# Examination of the adiabatic approximation for $(d,p)$ reactions

## TL;DR

This paper systematically evaluates the validity of the adiabatic approximation in deuteron-induced ($d,p$) reactions, highlighting its generally acceptable accuracy and the importance of closed channels at low energies.

## Contribution

It provides a comprehensive analysis of the adiabatic approximation's accuracy and the role of closed channels in ($d,p$) reactions using the CDCC method across 128 systems.

## Key findings

- AD approximation affects cross sections by less than 20%.
- Nonadiabatic cases where AD breaks down are identified.
- Closed channels significantly influence results below 10 MeV.

## Abstract

Background: Deuteron-induced one-neutron transfer reactions have been used to extract single-particle properties of nuclei, and the adiabatic (AD) approximation is often used to simply treat the deuteron breakup states. Purpose: The primary goal is to examine the validity of the AD approximation for the ($d,p$) reaction systematically. We clarify also the role of the closed-channels often ignored in the description of breakup reactions. Methods: We calculate the ($d,p$) cross sections with the continuum-discretized coupled-channels method (CDCC) for 128 reactions systems and compare the results with those obtained by the CDCC calculation with the AD approximation. Effect of the closed channels are investigated by ignoring the closed channels in CDCC. Results: The AD approximation affects in general the ($d,p$) cross section by less than 20 %, but some exceptional nonadiabatic cases for which the AD approximation breaks down are found. The closed channels turn out to give significant effects on the cross section at deuteron energies less than about 10 MeV. Conclusions: The use of the AD approximation in the description of the ($d,p$) reaction can be justified in many cases, with the uncertainty of less than about 20 %. The existence of some nonadiabatic cases nevertheless should be realized. The neglect of the closed channels without confirming the convergence of the CDCC result is not recommended.