Coupled-channels reactions for charged particles in harmonic traps

Based on our previous work about Coulomb corrections in the trap method [H. Zhang et al. Phys. Lett. B 850, 138490 (2024)], we extend the Coulomb-corrected Busch-Englert-Rza\ifmmode \dot{z}\else \.{z}\fi{}ewski-Wilkens formula in coupled-channels nuclear reactions and examine the reliability by taking $^{4}\mathrm{He}=[^{3}\mathrm{H}+p]+[^{3}\mathrm{He}+n]$ as an example. The obtained numerical results are generally well consistent with conventional methods. Our work lays some groundwork for analyzing the coupled-channel reactions involving light charged particles within the trap method.