# Core-excitation effects in three-body breakup reactions studied using the Faddeev formalism

## TL;DR

This study uses the Faddeev formalism to analyze core-excitation effects in three-body nuclear breakup reactions, finding that the cross section factorization approach is more reliable in breakup than in transfer reactions.

## Contribution

It extends the Faddeev formalism to include core excitation effects in three-body breakup reactions, providing new insights into reaction mechanisms.

## Key findings

- Cross section factorizes well in breakup reactions.
- Core excitation effects differ significantly between breakup and transfer.
- Rescaling by spectroscopic factors is reliable for breakup reactions.

## Abstract

Previous studies of $(d,p)$ reactions in three-body (proton, neutron, nuclear core) systems revealed a nontrivial effect of the core excitation: the transfer cross section cannot be factorized into the spectroscopic factor and the single-particle cross section obtained neglecting the core excitation. This observable, up to a kinematic factor, is the angular distribution of the core nucleus in the $(p,d)$ reaction. The study of the core excitation effect for the most closely related observable in the $(p,pn)$ three-body breakup, i.e., the core angular distribution, is aimed in the present work. Breakup of the one-neutron halo nucleus in the collision with the proton is described using three-body Faddeev-type equations extended to include the excitation of the nuclear core. The integral equations for transition operators are solved in the momentum-space partial-wave representation. Breakup of 11Be nucleus as well as of model $A=11$ $p$-wave nuclei is studied at beam energies of 30, 60, and 200 MeV per nucleon. Angular and momentum distributions for the 10Be core in ground and excited states is calculated. In sharp contrast to $(p,d)$ reactions, the differential cross section in most cases factorizes quite well into the spectroscopic factor and the single-particle cross section. Due to different reaction mechanisms the core excitation effect in the breakup is very different from transfer reactions. A commonly accepted approach to evaluate the cross section, i.e., the rescaling of single-particle model results by the corresponding spectroscopic factor, appears to be reliable for breakup though it fails in general for transfer reactions.