Testing the validity of the surface approximation for reactions induced by weakly bound nuclei with a fully quantum-mechanical model

TL;DR

This study evaluates the surface approximation in nuclear breakup reactions using a quantum-mechanical model, confirming its validity for $^6$Li but highlighting limitations for deuterons at higher energies.

Contribution

It introduces the IAV-cut method to test the surface approximation's validity across different reactions and energies, providing a systematic quantum-mechanical validation.

Findings

Surface approximation is valid for $^6$Li reactions across energies.

Deuteron reactions show interior wave function dependence, especially at higher energies.

IAV and IAV-cut agree well for $^6$Li, validating semi-classical models.

Abstract

We examine the validity of surface approximation for breakup reactions using a fully quantum-mechanical model proposed by Ichimura, Austern, and Vincent (IAV). Analogous to the semi-classical picture, we introduce radial cut-offs to scattering waves in the IAV framework, which we refer to as IAV-cut. Systematic calculations are conducted for nonelastic breakup reactions induced by $^6$Li and deuterons at various incident energies. A comparison between the results obtained from IAV and IAV-cut is performed. The excellent agreement observed between IAV and IAV-cut in $^{6}$Li induced reactions, regardless of incident energy and target nuclei, signifies their insensitivity to the inner part of the scattering wave function, thus providing validation for the semi-classical picture. However, for deuteron induced breakup reactions, the IAV-cut results exhibit a suppression in the cross section, suggesting a strong dependence on the interior wave functions. This suppression is further enhanced as the incident energy increases.