Analytic approach to the problem of constructing effective nucleon-nucleon potentials in the region of low and intermediate energies

A new relativistic approach to the problem of constructing effective local hadron-hadron potentials is proposed on the basis of analytic S-matrix theory and Gelfand-Levitan-Marchenko-Martin methods for solving the inverse quantum scattering problem. An effective potential is defined as a local operator in a partial-wave equation of the quasipotential type such that it generates an on-shell relativistic (Feynman) scattering amplitude that has required discontinuities at dynamical cuts. The method is used to construct nucleon-nucleon potentials in the ¹ S ₀-and ³ S ₁-wave states. The dynamical discontinuities of partial-wave amplitudes for nucleon-nucleon scattering are calculated on the basis of the one-bosonexchange model that takes into account the exchanges of π, σ, ρ, ω, η, and α ₀ mesons. It is shown that the nonlinear relation between the discontinuities of partial-wave scattering amplitudes at dynamical cuts and interaction operators generates additional short-range repulsion not associated with omega-meson exchange. The experimental energy dependences of phase shifts in the channels of nucleon-nucleon scattering that are considered here are faithfully reproduced by the results of the calculations up to the projectile-nucleon kinetic energies in the range T = 1.5–2.0 GeV.