Isospectral scattering for relativistic equivalent Hamiltonians on a coarse momentum grid

TL;DR

This paper presents a numerical method for calculating scattering phase shifts that remains invariant under unitary transformations of the Hamiltonian, using eigenvalues and Chebyshev angle shifts, effective even on coarse momentum grids.

Contribution

It extends a new prescription for phase shift calculation based solely on eigenvalues and Chebyshev angles, improving accuracy on coarse grids.

Findings

Method is effective for $\pi\pi$, $\pi N$, and $NN$ interactions.

Procedure is competitive with fewer grid points.

Invariance under Hamiltonian transformations is maintained.

Abstract

The scattering phase-shifts are invariant under unitary transformations of the Hamiltonian. However, the numerical solution of the scattering problem that requires to discretize the continuum violates this phase-shift invariance among unitarily equivalent Hamiltonians. We extend a newly found prescription for the calculation of phase shifts which relies only on the eigenvalues of a relativistic Hamiltonian and its corresponding Chebyshev angle shift. We illustrate this procedure numerically considering $\pi\pi$, $\pi N$ and $NN$ elastic interactions which turns out to be competitive even for small number of grid points.