Theoretical study of multinucleon transfer reactions by coupling the Langevin dynamics iteratively with the master equation

Abstract

Multinucleon transfer (MNT) reactions have received increasing interest in the synthesis of neutron-rich nuclei due to the distinct limitations of other reactions, particularly in the $N=126$ region, which represents the last waiting point of astrophysical nucleosynthesis. However, it is still a challenging endeavor to describe the MNT process between heavy nuclei. In this study, we develop a theoretical framework that couples the Langevin dynamics iteratively with the master equation, which is based on the HICOL model (CLIM-H). The random transfer process is achieved by solving the master equation using the Monte Carlo method, where the parametric transfer probability with a $Q$ window is employed. The isotope distributions for $^{58,64}\mathrm{Ni}+^{208}\mathrm{Pb}$, as well as the angular and isotope distributions of the recently measured $^{206}\mathrm{Pb}+^{118}\mathrm{Sn}$, could be generally reproduced based on this method. Contrary to previous theoretical predictions which show a high production cross section of $N=126$ nuclei, current calculations do not reveal appreciable cross sections. The distinguishing characteristic of this approach is its ability to generate not only the mass distribution but also the charge distribution self-consistently, which could provide references for many other studies using the multidimensional Langevin equation considering only the mass asymmetry degree of freedom.