Determination of Wolfenstein Parameters in NN Scattering Directly from Observables

Abstract

The Wolfenstein parameters are for the first time obtained analytically in terms of observables. It is shown that a set of ten nucleon-nucleon (NN) observables, which contains polarization observables together with the differential cross section, determines uniquely the solution for Wolfenstein parameters except for a common insignificant phase. Using such analytical solutions one expects to get more accurate theoretical parameters for the potential models by χ 2 fitting to the resulting Wolfenstein parameter data than the standard manner of a phase-shift analysis. An example of fixing a unique set of physical solutions for the Wolfenstein parameters from a set of 16 solutions based on nine observables alone and adding one more observable is illustrated using pseudo data generated by the CD Bonn potential.

The low-energy structure of the nucleon–nucleon interaction: statistical versus systematic uncertainties

“…Indeed, the NN scattering amplitude contains ten functions of energy and angle and a complete set of experiments is needed to determine it without model dependence [19]. While the usefulness of polarization was soon realized [20] as well as the strong unitarity constraints on the uniqueness of the solution [21,22] (see [23] for an analytical solution), complete sets of observables are scarce at the energies relevant to nuclear structure applications, corresponding to energies below or about the pion production threshold (see also 4 An editorial recommendation on the necessity of including uncertainties in theoretical evaluations in atomic and molecular physics was published in 2011 [14]. [24]).…”

Phenomenological high precision neutron–proton delta-shell potential

“…, a 10 ), which could be determined directly from experiment as shown in Ref. [24,25] (see also [26] for an exact analytical inversion). We follow an alternative procedure and construct, out of the high-quality analyses, the corresponding mean value of the Wolfenstein parameters, āi (E LAB , θ ), with their corresponding standard deviations, ∆a i (E LAB , θ ), for any given LAB energy and scattering angle θ as…”