Application of the Lagrange mesh method in continuum-discretized coupled-channels calculations

TL;DR

This paper introduces an efficient Lagrange-mesh discretization method for continuum states in CDCC calculations, demonstrating high accuracy and computational speed in modeling weakly bound nuclei reactions, especially for $^6$Li induced processes.

Contribution

The paper develops a new CDCC model code using the Lagrange-mesh method combined with the Numerov algorithm, improving the accuracy and efficiency of continuum discretization in nuclear reaction calculations.

Findings

Lagrange-mesh method outperforms the bin method in accuracy and speed.

Coupling effects of high angular momentum states are moderate at high energies.

Closed channels are crucial near the Coulomb barrier for accurate $^6$Li breakup modeling.

Abstract

We apply the Lagrange-mesh method to discretize continuum states of weakly bound nuclei for continuum-discretized coupled-channel (CDCC) calculations of three-body breakup reactions. This discretization method is compared with the bin method, which is regarded as the standard continuum discretization method, for the $d$ and $^6$Li induced reactions. An improved Numerov algorithm is used to solve the coupled channels equations, which permits a fast integration of equations and a convenient treatment of the closed channels. A new CDCC model code named \emph{CDCC-R} is developed. In all cases, the combination of the Lagrange-mesh method and the Numerov algorithm shows high efficiency and accuracy for the CDCC calculations of the elastic scattering and breakup reactions. Especially, various numerical and physical aspects are discussed for $^6$Li induced reactions. The coupling effects of the continuum states with high orbital angular momentum and closed channels are discussed. Moderate effects are found in the calculations for elastic scattering and breakup reaction when $F$- and $G$-wave continuum states are included in CDCC model space for $^6$Li induced reactions at the incident energies well above the Coulomb barrier. The closed channel effect is found to be indispensable for $^6$Li breakup reaction calculation when the incident energy is around the Coulomb barrier.