Inelastic Electron-Nucleus Scattering and Nucleon-Nucleon Correlations

A constant-q and -θ 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 θ. A consistent treatment of the nucleon current interaction through second order in q/M, the recoil nucleon velocity, gives a result reliable to 5-10% out to q~2.5 f^-1, 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 O¹⁶; the effect of the Pauli exclusion principle on the sum is found to be large for q~1 f^-1, but the effect of a hard-core force of radius {≤}0.4 f appears to be small for all values of q.