A Dynamical Study of Fusion Hindrance with Nakajima-Zwanzig Projection Method

TL;DR

This paper introduces a new theoretical framework using the Nakajima-Zwanzig projection method to study fusion hindrance in heavy-ion collisions, linking microscopic dynamics to the injection point parameter in super-heavy element synthesis.

Contribution

It develops a dynamical model that derives equations for slow variables in heavy-ion fusion, providing a physical basis for the injection point parameter used in cross section calculations.

Findings

Derivation of a dynamical equation with an inhomogeneous term for slow variables.

Identification of a slip term explaining the injection point parameter.

Confirmation of results with Langevin equation approaches.

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 variable 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 of parameter "injection point $s$" introduced by Swiatecki et al in order to reproduce absolute values of measured cross sections for SHE. Formula for the slip is given in terms of physical parameters of the system, which confirms the results recently obtained with a Langevin equation.