An Optical Model for High-Energy Scattering

An attempt is made to show that the behavior of the diffraction width in high-energy scattering can be attributed to the presence of the inelastic threshold in one of the channels that dominates the process. The theory which originally concerns itself with $p-p$ diffraction scattering is a pure optical model. It starts with the assumption that high-energy scattering is dominated by inelastic processes and that the degree of inelasticity is determined by the overlap of the meson clouds surrounding the colliding particles. Three input parameters are introduced into the framework, viz. the inverse range of the nucleonic meson cloud $\mu$, the power $\lambda$ in the ansatz that we use to relate the overlap function with the transparency coefficient, and the cutoff mass ${\mu }_i$ which originates in the requirement that there be a minimal energy of local excitation in order that an inelastic process can take place. In this optical model we can identify $\lambda$ with the strength of the absorptive potential. We can fix these parameters by using the experimental data as follows: The limits ($\frac{{\sigma }_{\mathrm{el}}}{{\sigma }_T}$) and ${\sigma }_T$ at infinite-energy give the values of $\lambda$ and $\mu$, respectively, while ${\mu }_i$ is determined from the approach ${\sigma }_T\mathrm{}\left(E\right)\mathrm{}\to {\sigma }_T\left(\infty \right)$ in the asymptotic region. With the appropriate values of the parameters we can predict the transient shrinkage of the diffraction width in $p-p$ and $K^{+}-p$ scattering and also the transient expansion of the diffraction width in $\overline{p}-p$ and $K^{-}-p$ scattering. We can also show that the widths of the diffraction peak in ${\pi }^{+}-p$ and ${\pi }^{-}-p$ scattering are almost energy-independent. The consequences of the application of the model on nondiffractive processes are the following: In large angle scattering the differential cross section tends to flatten with increasing momentum transfer. At relativistic energies the one-fourth-power law for the average multiplicity of the secondaries in Fermi's statistical theory is quenched by a logarithmic factor.