Correlations and the cross section of exclusive (e,e′p) reactions for 16O

The reduced cross section for exclusive (e, e′p) reactions has been studied in DWIA for the example of the nucleus ¹⁶O using a spectral function containing effects of correlations. The spectral function is evaluated directly for the finite nucleus starting from a realistic nucleon-nucleon interaction within the framework of the Green's function approach. The emphasis is focused on the correlations induced by excitation modes at low energies described within a model-space of shell-model configurations including states up to the sdg shell. Cross sections for the p-wave quasi-hole transitions at low missing energies are presented and compared with the most recent experimental data. In the case of the so-called perpendicular kinematics the reduced cross section derived in DWIA shows an enhancement at high missing momenta as compared to the PWIA result. Furthermore the cross sections for the s- and d-wave quasi-hole transitions are presented and compared to available data at low missing momenta. Also in these cases, which cannot be described in a model without correlations, a good agreement with the experiment is obtained.     

Charge-exchange processes in the quasi-elastic (e,e′p) and (e,e′n) reactions

Calculations of charge-exchange processes in the final state of the quasi-elastic (e, e′N) reaction have been performed employing the Lane formalism. The Lane equations were decoupled by means of a transformation to the isospin representation. It is found that charge exchange has a small effect on the (e, e′p) cross section, but may play an appreciable role in the (e, e′n) reaction.     

Determination of the neutron electric form factor in the D(e,e′n)p reaction and the influence of nuclear binding

The electric form factor of the neutron G _E,n has been determined at the Mainz Microtron MAMI at the low momentum transfer Q ²= 0.15 (GeV/c)² in a measurement of the recoil polarisation ratio P _x/P_z in the quasifree reaction D(e,e′n)p. At this Q ² the influence of the nuclear binding is strong. A purely kinematical model is used to get some insight into the effect of the initial Fermi momentum distribution of the neutron. The influence of the final state interaction is determined quantitatively by a model of Arenh?vel et al.. After the corresponding corrections a value of G _E,n(0.15 (GeV/c)²) = 0.0481±0.0065_stat±0.0053_syst is obtained. Received: 12 April 1999     

First measurement of the exclusive (p,e+e−) reaction

We present the first data on the exclusive (p,e⁺e⁻) reaction in a nucleus. Cross sections for populating the ground state and first excited state in the residual nucleus are presented for the reaction ¹¹B(p, e⁺e⁻)¹²C at 98 MeV. The e⁺e⁻ momentum vectors were measured with a high-resolution magnetic pair spectrometer. The distributions of the virtual photon invariant mass and of the direction of the electron in the virtual photon rest system are compared with a simple single-nucleon model. The (p,e⁺e⁻) cross sections are compared with corresponding data for the (p, γ) reaction obtained with the same apparatus. The (p,e⁺e⁻) cross sections show substantial enhancement over what is expected from the simple model.     

The role of the neutron electric form factor ind(e,e′ N)N including polarization observables

The influence of the neutron electric form factor on various observables in two-body break-up of deuterons by electrons such as differential cross section, beam, target and beam-target asymmetries and outgoing nucleon polarization as well is investigated for different kinematic regions. The electron-deuteron vector asymmetryA _ed ^V and the outgoing nucleon polarization component P′_x(n) are the most promising observables in and off the quasi-free region for a determination ofG _En. Also the single polarization observablesA _d ^T and P_y ⁰(p) and the double polarization observable P′_z(n) show significant influences fromG _En.     

Probing the mesonic structure of the nucleon by means of exclusive quasielastic pion knockout in (e, e′π) reactions at high energies

