A dynamical study of fusion hindrance with the Nakajima–Zwanzig projection method

Yasuhisa Abe,Caiwan Shen,Quentin Hourdillé,David Boilley

doi:10.1093/ptep/ptab005

Abstract

Abstract A new framework is proposed for the study of collisions between very heavy ions which lead to the synthesis of Super-Heavy Elements (SHE), to address the fusion hindrance phenomenon. The dynamics of the reaction is studied in terms of collective degrees of freedom undergoing relaxation processes with different time scales. The Nakajima–Zwanzig projection operator method is employed to eliminate fast variables and derive a dynamical equation for the reduced system with only slow variables. There, the time evolution operator is renormalised and an inhomogeneous term appears, which represents a propagation of the given initial distribution. The term results in a slip to the initial values of the slow variables. We expect that gives a dynamical origin for the so-called “injection point $s$” introduced by Swiatecki et al. in order to reproduce absolute values of measured cross sections for SHE. A formula for the slip is given in terms of physical parameters of the system, which confirms the results recently obtained with a Langevin equation, and permits us to compare various incident channels.

Highlights

Finding the limit of existence of nuclei is one of the challenging research programs in nuclear physics. vIt gives the limit of chemical elements, with which all the matter of the world is made
We consider the dynamical evolution of di-nucleus systems of very heavy ions as relaxation processes of collective degrees of freedom with different time scales, starting with the initial conditions given by the incident channel
We have found that Smoluchowski operator is renormalised and that the inhomogeneous term appears to result in a slip in the initial values of the slow variables, which provides a dynamical origin of the injection point phenomenologically introduced in Fusion-by-Diffusion model (FBD)

Summary

Introduction

Finding the limit of existence of nuclei is one of the challenging research programs in nuclear physics. vIt gives the limit of chemical elements, with which all the matter of the world is made. Later, combining of the elimination of both neck degree of freedom and momentum ones in case of strong friction lead to the incident-energy dependence of the initial slip, explaining the behaviour of the injection point parameter, systematically both for the cold and the hot fusion paths [33]. This is encouraging for theoretical predictions on on-going and/or future experiments for synthesis of heavier elements with various incident channels.

Projectors

Renormalised Smoluchowski operator and initial slip

Formation Probability with the initial shift: A New Dynamical Hindrance

Concluding Remarks