Asymptotic Behavior of Nucleon-Nucleon Scattering

Abstract

In this paper, a detailed analysis of $\mathrm{NN}$ and $N\overline{N}$ scattering on the basis of the Regge hypothesis is carried out. The Regge expansions of a set of ten invariant amplitudes describing $\mathrm{NN}$ scattering are presented, with residues expressed in factorized form. Expressions involving both the full Legendre functions and their asymptotic forms are given. Spin sums are carried out to obtain simple and convenient expressions for the contributions of the $P$, $\rho$, $\omega$, and $P^{\prime }$ trajectories to the differential cross sections. The optical theorem has been applied to find the contribution of the $P$, $P^{\prime }$, $\rho$, and $\omega$ trajectories to the spin-averaged total cross sections. Finally, we have analyzed the available data on the total and differential cross sections for $\mathrm{NN}$ scattering to extract information about the Regge-pole parameters. The possible effect of the spin structure of the amplitudes, and the variation with energy of the Legendre functions has been taken into account. We show, by a natural definition of helicity flip and no-flip couplings, that the amplitudes, and especially the cross sections, for $\mathrm{NN}$ scattering are very simple in the asymptotic limit. In an Appendix, the decay properties of a spin-2 meson associated with the Pomeranchuk Regge pole are discussed.