Recent developments in heavy-ion fusion reactions around the Coulomb barrier

TL;DR

This paper reviews recent theoretical advances in heavy-ion fusion reactions near the Coulomb barrier, focusing on a generalized fusion cross section formula and a semi-microscopic modeling approach incorporating nuclear structure effects.

Contribution

It introduces a generalized Wong formula with energy-dependent barrier parameters and a semi-microscopic coupled-channels model integrating nuclear structure calculations.

Findings

Generalized formula matches full quantum calculations for light systems.

Semi-microscopic model explains subbarrier fusion enhancement.

Anharmonicity influences low-lying vibrational contributions.

Abstract

The nuclear fusion is a reaction to form a compound nucleus. It plays an important role in several circumstances in nuclear physics as well as in nuclear astrophysics, such as synthesis of superheavy elements and nucleosynthesis in stars. Here we discuss two recent theoretical developments in heavy-ion fusion reactions at energies around the Coulomb barrier. The first topic is a generalization of the Wong formula for fusion cross sections in a single-channel problem. By introducing an energy dependence to the barrier parameters, we show that the generalized formula leads to results practically indistinguishable from a full quantal calculation, even for light symmetric systems such as $^{12}$C+$^{12}$C, for which fusion cross sections show an oscillatory behavior. We then discuss a semi-microscopic modeling of heavy-ion fusion reactions, which combine the coupled-channels approach to the state-of-the-art nuclear structure calculations for low-lying collective motions. We apply this method to subbarrier fusion reactions of $^{58}$Ni+$^{58}$Ni and $^{40}$Ca+$^{58}$Ni systems, and discuss the role of anharmonicity of the low-lying vibrational motions.