By including the Z diagram in an analysis performed in the laboratory frame (instantaneous form of dynamics), the notion of quasielastic pion knockout by protons and electrons [(p, 2p) and (e, e′p) reactions treated in terms of the relevant pole diagrams] is generalized to the relativistic case where a meson is quasielastically knocked out of a nucleon by an electron having an energy of a few GeV. The concept of the wave function is introduced for the pion (and for other mesons), and its relation to the vertex constant G _πNN and the vertex function g _πNN(k ²) is indicated. The spectroscopic factor S _N ^B? is defined as the normalization of the wave function for the meson ?. It is shown by two methods that, under the kinematical conditions of quasielastic knockout that include the condition E _π?m _π (E _π is the energy of the knock-on pion) and the condition that the square Q ² of the virtual pion mass is large, the competing tree diagram is suppressed in relation to the pole diagram (this is not so in the case of pion photoproduction). From data of a p(e, e′π ⁺)n experiment involving longitudinal virtual photons γ _L ^* , the momentum distribution |Ψ _p ^nπ (k)|² of pions in the nucleon is extracted for the first time over the entire range of significant momenta k, and this result is used to determine the cutoff constant Λ_π and the value of S _p ^nπ ≈0.2. The momentum distribution of positive rho mesons in the soft section of the spectrum is determined from experimental data on the process p(e, e′π ⁺)n proceeding through the mechanism ρ ⁺+γ _T ^* → π ⁺ involving transverse photons. A way to determine the momentum distribution of omega mesons through data on the process p(e, e′π ⁰)p is indicated. Two forms of dynamics—instantaneous form and that of light-front dynamics (the latter does not involve the Z diagram)—are compared for the example where the calculations are performed for the spectroscopic factor S _N ^B? .     

Final-state interactions in (e,e′p) reactions with polarized nuclei

The cross section for coincidence, quasielastic proton knock-out by electrons from a polarized ³⁹K nucleus is computed in DWIA using an optical potential in describing the wave function of the ejected nucleon. The dependence of the FSI on the initial polarization angles of the nucleus is analyzed and explained in a new, semi-classical picture of the reaction in which the nuclear transparency decreases as a function of the amount of nuclear matter that the proton has to cross, thus providing a method for obtaining detailed information on its mean free path in finite nuclei. We propose a procedure to find the best initial kinematical conditions for minimizing the FSI which will be useful as a guide for future experiments with polarized nuclei.     

Study of relativistic bound state wave functions in quasielastic (e,e′ p) reactions

The unpolarized response functions of the quasielastic ¹⁶O(e,e′ p)¹⁵N reaction are calculated for three different types of relativistic bound-state wave functions. The wave functions are obtained from relativistic Hartree, relativistic Hartree-Fock and density-dependent relativistic Hartree calculations that reproduce the experimental rms charge radius of ¹⁶O. The sensitivity of the unpolarized response functions to the single-particle structure of the different models is investigated in the relativistic plane-wave impulse approximation. Redistributions of the momentum dependence in the longitudinal and transverse response function can be related to the binding energy of the single-particle states. The interference responses R_LT and R_TT reveal a strong sensitivity to the small component of the relativistic bound-state wave function.     

Exclusive (e,e′pp) knockout reactions

Exclusive cross sections of the ¹⁶O(e,e′pp) ¹⁴C knockout reaction are calculated for transitions to the low-lying discrete final states of the residual nucleus. Short-range correlations and two-body currents, due to the excitation of a Δ resonance in the intermediate state, are included in the calculations. Final-state interactions are taken into account by means of phenomenological spin-dependent optical potentials. Recoil-momentum distributions for transitions to states with different angular momentum exhibit different shapes, which are basically determined by the cm orbital angular momentum of the initial proton pair.     

Analysis of factorization in (e,e′p) reactions: A survey of the relativistic plane wave impulse approximation

The issue of factorization within the context of coincidence quasi-elastic electron scattering is revisited. Using a relativistic formalism for the entire reaction mechanism and restricting ourselves to the case of plane waves for the outgoing proton, we discuss the role of the negative-energy components of the bound nucleon wave function.     

Measurement of the exclusive D(p,e+e−)3He and D(p, γ)3He reactions at 98 and 176 MeV

A high resolution magnetic pair spectrometer for medium energy photons has been used for studies of the exclusive (p, e⁺e⁻) and (p, γ) reactions on deuterium at 98 and 176 MeV. The (p, e⁺e⁻) cross sections, obtained at 40° and 80°, are compared with the corresponding data for the (p, γ) reaction measured with the same apparatus. At small virtual photon masses the (p, e⁺e⁻) cross sections show significant enhancement over what is expected from model calculations, a behaviour which has earlier been observed also for the ¹¹B(p, e⁺e⁻)¹²C reaction.     

Towards spin degrees of freedom in (e,e′p)

The expeprimental (e, ep) program at Mainz is presented. The reaction (e, ep) without spin degrees of freedom is compared with the case when polarization observables are considered. It is demonstrated on some examples how the new information can be used to extend the knowledge of the reaction mechanism and nucleon/nuclear structure. Construction and operation of a focal-plane proton polarimeter at Mainz is described.Lectures held at the Indian-Summer School on Electromagnetic and Weak Interactions of Particles with Nuclei, Sázava, Czechoslovakia, 6–11 September 1992.     

