Numerical calculations are a powerful tool for understanding the properties of atomic nuclei. However, a discrepancy exists between the typical bases used for bound and continuum state calculations. Bound state calculations use a square-integrable (L2) basis while scattering state calculations use the momentum basis. In this work, I implement the J-matrix method, which is an exact representation of the scattering states in the oscillator (L2) basis. Numerical instability is a problem for this harmonic oscillator representation of scattering equations (HORSE), so we institute a new approximation to the irregular asymptotic solution to stabilize phase shifts at higher energies. Further exploration of the J-matrix method in this work leads to a novel approach analogous to “integral methods” in coordinate space for phase shift extraction. I outline the properties of the J-matrix method and lay the groundwork for extending many-body shell-model calculations beyond standard bound state calculations to multi-channel scattering using the new integral method. As a proof of concept, I apply the J-matrix method to model low-energy elastic n-4He differential cross-sections.