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

K Hagino,J.M Yao,N Rowley

doi:10.1051/epjconf/201612207002

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.

Highlights

Fusion is defined as a reaction in which two separate nuclei combine together to form a compound nucleus
This is in marked contrast to high energy nuclear reactions, in which the reaction dynamics is much simpler and the distorted wave Born approximation (DWBA) often suffices its treatment
The research field of heavy-ion subbarrier fusion reactions started in the late ’70s, when a large enhancement of fusion cross sections was experimentally discovered with respect to the prediction of a simple potential model

Summary

Introduction

Fusion is defined as a reaction in which two separate nuclei combine together to form a (hot) compound nucleus. Heavy-ion fusion reactions are unique in this respect because a variety of intrinsic degrees of freedom are involved, such as a surface vibration with several multipolarities, various sort of nuclear deformations and the associated rotational motion, and several types of particle transfer processes This is in contrast to atomic and molecular collisions, in which only a limited types of intrinsic motion are involved. The second topic is a semi-microscopic modeling of heavy-ion fusion reactions [7] For this purpose, we first describe microscopically low-lying collective excitations of atomic nuclei with the multi-reference covariant density functional theory, and combine them with coupled-channels calculations. We apply this method to subbarrier fusion reactions of 58Ni+58Ni and 40Ca+58Ni systems, and discuss the role of anharmonicity in subbarrier fusion of these systems

Generalization of the Wong formula for fusion cross sections

Summary