Background: Physics-based emulators offer a fast and reliable replacement for an exact solution of the scattering problem in nuclear physics. Previous work developed a reduced-basis single channel emulator for nonaffine projectile-target interactions, such as optical potentials, to describe elastic scattering.

Purpose: Since many reactions of interest can be cast as a coupled-channel problem, the purpose of this work is to extend the reduced basis methods (RBM) to a coupled-channel framework.

Method: We generalize the reduced basis method to coupled-channel equations (CC-RBM) to describe inelastic scattering. Although our framework is general, in this work we apply it to reactions where the Hamiltonian coupling term comes from assuming a rotational structure model for the target. From a set of training coupled-channel wave functions, we perform a singular value decomposition to obtain a reduced set of basis wave functions, and then solve the extended (Petrov-)Galerkin equations in that basis. In addition, the empirical interpolation method is used to expand the nonaffine coupling potentials.

Results: We apply the CC-RBM method to elastic and inelastic scattering of neutrons on ${}^{48}\mathrm{Ca}$ including a quadrupole coupling to populate the first $2^{+}$ state, and neutrons on ${}^{208}\mathrm{Pb}$, including an octupole coupling to populate its first $3^{-}$ state. We demonstrate that the CC-RBM calculated elastic and inelastic cross sections match those obtained using traditional finite-difference (high-fidelity) methods. We show that the CC-RBM results can reliably reproduce the nuclear scattering cross sections at different energy regimes.

Conclusions: The computational accuracy versus time plots demonstrate that the CC-RBM method efficiently increases precision with increasing basis size. Most importantly, for the precisions required in reaction calculations (a percent on the cross section), we find the CC-RBM method offers roughly 1.5 orders of magnitude gain in computational speed compared to the traditional coupled-channels solver. However, we also discuss how this scaling becomes less favorable, the larger the number of channels included in the original coupled-channel set.

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• Direct reactions
• Inelastic scattering reactions
• Models & methods for nuclear reactions
• Nuclear reactions
• Nucleon induced nuclear reactions