Eikonal Model for Current-Nucleon Scattering: Electron-Proton Deep-Inelastic Scattering

A high-energy, small-angle diffraction model in the eikonal approximation is adapted to current-nucleon scattering. Within the framework of certain assumptions, both the longitudinal and transverse electroproduction cross sections fall off as $\frac{1}{\left|q^2\right|}$ for high-energy $\nu$ and large momentum transfer $\left|q^2\right|$, with the ratio $\omega =\frac{\left|q^2\right|}{\nu }$ fixed in the asymptotic region. Furthermore, expressions are given for the functional dependence on $\omega$ of the electroproduction structure functions $W_1$ and $W_2(\nu , q^2)$.