Wavefunction-Based Emulation of Coupled-Channels Scattering with Non-Affinely Parametrized Interactions

TL;DR

This paper extends a reduced-basis emulator to coupled-channel nuclear scattering problems, demonstrating it can accurately and efficiently reproduce cross sections with significant speed gains over traditional methods.

Contribution

The work develops a general coupled-channel reduced-basis method (CC-RBM) for nuclear scattering, applying it to complex reactions with rotational couplings, and shows substantial computational efficiency improvements.

Findings

CC-RBM accurately reproduces traditional scattering cross sections.

The method achieves roughly 1.5 orders of magnitude speedup.

CC-RBM maintains accuracy across different energy regimes.

Abstract

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 emulator for single-channel elastic scattering using an optical potential. Since many reactions of interest can be cast as a coupled-channel problem, the purpose of this work is to extend the RBM to a coupled-channel framework (CC-RBM). Although the framework derived 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 wavefunctions, we perform a singular value decomposition to obtain a reduced set of basis wavefunctions, and then solve the extended (Petrov-)Galerkin equations. In addition, the empirical interpolation method is used to expand the potentials. We apply the CC-RBM method to elastic and inelastic scattering of neutrons on 48Ca including a quadrupole coupling to populate the first 2+ state, and neutrons on 208Pb, including an octupole coupling to populate its first 3- state. We demonstrate that the CC-RBM calculated cross sections match those obtained using traditional finite-difference methods. We show that the CC-RBM results can reliably reproduce the nuclear scattering cross sections at different energy regimes. 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 one and a half 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 coupled-channel set.