Fusion of light nuclei in a multicluster realization of the three-body problem

TL;DR

This paper develops a few-body dynamics method using Faddeev equations in momentum space to calculate fusion cross sections of light nuclei with cluster representations, accounting for Coulomb effects and comparing with experimental data.

Contribution

It introduces a novel approach combining Faddeev integral equations and a two-potential method to accurately model light nuclei fusion reactions with Coulomb effects.

Findings

Calculated total cross sections agree with experimental data across 1 keV to 20 MeV.

Implemented Coulomb t-matrix and off-shell effects in the momentum space framework.

Estimated atomic electron anti-screening effects on Coulomb interactions.

Abstract

This work describes a few-body dynamics method based on the Faddeev integral equations in momentum space for determining the total cross sections of fusion and breakup reactions with two- and three-body final channels in the continuum, employing a cluster representation of the colliding nuclei. Total cross sections were obtained for the reactions $^3\text{He}(T,D)^4\text{He}$, $^3\text{He}(T,np)^4\text{He}$, $^3\text{He}(T,nD)^3\text{He}$, $^3\text{He}(^3\text{He},2p)^4\text{He}$, $^3\text{He}(^3\text{He},pD)^3\text{He}$, $^7\text{Li}(^3\text{He},\phantom{0}^4\text{He})^6\text{Li}$, $^7\text{Li}(^3\text{He},D^4\text{He})^4\text{He}$, and $^7\text{Li}(^3\text{He},T^3\text{He})^4\text{He}$, in which both the projectile and the target nucleus were treated in a cluster representation. The work also implements a two-potential method to determine the Coulomb $t-$matrix and to account for Coulomb effects in short-range dynamics in momentum space. Calculations of the initial-state Coulomb interaction were performed; furthermore, an estimate was obtained for the magnitude of the off-shell effect of the Coulomb $t-$matrix, as well as the magnitude of the atomic electron anti-screening effect on the Coulomb interaction of the colliding nuclei. The calculated contribution of the cluster mechanism to the total cross section of the considered fusion reactions in the kinetic energy range $T\in[1~\text{keV},20~\text{MeV}]$ is in good agreement with known experimental data.