Scattering phase shifts from overlap relations in the -matrix method
Phys. Rev. C 113, 024004 – Published 17 February, 2026
DOI: https://doi.org/10.1103/nd89-xtlw
Abstract
We present an approach to the quantum mechanical scattering problem in which computation of a wave function and determination of scattering parameters are separate steps. This approach is built on the -matrix formalism, but in place of the usual -matrix procedures we introduce a novel formula that extracts phase shifts accurately from scattering states computed in a square-integrable basis. This formula is closely analogous to existing integral relations or overlap integrals in a (continuous) position basis. We then demonstrate the extraction of phase shifts from wave functions in single-channel potential scattering. For a soft but realistic nucleon-nucleon potential, Daejeon16, we obtain good phase shifts with as few as six oscillator basis states, using the Lippmann-Schwinger equation to obtain scattering states at arbitrary energies even in this highly truncated space. These results constitute a step towards calculations in which scattering observables are extracted from scattering states generated in a many-body framework with square-integrable basis functions, such as the configuration-interaction shell model.
