Spectral-shift and scattering-equivalent Hamiltonians on a coarse momentum grid

• Main Authors: María Gómez-Rocha, Enrique Ruiz Arriola
• Format: Article
• Language: English
• Published: Elsevier 2020-01-01
• Series: Physics Letters B
• Online Access: http://www.sciencedirect.com/science/article/pii/S0370269319308299

The solution of the scattering problem based on the Lippmann-Schwinger equation requires in many cases a discretization of the spectrum in the continuum which does not respect the unitary equivalence of the S-matrix on the finite grid. We present a new prescription for the calculation of phase shifts based on the shift that is produced in the spectrum of a Chebyshev-angle variable. This is analogous to the energy shift that is produced in the energy levels of a scattering process in a box, when an interaction is introduced. Our formulation holds for any momentum grid and preserves the unitary equivalence of the scattering problem on the finite momentum grid. We illustrate this procedure numerically considering the non-relativistic NN case for S01 and S13 channels. Our spectral shift formula provides much more accurate results than the previous ones and turns out to be at least as competitive as the standard procedures for calculating phase shifts. Keywords: Lippmann-Schwinger equation, Phase shifts, Scattering, Momentum grid, Equivalent hamiltonian