A New Formula for Phase Shift Calculations Using Square-Integrable Bases

Nuclear scattering and reactions are crucial for nuclear physics, with experiments measuring cross-sections and theoretical methods producing phase shifts. Traditionally scattering is usually computed in coordinate or momentum space, while bound system methods like the configuration-interaction model (shell model) use square-integrable bases, which converge poorly at large asymptotic distances. While the so-called J-matrix theory has been applied to compute phase shifts in square-integrable bases, we introduce a new phase shift formula in these bases, eliminating the need for the asymptotic tail of the scattering wave function. We demonstrate this method in single-channel potential scattering. Our encouraging results provide a concrete step towards a more general approach to scattering and reactions in popular many-body methods such as the shell model.