Cross section calculation of T($^3$He, np)$^4$He and (Ty$^-$)($^3$He, npy$^-$) $^4$He in the three-body dynamics

TL;DR

This paper performs detailed three-body calculations of the $^3$He+T fusion reaction cross sections, incorporating complex interactions and Coulomb effects, and explores the influence of muons on the reaction process.

Contribution

It introduces a comprehensive three-body Faddeev approach to calculate fusion cross sections and examines muon effects within this framework, advancing understanding of muon-catalyzed fusion mechanisms.

Findings

Three-body calculations provide detailed cross sections for $^3$He+T fusion.

Muon presence can enhance reaction cross sections via a phase factor.

The muon effect persists even in the first Born approximation.

Abstract

This work presents three-body calculations of the cross sections for the $^3$He+T $\to$ n+p+$^4$He fusion reaction. These calculations were performed by solving a set of six coupled Faddeev integral equations, utilizing a cluster representation of the target nucleus, the triton, as a bound neutron-deuteron system. Short-range interactions within the two-body subsystems included microscopic np, nd, n4He, and n3He scattering matrices, as well as phenomenological d3He models that allow for the coupling of the elastic channel with the d3He reaction channel. The roles of the d3He models and the Coulomb interaction between the 3He and T nuclei are briefly discussed. The resulting three-body reaction matrix was then utilized to estimate the role of a muon in the process $^3$He+(Ty$^-$) $\to$ n+p+$^4$He+y$^-$ involving a Ty$^-$ atom, where y$^-$ in [$e^-$,$\mu^-$]. It is demonstrated that the effect of cross-section enhancement induced by the muon's presence in the reaction zone is governed by a phase factor and persists in the first Born approximation for the exact four-body scattering matrix.