Nuclear Pair-Correlation Function via Electron Scattering

Abstract

A theoretical analysis is made of the differential cross section for the process of inelastic scattering of electrons by a nucleus accompanied by the emission of two nucleons. The analysis is twofold. First, assuming a purely electromagnetic interaction (of the semiclassical M\oller type), and invoking closure and impulse approximations, the above cross section is shown to be simply proportional to the Fourier transform of the nucleon-nucleon correlation function in the nucleus (at a momentum determined experimentally). Secondly, following a physical idea due to Gottfried and employed in a similar context, the nuclear cross section is compared to that of the electrodisintegration of a deuteron. This has the advantage in that it eliminates the need to introduce an explicit Hamiltonian (as in the first case), and also it allows us to include some very important mesonic effects due to the virtual pion exchange between the two outgoing nucleons. This approach, therefore, shifts the problem to a theoretical understanding of the connection between the deuteron wave function and the pair-correlation function in a nucleus. A computation of the cross section is made, which is rather low, yet is seen to be within the reach of the present experimental techniques. Detailed kinematical questions are explored and the optimal experimental setup indicated. The corrections due to (1) the final-state interactions and (2) real-meson-production channels are also discussed. In conclusion, we surmise that there is a definite need for detailed experimental study of two or more nucleon emission phenomena for the determination of the correlation function at high momentum (or small distances). Beyond fixing some qualitative guidelines, the no-nucleon and one-nucleon emission cross sections seem to be less than adequate.