Computation of Elastic Scattering Phase Shifts via Analytic Continuation of Fredholm Determinants Constructed Using an L 2 Basis

TLDR: In this article, it was shown that the Fredholm determinant for the Lippmann-Schwinger equation can be computed for complex energies using only ${L}^{2}$ basis functions, showing that it is not necessary to explicitly enforce asymptotic boundary conditions for numerical scattering computations.

Abstract: It is shown that the Fredholm determinant for the Lippmann-Schwinger equation may be computed for complex energies using only ${L}^{2}$ basis functions. Analytic continuation to the real axis in the $E+i\ensuremath{\epsilon}$ limit gives elastic scattering phase shifts over a continuous range of energies, showing that it is not necessary to explicitly enforce asymptotic boundary conditions for numerical scattering computations, and suggesting that elastic electron-atom or -ion scattering information may be obtained using standard bound-state configuration-interaction methods.