Abstract
The eigenvector continuation $R$-matrix theory is an algorithm to emulate the nuclear reaction observables at different coupling constants. It exploits the analytic properties of eigensolutions in coupling constants. In this work, several extensions of the eigenvector continuation $R$-matrix theory are proposed by utilizing the analytic properties of regular eigensolutions in momentum and angular momentum. Taking a two-body scattering problem as the proof of concept, the specific extension based on analyticity in momentum is shown to be particularly useful, resulting in new phase-shift emulators with good extrapolation and interpolation properties with respect to momentum. It can be further hybridized with the original eigenvector continuation $R$-matrix theory to give an emulator that predicts the phase shifts at different coupling constants and different momenta simultaneously.
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