The theory of electron-scattering coincidence experiments: W. E. Kleppinger and J. D. Walecka. Institute of Theoretical Physics, Department of Physics, Stanford University, Stanford, California

Abstract

Abstract A general expression for the electron-scattering coincidence cross section for the reaction A1(e, e′ X) A2 with a nuclear target is derived in the one-photon exchange approximation. The result is exact to lowest order in α, the fine-structure constant. It is expressed in terms of four kinematic factors involving the electron scattering variables in the laboratory frame, and four combinations of transition matrix elements of the nuclear current operator expressed in the center-of-momentum (COM) frame. The nuclear matrix elements are decomposed into transition amplitudes of definite angular momentum using a helicity analysis. General expressions for the angular distribution of particle X in the COM frame are then derived. The analysis is independent of the detailed structure of the nucleus and particle X and depends only on general symmetry considerations and the existence of a local electromagnetic current operator for the hadronic target. A unitary transformation from the helicity basis for the final particle X and A2 to an LS coupling basis is relevant if X is massive and a finite number of total angular momenta J are involved in the reaction. Tables of angular correlation coefficients are given for the case where the initial nucleus A1 has J1π = 0+. They constitute one of the most useful results of this paper. Connection is made in the “static limit,” and with the assumption that the reaction proceeds through a finite number of Breit-Wigner resonances with a corresponding factorization of the electroproduction transition matrix elements, to the familiar electromagnetic transition multipole moments involving excitation of a nuclear state Jπ. The relation to previous work by de Forest and by Drechsel and Uberall is discussed. Analytic expressions for the coincidence cross sections are given for spin-zero systems and some very simple, basic models of nuclear “giant resonance” excitations. It is hoped that they will be useful in obtaining insight into the coincidence cross section and in planning future experiments. Finally, a reanalysis of the recent Stanford data of Calarco et al. on 12 C (e, e′ p 0 ) 11 B ( 3 2 − ) in the vicinity of the giant dipole resonance in 12C is carried out using a very simple nuclear model but retaining all the terms in the coincidence cross section, some of which were previously neglected.