Comparison of Monte Carlo simulation and direct multistep scattering theory in (e,e′p) nuclear reactions

Two methods to deal with final state interactions in (e,e′p) reactions in nuclei are compared. One of them uses a Monte Carlo semiclassical approach while the other uses a statistical quantum mechanical approach. The comparison serves to give support to both approaches, showing at the same time their limitations.     

Multi-scattering effects in (e,e′p) knockout

Multistep direct scattering of the ejectile proton is considered in (e,e′p) reactions in the quasi-free region as an improvement over the usual treatment of final-state interactions by means of an optical potential. The theory is applied to ⁴⁰Ca(e,e′p) as a case example. Important contributions of two- and three-step processes are found at high missing energy and momentum in agreement with the experimental trend.     

3He(e,e′pp) and 3He(e,e′pn) reactions at AmPS and MAMI

This paper reports on measurements of the ³He(e,e′pp) reaction measured at AmPS and the ³He(e,e′pn) reaction measured at MAMI. The measurements were performed in similar kinematics to allow a comparison to be made between the cross sections of the two reactions. Results are shown for both reactions together with a comparison for the ³He(e,e′pp) data with continuum Faddeev calculations.     

Inclusive (e,e′ N), (e,e′ NN), (e,e′ π), …v reactions in nuclei

We study the inclusive (e, e′ N), (e, e′ NN), (e, e′ π), (e, e′ πN) reactions in nuclei using a Monte Carlo simulation method to treat the multichannel problem of the final state. The input consists of reaction probabilities for the different steps evaluated using microscopical many body methods. We obtain a good agreement with experiment in some channels where there is data and make predictions for other channels which are presently under investigation in several electron laboratories. The comparison of the theoretical results with experiment for several kinematical conditions and diverse channels can serve to learn about different physical processes occurring in the reaction. The potential of this theoretical tool to make prospections for possible experiments, aiming at pinning down certain reaction probabilities, is also emphasized.     

The quasi-free 3He(e,e′p) reaction

The proton spectral function has experimentally been determined with the ³He(e, e′p) reaction for missing energies, 0<E_m<70MeV, and recoil momenta, 0<P_B<310 MeV/c. Experimental results are obtained for both the two-body, ³He(e, e′p)²H, and three-body breakup processes. Proton momentum density distributions, obtained in a PWIA analysis, are compared with theoretical calculations: Faddeev solutions with the RSC and Paris potentials, and variational calculations with various potentials, including those with a three-nucleon interaction term. Energy-weighted sum rule results are presented and compared with theoretical predictions. The coincidence cross sections are also compared with calculations which include the effects of final state interactions and meson exchange currents. Consistency of the results with PWIA is investigated in the framework of the Chew-Low extrapolation procedure.     

Relaxation of the analyzing power of the (p, τX) and (p, αX) reactions in the continuum

The observed continuous decrease of the analyzing power for the reactions ($\text{p}$, τX) and ($\text{p}$, αX) on ⁹⁰Zr and ²⁰⁹Bi at E_p = 72 MeV as a function of the excitation energy of the final nucleus is described by a phenomenological relaxation process.     

Measurement of the 6Li(e,e′p) reaction cross sections at low momentum transfer

The triple differential cross sections for the ⁶Li(e,e′p) reaction have been measured in the excitation energy range from 27 to 46 MeV in a search for evidence of the giant dipole resonance (GDR) in ⁶Li. The cross sections have no distinct structures in this energy region, and decrease smoothly with the energy transfer. Angular distributions are different from those expected with the GDR. Protons are emitted strongly in the momentum-transfer direction. The data are well reproduced by a DWIA calculation assuming a direct proton knockout process.     

Longitudinal-transverse interference structure function in the reaction2H(e,e′ p)

The longitudinal-transverse interference structure functionf ₀₁ has been measured in deuterium electrodisintegration experiments at various values of the four-momentum transferQ ². Data taken at different laboratories and at roughly the same value ofQ ² are shown to be consistent. When compared to non-relativistic impulse-approximation calculations mostf ₀₁ data show an enhancement. A relativistic treatment of the reaction²H(e, e p) removes the discrepancy. More definite evidence for relativistic effects in deuterium electrodisintegration can be obtained at higher values of the recoil momentum. The experimental implications for such²H(e, e p) experiments are discussed as well.Dedicated to Prof. Werner Sandhas on the occasion of his 60th birthday