A consistent four-body CDCC model of low-energy reactions: Application to 9Be + 208Pb

TL;DR

This paper develops a consistent four-body CDCC model for low-energy reactions involving 9Be and 208Pb, accurately describing elastic scattering, breakup, and fusion processes by treating 9Be as a three-body system and discretizing its continuum.

Contribution

It introduces a novel four-body CDCC approach that simultaneously models elastic, breakup, and fusion reactions with a detailed three-body description of 9Be.

Findings

The model accurately reproduces low-lying states of 9Be.

Elastic scattering and fusion cross sections are successfully calculated.

The approach provides a comprehensive framework for low-energy nuclear reactions.

Abstract

We investigate the $^9$Be + $^{208}$Pb elastic scattering, breakup and fusion at energies around the Coulomb barrier. The three processes are described simultaneously, with identical conditions of calculations. The $^{9}$Be nucleus is defined in an $\alpha + \alpha$ + n three-body model, using the hyperspherical coordinate method. We first analyze spectroscopic properties of $^9$Be, and show that the model provides a fairly good description of the low-lying states. The scattering with $^{208}$Pb is then studied with the Continuum Discretized Coupled Channel (CDCC) method, where the $\alpha+\alpha$ + n continuum is approximated by a discrete number of pseudostates. Optical potentials for the $\alpha$+ $^{208}$Pb and n+ $^{208}$Pb systems are taken from the literature. We present elastic-scattering and fusion cross sections at different energies.