Nonlocal Scattering Problem in Harmonic-Oscillator-Based R-matrix Approach

A nonlocal two-body scattering problem for optical potentials of the Perey–Buck type is solved within a newly-developed version of the R -matrix approach. The approach is based on harmonic oscillator expansion of the scattering wave functions within the range of the optical potential. It results in structurally identical algebraic representations both for local and nonlocal optical potentials as well as for the kinetic energy and norm operators, which simplifies and optimizes the coding procedure. The method has been tested for proton scattering at 10, 30 and 90 MeV. With a sufficient number of harmonic oscillator basis states the new method reproduces differential cross sections obtained using available reaction codes. The nonlocal calculations were also used as a testing ground for local-equivalent models. It was found that below 30 MeV next-to-leading order models are sufficient to describe elastic scattering, while at 90 MeV this approximation works well only up to 100∘ 100 ∘ . The method developed could be used in reaction calculations within distorted-wave models and in combining scattering calculations with various few- and many-body structure methods that use harmonic oscillator expansions.