Inverse-scattering separable NN potential constrained to phase-shift data up to 2.5 GeV. I.—Uncoupled states

Abstract

We introduce a new method to construct, within inverse-scattering theory, an energy-independent separable potential capable of reproducing exactly both phase shift and absorption over a predefined energy range. The approach relies on the construction of non-overlapping multi-rank separable potentials, whose form factors are obtained by solving linear equations on intervals where the K matrix does have zeros. Applications are made to nucleon–nucleon (NN) interactions constrained to the SAID-SP07 phase-shift analysis up to 2.5 GeV lab energy. The inversion potentials are channel dependent with rank dictated by the number of zeros of the K matrix, reproducing the data up to a selected upper momentum. The account for absorption yields complex separable form factors, resulting in a non-Hermitian potential. Applications are restricted to NN spin-uncoupled states considering a Schrödinger-like wave equation with minimal relativity. Its extension to spin-coupled states and relativistic kernels are discussed.