# Toward a reliable description of ${(p,pN)}$ reactions in the distorted-wave impulse approximation

## TL;DR

This paper evaluates the accuracy of the distorted-wave impulse approximation (DWIA) in describing proton-induced nucleon knockout reactions at intermediate energies, highlighting the importance of corrections and the consistency of reduction factors with other methods.

## Contribution

It provides a detailed analysis of the effects of various corrections within DWIA on $(p,pN)$ cross sections and assesses the consistency of reduction factors with other approaches.

## Key findings

- Nonlocality corrections and Møller factor significantly impact cross sections.
- Proton-neutron asymmetry dependence of reduction factors is weak and consistent across methods.
- Higher-order effects may be necessary for accurate descriptions at large recoil momentum.

## Abstract

Background: Proton-induced nucleon knockout $(p,pN)$ reactions have been successfully used to study the single-particle nature of stable nuclei in normal kinematics with the distorted-wave impulse approximation (DWIA) framework. Recently, these reactions have been applied to rare-isotope beams at intermediate energies in inverse kinematics to study the quenching of spectroscopic factors. Purpose: Our goal is to investigate the effects of various corrections and uncertainties within the standard DWIA formalism on the $(p,pN)$ cross sections. The consistency of the extracted reduction factors between DWIA and other methods is also evaluated. Method: We analyze the $(p,2p)$ and $(p,pn)$ reactions data measured at the R$^3$B/LAND setup at GSI for carbon, nitrogen, and oxygen isotopes in the incident energy range of 300--450 MeV/u. Cross sections and reduction factors are calculated by using the DWIA method. The transverse momentum distribution of the $^{12}$C($p$,$2p$)$^{11}$B reaction is also investigated. Results: We have found that including the nonlocality corrections and the M\o ller factor affects the cross sections considerably. The proton-neutron asymmetry dependence of reduction factors extracted by the DWIA calculation is very weak and consistent with those given by other reaction methods and \textit{ab initio} structure calculations. Conclusions: The results found in this work provide a detailed investigation of the DWIA method for $(p,pN)$ reactions at intermediate energies. They also suggest that some higher-order effects, which is essential for an accurate cross-section description at large recoil momentum, is missing in the current DWIA and other reaction models.