Inclusion of virtual nuclear excitations in the formulation of the(e,e′N)reaction

Abstract

A wave-function framework for the theory of the (e,e'N) reaction is presented in order to justify the use of coupled channel equations in the usual Feynman matrix element. The overall wave function containing the electron and nucleon coordinates is expanded in a basis set of eigenstates of the nuclear Hamiltonian, which contain both bound states as well as continuum states.. The latter have an ingoing nucleon with a variable momentum Q incident on the daughter nucleus as a target, with as many outgoing channels as desirable.The Dirac Eqs. for the electron part of the wave function acquire inhomogeneous terms, and require the use of distorted electron Green's functions for their solutions. The condition that the asymptotic wave function contain only the appropriate momentum Q k for the outgoing nucleon, which corresponds to the electron momentum k through energy conservation, is achieved through the use of the steepest descent saddle point method, commonly used in three-body calculations. I. INTRODUCTION.The commonly accepted starting point for writing down the (e,e'N) matrix element is a Feynman diagram. The Feynman diagram consists of two vertices: one in which a nucleon is detached from the target nucleus, and the other which represents the electron-nucleon interaction, which scatters the nucleon into the appropriate final state. In 1970 Gross and Lipperheide [1] wrote down such a matrix element, and Boffi and collaborators [2] based their work [3] on this approach. Walecka and collaborators [4], as well as Donnelly and co-workers [5] also start from this type of approach. Additional refinements were gradually introduced. The optical model, initially used to describe the nucleon-nucleus distortion [2], was later refined by using the Random Phase Approximation for the nuclear excitations [6], electron spin variables were introduced [5], the relativistic nucleon-nucleus interaction was considered [7], and two-step processes (or coupled channel effects) were included [8], [9].Many good reviews of the (e,e'N) formalism exist, the latest one being due to Kelly [10].The objective of the present paper is to formulate the (e,e' N) reaction in terms of a wave function expansion, rather than Feynman-diagram matrix elements This treatment permits one a) to understand the assumptions which underlie the coupled-channel treatment of the hadron-nucleus channels, which are commonly inserted into the Feynman matrix elements, b) to include the effect of the (e,e' N) channels into the treatment of dispersion corrections to electron-nucleus scattering, c) to provide a foundation for the treatment of the (e,e' 2N) processes.The wave function method described here is similar in nature to the expansions employed in three-body reaction theory [11], [12], [13]. In particular, the saddle-point method is used to obtain the asymptotic limit of the wave function for the two particles in the continuum (the electron and the emitted nucleon), thus making contact with the matrix element written conventionally for the Feynman diagram mentioned ...

Channel coupling inA(e→,e′N→Kelly1 1999Phys. Rev. C452640View full textAdd to dashboardCite

“…(4.7) of Ref. [26], for the inhomogeneous driving terms for electron scattering is very similar to our Eqs. (9)(10).…”

“…Hence, dispersion corrections appear as final-state interactions here and as initialstate interactions in Ref. [26], but these representations should be equivalent in the absence of subsequent approximations.…”

Dynamics of the quasielasticO16(e,e′p)reaction atFissum1, Liang2, Anderson3 et al. 2004Phys. Rev. C

“…Specific details regarding the boundary conditions may be found in Refs. [86][87][88]. The Madrid rdwia calculations [16] employ a partialwave expansion of the first-order Dirac equation, leading to a pair of coupled first-order differential equations.…”

Influence of the Dirac sea on proton electromagnetic knockout

“…In this short paper we will explore the Q 2 dependence of such effects using data for 16 O and 12 C(e, e ′ p) in quasiperpendicular kinematics for Q 2 between about 0.2 and 1.8 (GeV/c) 2 . The data for 16 O have already been analyzed in considerable detail and the enhancement of the left-right asymmetry for Q 2 = 0.8 (GeV/c) 2 has been interpreted as evidence for spinor distortion [8,9]. Here we use the availability of both 1p 3/2 and 1p 1/2 magnetic substates to illustrate the sensitivity to several important aspects of spinor distortion.…”

“…We use the relativistic distorted-wave impulse approximation (RDWIA) to study the effects of negative-energy components of Dirac wave functions on the left-right asymmetry for (e, e ′ p) reactions on 16 O with 0.2 ≤ Q 2 ≤ 0.8 and 12 C with 0.6 ≤ Q 2 ≤ 1.8 (GeV/c) 2 . Spinor distortion is more important for the bound state than for the ejectile and the net effect decreases with Q 2 .…”