Quantal diffusion approach for multinucleon transfer processes in the $^{58,64}$Ni+$^{208}$Pb reactions: Toward the production of unknown neutron-rich nuclei

Abstract

Background: In recent years, substantial efforts have been made for the study of multinucleon transfer reactions at energies around the Coulomb barrier both experimentally and theoretically, aiming at the production of unknown neutron-rich heavy nuclei. It is crucial to provide reliable theoretical predictions based on microscopic theories with sufficient predictive power.Purpose: This paper aims to clarify the applicability of the quantal diffusion approach based on the stochastic mean-field (SMF) theory for multinucleon transfer processes. Isotope production cross sections are evaluated for the reactions of 64 Ni+ 208 Pb at Ec.m. = 268 MeV and 58 Ni+ 208 Pb at Ec.m. = 270 MeV and are compared with available experimental data. Methods: Three-dimensional time-dependent Hartree-Fock (TDHF) calculations are carried out for a range of initial orbital angular momenta with Skyrme SLy4d functional. Quantal diffusion equations, derived based on the SMF theory, for variances and covariance of neutron and proton numbers of reaction products are solved, with microscopic drift and diffusion coefficients obtained from the time evolution of occupied single-particle orbitals in TDHF. Secondary deexcitation processes, both particle evaporation and fission, are simulated by a statistical compound-nucleus deexcitation model, GEMINI++.Results: Dynamics of a fast isospin equilibration process followed by a slow drift towards the mass symmetry are commonly observed, as expected. Various reaction outcomes are evaluated, including average mass and charge numbers of reaction products, total kinetic energy loss (TKEL), scattering angle, contact time, and production cross sections for primary and secondary products. By comparing with the experimental data, we find that SMF and TDHF quantitatively reproduce experimental data for few-nucleon-transfer channels around the average values. In contrast, for many-nucleon-transfer channels, we find that the SMF approach provides much better description of the experimentally measured isotopic distributions. The results underline the importance of beyond mean-field effects, especially one-body (mean-field) fluctuations and correlations, in describing multinucleon transfer processes. Moreover, through a combined analysis of SMF with a statistical model, GEMINI++, we find a significant contribution of transfer-induced fission, which is consistent with the experimental observation. In some cases, the SMF approach overestimates the isotopic width, requiring further improvements of the theoretical description. Possible ways to improve the description are discussed. Conclusions:The SMF approach is designed to describe the quantum many-body problem according to a classical ensemble of mean-field trajectories, taking into account part of many-body correlations in the description. As it requires feasible computational costs comparable to the ordinary TDHF approach, together with further model improvements, it will be a promising tool to search for optimal reaction conditions to produce yet-unknown neutron-r...

Merging of transport theory with TDHF: multinucleon transfer in U+U collisions

“…In this manner, the SMF approach provides a ground for merging transport theory with the mean-field description. For the detail description of the SMF approach and the applications, we refer the reader the previous publications [39][40][41][42][43][44]. Here we take the neutron N λ 1 and the proton Z λ 1 numbers of the projectile-like fragments as the macroscopic variables.…”