Inelastic Electron-Nucleus Scattering and Nucleon-Nucleon Correlations

Abstract

A constant-$q$ and -$\theta$ sum rule is constructed in Born approximation for inelastic scattering of electrons on nuclei by integrating over the outgoing electron energy spectrum at constant 3-momentum transfer, $q$, and scattering angle $\theta$. A consistent treatment of the nucleon current interaction through second order in $\frac{q}{M}$, the recoil nucleon velocity, gives a result reliable to 5-10% out to $q\sim 2.5$ ${\mathrm{f}}^{-1\mathrm{}}$, and shows that the often neglected Darwin-Foldy term contributes substantially. It is well known that the $q$ dependence of the sum can be directly related by closure to the Fourier transform of two-nucleon correlation functions in the ground state of the nucleus. This $q$ dependence is studied for various nuclear models of ${\mathrm{O}}^{16}$; the effect of the Pauli exclusion principle on the sum is found to be large for $q\sim 1$ ${\mathrm{f}}^{-1\mathrm{}}$, but the effect of a hard-core force of radius ≤0.4 f appears to be small for all values of $q$.