Systematic study of the heavy-ion fusion dynamics at near-barrier energies

Abstract

In recent decades, the study of capture and fusion dynamics in heavy-ion collisions has been a subject of intense experimental and theoretical interests because the heavy-ion capture not only is of central importance for nucleosynthesis but also can reveal rich interplay between nuclear structure and reaction dynamics. Theoretically, the heavy-ion capture and fusion processes at energies near the Coulomb barrier can be treated as a multidimensional barrier penetration problem. The multidimensional barrier penetration process can be described by solving the coupled-channel equations, i.e., the coupled-channel (CC) model. However, for heavy reaction systems, it is necessary to take into account a large number of channels which is not easy to realize in the CC model. Moreover, the structure information of the interacting nuclei are needed as inputs. Therefore, full CC calculations become intractable in many cases including many fusion reactions leading to superheavy nuclei. On the other hand, in the eigenchannel framework, the couplings to other channels split the single potential barrier into a set of discrete barriers. Based on the concept of the barrier distribution, several empirical CC approaches have been developed. Recently, we have developed an empirical coupled-channel (ECC) model and performed a systematic study of capture excitation functions for 220 reaction systems. In this ECC model, an asymmetric Gaussian-form barrier distribution function was used to take effectively into account the effects of inelastic excitation couplings and neutron transfer coupling. Based on the interaction potential between the projectile and the target, empirical formulas were proposed for the parameters of the barrier distribution according to the static and dynamical deformations of the two colliding nuclei. For the vibrational coupling effect and the rotational coupling effect, the parameters of the empirical formulas were given, respectively. For spherical reaction systems (vibrational coupling effect), the width of the barrier distribution increases with the charge product of the reaction system, while for the deformed reaction systems (rotational coupling effect), besides the charge product of the reaction system, the width of the barrier distribution is also related to the static deformation parameters of the projectile and the target. For some reaction systems, the coupling effects of the positive Q -value neutron transfer (PQNT) channels are needed to explain the enhancement of sub-barrier capture cross sections. In this ECC model, the effects of PQNT are simulated by broadening the barrier distribution. Moreover, the positive Q value for one neutron pair transfer is used to broaden the barrier distribution in the present model. Among these 220 reaction systems, there are 89 systems with positive Q value for one neutron pair transfer channel. The calculated capture cross sections of most of these 89 reaction systems are in good agreement with the experimental values, which implies that the Q value for one neutron pair transfer is very important to understanding of the coupling to PQNT channels. Generally speaking, the ECC model together with the empirical formulas for parameters of the barrier distribution works quite well in the description of the capture cross sections at near-barrier energies. This model can provide useful information on capture dynamics and predictions of capture cross sections for the synthesis of superheavy nuclei. In the present paper, we will review this ECC model and its applications.