The astonishing and complete success of the optical model for nucleon-nucleus scattering was one of the earliest triumphs of early 1950s scientific computing, and taught physicists that relatively simple physical models could yield astonishingly realistic physical predictions, even for enormously complex systems. It's not much of an exaggeration to say that almost all the giant wave of scientific computing that characterized the late 1950s and the 1960s, and the continuing push for larger and faster mainframe computers, originated with the optical model in the early 1950s. It was found that using the same potentials that worked for bound states in the independent particle model also worked for nucleon-nucleus scattering. The only needed additional feature was an imaginary term in the central potential, -iW(r), to account for the fact that fewer particles are scattered elastically than are present in the incident beam. When polarized beams became available, the cross sections could be measured with spin-up and with spin-down beams, and this allowed the calculation of the polarization P(θ) or analyzing power A_y(θ), both of which depend on the difference between spin up dσ/dΩ and spin down dσ/dΩ.

The calculations are easy to do. For neutrons, you solve the ordinary Schrödinger equation for each partial wave jℓ and compare the solution to the analytic free particle solutions for those partial waves, to extract the phase shift δ_jℓ of the wave scattered by the potential, in the asymptotic region. This phase shift is easily related to the differential cross section, dσ/dΩ. You will find that the same potential that describes bound states will also describe elastic scattering! In fact generic potentials can be constructed that are very simple functions of (N - Z)/A and of center-of-momentum energy, that will work for almost all nuclei as targets.  [For protons, or other charged projectiles, you have to match asymptotically to the analytic Coulomb functions that describe scattering from a simple nuclear charge distribution.]