A three-body model for the analysis of quasi-free scattering reactions in inverse kinematics

TL;DR

This paper introduces a new three-body model for calculating cross sections of quasi-free scattering reactions in inverse kinematics, using an expansion of the three-body wave function and microscopic optical potentials, applicable at intermediate energies.

Contribution

It presents a novel formalism combining three-body wave function expansion and microscopic optical potentials for analyzing inverse kinematics scattering reactions.

Findings

Validated the method with numerical calculations on $^{12}$C and $^{23}$O reactions.

Discussed the impact of final-state interactions and Pauli principle.

Extended the formalism to energies of current experimental interest.

Abstract

A new method to calculate cross sections for $(p,pn)$ and $(p,2p)$ reactions measured under inverse kinematics conditions is proposed. The method uses the prior form of the scattering transition amplitude, and replaces the exact three-body wave function appearing in this expression by an expansion in terms of $p$-$n$ or $p$-$p$ states, covering the physically relevant excitation energies and partial waves. A procedure of discretization, similar to that used in continuum-discretized coupled-channels calculations, is applied in order to make this expansion finite and numerically tractable. The proposed formalism is non-relativistic but several relativistic kinematical corrections are applied to extend its applicability to energies of current interest. The underlying optical potentials for the entrance and exit channels are generated microscopically, by folding an effective density-dependent G-matrix with the density of the composite nucleus. Numerical calculations for $^{12}$C($p$,$2p$), $^{12}$C($p$,$pn$) and $^{23}$O($p$,$pn$) at $\sim$400~MeV/nucleon are presented to illustrate the method. The role of final-state interactions and Pauli principle between the outgoing nucleons is also discussed.