Deep Hole States and (e, e'N) Reactions

Abstract

Quasielastic electron scattering by nuclei is considered on the basis of the many-bucly theory. Properties of the hole states are described. Cross sections for the (e, e'p) and (e, e 1n) reactions are obtained. The role of nucleon correlations in these reactions is also discussed. § l. Introduction The hole state in the many-body system is a basic type of excitation. Analysis of the hole states in an atomic nucleus yields information on the single-particle properties of nuclei and on how these are affected by the correlation interaction betvveen nucleons. Deep-lying hole states are created by reactions of the types (jJ, 2p), (e, e'jJ), (P, d) and (d', He),n~sJ etc. In the analysis one assumes that such reactions, initiated with bombarding energies of several hundred MeV, can be described as direct or knock-out process involving only a single collision between an incident projectile and one of the target nucleous. Usually multiple scattering and compound nucleus formation are only taken into account through a complex optical model potential describing the motion of the projectiles before and after the collision. Deep-lying quasi-hole states (dressed holes) are there­ fore expected to lead to peaks in the cross section as a function of transferred energy. vVith quasi-free secattering one can measure the energ1es, lifetimes and momentum distributions of the dressed hole states. Experiments ha\·e pointed to a complicated nature for the deep hole states of the nucleus. The peaks observed in the summed energy spectra have large widths and the centre of these peaks lie much lower than those predicted by the independent-particle model. In this paper, we investigate the hole states and (e, e' N) reactions within the framework of the many-body theory! 1 ~ 61 Our approach has an advantage that it does not depend on any particular model from the begin­ ning.71~111 In § 2 the properties of the mass operator for the hole states are con­ sidered. In this way the mass operator, which corresponds to the nuclear potential for quasihole states, is nonlocal, complex and energy-dependent due to correlation interactions. This leads to a qualitative explanatio11- for the singularities in the hole-excitation spectrum. In § 3 the (e, e'lJ) reactions are investigated by using Green's function method. The cross~section obtained has a resonance form. In