Coupled-channel scattering from artificial confinement

Abstract

Artificial confinement encodes continuum scattering information in discrete, bound-state-like spectra, allowing reaction observables to be extracted with finite-basis or finite-domain methods. We apply this strategy to a two-channel cluster model of ${}^4$He with open ${}^3$H+p and ${}^3$He+n channels. We extract coupled-channel observables from spectra generated by a harmonic-oscillator (HO) trap, a spherical hard wall, and, within a single-partial-wave truncation, a periodic cubic box. The three geometries are formulated in a unified quantization-condition framework and benchmarked against a continuum $R$-matrix calculation. Above the second-channel threshold, several confined levels at a common scattering energy are combined in an overdetermined fit to determine two phase shifts and an inelasticity. Without Coulomb interactions, all three geometries yield consistent results for the ${}^1{S}_0$ and ${}^3{P}_1$ partial waves. With Coulomb interactions in the charged ${}^3$H+p channel, the HO and spherical-wall results also agree closely with the continuum reference. A Monte Carlo propagation study shows that spectral uncertainties are amplified near trap-function poles and along poorly conditioned directions associated with the inelasticity and phase-shift difference, whereas the phase-shift sum remains comparatively robust. These results provide a controlled benchmark for confinement-based scattering methods and delineate their strengths and limitations for future few-body and ab initio reaction calculations.