Diffraction scattering and group contraction

We employ the method of group contraction in order to study diffraction scattering at high energies. The elastic scattering amplitude is assumed to be pure imaginary. We then obtain that $\frac{d\sigma }{dt}={\left(\frac{d\sigma }{dt}\right)}_0{e}^{\mathrm{bt}}$, where $b=\frac{\sigma _t^{}{}_{}{}^2}{\left(16\mathrm{}\pi {\sigma }_{\mathrm{el}}\right)}$. This simple result explains in a universal manner ${\pi }^{\pm }p$, $K^{\pm }p$, $\overline{p}p$, and $pp$ scattering data over a wide energy range.