Transfer reactions with the Lagrange-mesh method

TL;DR

This paper introduces an efficient Lagrange-mesh based R-matrix method within DWBA for transfer reaction calculations, demonstrating rapid convergence and analyzing uncertainties in spectroscopic factors.

Contribution

The paper presents a novel application of the Lagrange-mesh technique to R-matrix DWBA calculations, improving computational efficiency and convergence in transfer reaction modeling.

Findings

Excellent convergence with small basis sizes.

Sensitivity of cross sections to R-matrix parameters.

Potential underestimation of spectroscopic factor uncertainties.

Abstract

We apply the $R$-matrix method in Distorted Wave Born Approximation (DWBA) calculations. The internal wave functions are expanded over a Lagrange mesh, which provides an efficient and fast technique to compute matrix elements. We first present an outline of the theory, by emphasizing the $R$-matrix aspects. The model is applied to the 16O(d,p)7Li and 12C(7Li,t)16O reactions, typical of nucleon and of $\alpha$ transfer, respectively. We illustrate the sensitivity of the cross sections with respect to the $R$-matrix parameters, and show that an excellent convergence can be achieved with relatively small bases. We also discuss the effects of the remnant term in DWBA calculations, and address the question of the peripherality in transfer reactions. We suggest that uncertainties on spectroscopic factors could be underestimated in the literature.