# Theory of surrogate nuclear and atomic reactions with three charged particles in the final state proceeding through a resonance in the intermediate subsystem

## TL;DR

This paper develops a comprehensive three-body formalism for surrogate nuclear and atomic reactions involving resonances, accounting for Coulomb interactions in intermediate and final states, and derives an expression for the triply differential cross section.

## Contribution

It introduces a general theory incorporating Coulomb effects in both intermediate and final states for three charged particles in surrogate reactions, extending previous models.

## Key findings

- Coulomb effects reduce the impact of final-state Coulomb interactions on the cross section.
- Derived an explicit expression for the triply differential cross section.
- The formalism can analyze Coulomb effects on resonance line shapes.

## Abstract

Within a few-body formalism, we develop a general theory of surrogate nuclear and atomic reactions with the excitation of a resonance in the intermediate binary subsystem leading to three charged particles in the final state. The Coulomb interactions between the spectator and the resonance in the intermediate state and between the three particles in the final state are taken into account. Final-state three-body Coulomb multiple-scattering effects are accounted for using the formalism of the three-body Coulomb asymptotic states based on the work published by one of us (A.M.M.) under the guidance of L. D. Faddeev. An expression is derived for the triply differential cross section. It can be used for investigation of the Coulomb effects on the resonance line shape as well as the energy dependence of the cross section. We find that simultaneous inclusion of the Coulomb effects in the intermediate and final state decreases the effect of the final-state Coulomb interactions on the triply differential cross section.