Models for differential cross section in neutron-proton scattering and their implications

Abstract

A few analytic exponential models of the elastic differential cross section are proposed to analyse elastic neutron-proton (np) scattering. The models incorporate energy-dependent exponential slopes, power-law prefactors, and localized Gaussian modifications. Sub-leading exponential terms representing charge conjugation and isospin roles increase the applicability and quality of fit of the models to describe the differential cross section data of np, n \bar{p}, pp, and p \bar{p} elastic scattering. The models describe the characteristic features of all the elastic scattering data such as the dip-bump structure, shrinkage of the forward peak, and controlled curvature around the diffractive dip. Parameter values of the models are found by fitting the np experimental data in an energy range of (\sqrt{s}\) = 3.363 to 26.019 GeV and a momentum transfer range of 0.065 to 5.341 GeV^2. Employing the proposed models, total, elastic, and inelastic cross sections, slope parameters, interaction radii, and cross-section ratios for np scattering are calculated. A multi-stage error analysis is performed to evaluate the error in the calculations of the models. Implications of the results obtained by the models for nucleon structure and dynamics are discussed. The results show that the proposed models can be used for effective description of the np elastic differential cross section and for accurate estimation of the observables of elastic hadronic scattering. The findings of this study emphasize the significance of combining theoretical and phenomenological approaches, providing valuable information for investigations of future experimental data on the differential cross section from various colliders.

arXiv comment29 pages, 23 tables, 11 figures