion process is expected to provide information on the nuclear potential in this inner region. We compare calculations with available data to show that the results are consistent with this expectation.