Simple Formula for Quasi-Elastic Electron Scattering

An approximate analytic formula is developed for high-energy (several BeV or higher) quasi-elastic electron scattering from a complex nucleus, on the basis of a simple nuclear model. The approximation should be good enough to be useful in estimating experimental counting rates and backgrounds. For scattering at an angle $\theta$, the quasi-elastic peak is centered, in this approximation, at the energy ${\epsilon }_0=\frac{\epsilon }{[1+2(\frac{\epsilon }{M})\times {sin}^2(\frac{1}{2}\theta \left)\right]}$, where $\epsilon$ is the incident energy and $M$ is the nucleon mass. The peak has a full width at half maximum of about $\sqrt{2}\left(\frac{{{\epsilon }_0}^2}{\epsilon }\right)v+{[1+{(1+\frac{\epsilon }{M})}^2{tan}^2(\frac{1}{2}\theta \left)\right]}^{\frac{1}{2}}sin\theta$, where $v_{+}$ is a characteristic nucleon velocity in the nucleus, $v_{+}\approx 0.28$. Inelastic electron scattering from complex nuclei is briefly discussed.