High-Energy Cross Sections in a "Quark-Droplet" Model

The following experimental information is available about the high-energy scattering of $\mathrm{pp} \mathrm{}\left(\mathrm{pn}\right)\mathrm{}$, $\overline{p}p \left(\overline{p}n\right)$, ${\pi }^{\pm }p$, and $K^{\pm }p$: (a) the total cross sections, (b) the coefficients $b$ and $c$ in the small-angle parametrization of the differential cross section $\frac{d\sigma }{\mathrm{dt}}=A{e}^{(bt+c{t}^2)}$, (c) the ratios of elastic to total cross sections, and (d) the qualitative feature of whether or not the diffraction peak shrinks for the different processes. At the highest available energy, the dependence of these characteristics on the energy becomes relatively weak. In this paper we study their dependence on the quantum numbers of the particles involved; that is, we study how these characteristics are interrelated for the different processes. A "quark-droplet" model is introduced for this purpose. In the approximation where the small differences between $\mathrm{pn}$ and $\mathrm{pp}$ scattering and between ${\pi }^{+}p$ and ${\pi }^{-}p$ scattering are neglected, a three-parameter model gives a good description of the relative magnitude of the total cross sections and the absolute magnitudes of $b$. It gives a poorer but still reasonable description of the relative magnitudes of ($\frac{{\sigma }_{\mathrm{el}}}{\sigma }$), and the absolute magnitudes of $c$. It is shown how a small energy dependence of the three parameters can lead to an increase or decrease of $b$ with energy for the different processes, and how a further splitting of the three parameters can satisfactorily account for the differences between $\mathrm{pn}$ and $\mathrm{pp}$, and between ${\pi }^{+}p$ and ${\pi }^{-}p$. The difference between this analysis and the Regge-pole analysis is discussed. A few unsettled points requiring further experimental check are summarized at the end.