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A relativistic Green's function approach to parity-violating quasielastic electron scattering is presented. The components of the hadron tensor are expressed in terms of the single particle Green's function, which is expanded in terms of the eigenfunctions of the non-Hermitian optical potential, in order to account for final state interactions without any loss of flux. Results for $^{12}$C, $^{16}$O, and $^{40}$Ca are presented and discussed. The effect of the strange quark contribution to the nuclear current is investigated., Comment: 24 pages, 13 figures

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.

Exclusive cross sections of the 16 O(e,e′pp) 14 C 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.

Coincidence cross sections for the 12 C(e, e′pp) and 12 C(e, e′p) reactions have been measured in the Δ-resonance region. The 12 C(e, e′pp) reaction has been measured at three different angular settings of the proton detectors to investigate the angular correlation between the emitted protons. The data, which have a low statistical accuracy, are compared with a calculation based on the direct-knockout mechanism, which includes one- and two-body currents. NN-correlations are accounted for via a correlation function, Δ-excitation via a two-body current and final-state interactions of the emitted protons via an optical potential. The 12 C(e, e′p) data, taken at large proton-emission angles, cover the region of high missing-energy values (145–275 MeV). The data are compared to results of a calculation taking into account meson exchange, intermediate Δ-excitation and pion production. This comparison shows that there is ample evidence for processes leading to multi-nucleon knockout.

The charge-exchange mechanism due to the isospin-dependent part of the optical potential is investigated for the (e,e′ pp) reaction and added to the direct one-step knockout. A small contribution is found, which is practically independent of the kinematics and of the different ingredients of the calculation.

The role of meson-exchange currents in (γ, p) and (γ, n) reactions at intermediate energies is investigated in the frame of a direct knockout model where the photon interacts with a pair of correlated nucleons. Realistic short-range correlations and final-state interactions are included in the calculations. Direct and exchange terms are considered. The results for 16 O(γ, p) and 16 O(γ, n) indicate that the two-body seagull current significantly affects the cross sections. In both cases the size and the shape of the experimental angular distributions are fairly well reproduced.

A two-nucleon emission model is applied to the (e,e′pn) reaction. Realistic short-range correlations and final state interactions are taken into account. The asymmetry for a polarized electron, which results vanishing in a coplanar kinematics, is investigated under different conditions. The contribution of (e,e′pn) and (e,e′pp) to (e,e′p) knockout above the two-nucleon emission threshold is evaluated and the experimentally observed enhancement of the transverse over the longitudinal component of the nuclear response is explained. Spectroscopic factors for one- and two-hole states in this energy region are determined.

Direct photoemission of proton-neutron pairs is investigated in an unfactorized approach, where short-range correlations in the initial-state and final-state interactions are also taken into account. The nuclear current is the sum of a one-body and a two-body part including meson-exchange currents and isobar excitations in the intermediate state. The role of the different dynamical aspects is studied for the 16 O(γ, pn) 14 N reaction in the photon energy range between 80 and 350 MeV. In particular, the photon asymmetry is shown to be a crucial test of the reaction mechanism.

The cross sections of the (e, e′2p) and (γ, 2p) reactions are calculated in an unfactorized form by integrating over the coordinates of the two ejected protons. Realistic short-range correlations and distorted wave functions for the two outgoing particles are included in the calculation. The nuclear current is the sum of a one- and a two-body part, corresponding to the process where a Δ-resonance is excited in the intermediate state. The (e, e′2p) cross section essentially depends on correlations, while the two-body current gives a minor contribution. In the (γ, 2p) cross section both effects are important. The asymmetry of the cross section produced by linearly polarized photons is extremely sensitive to the two-body current and could be exploited to investigate its contribution.

The longitudinal and transverse response functions of the inclusive quasi-elastic (e, e') scattering are calculated in a many-body approach where the Green function is expanded over the eigenfunctions of a non-hermitian optical potential. Direct and interference contributions of all the channels are included in a simple way and final-state interaction is treated consistently with the excluive (e, e'p) reaction. The response functions of 12C and 40Ca are evaluated for momentum transfers between 400 and 550 MeV c .

Polarization observables are considered for the outgoing nucleon knocked out in quasi-free electron scattering. The theoretical framework is based on the one-photon exchange approximation and the electromagnetic current of the target nucleus is built with one- and two-body contributions coming from meson-exchange currents and isobar configurations in intermediate nuclear states. Specific calculations are presented for both proton and neutron knockout, taking an 16 O target nucleus as an example to set the scale for possible experiments. The sensitivity to final-state interactions, mesonic effects and isobaric configurations is discussed.

In the frame of a program aiming at examining the approximations involved in the theoretical treatment of (e, e′p) reactions, the electron-nucleon interaction producing the knock-out mechanism is considered in the non-relativistic approach of McVoy and Van Hove and compared with the relativistic one based on the one-photon-exchange Feynman graph. In this paper the non-relativistic Hamiltonian through second order in the nucleon recoil velocity is adopted; in the next paper higher order terms are included. The two approaches appear equivalent as far as the usual DWIA cross section is concerned, where a factorization occurs between the electron-nucleon cross section and the nucleon momentum distribution. However the unfactorized DWIA cross section behaves differently. This is attributed to a different off-shell behaviour of the two scattering amplitudes.

Effects of Coulomb distortion of the electron wave functions in the quasifree (e, e′p) reactions are investigated in DWBA. Electron waves are described by a high energy approximation. The coincidence cross section is calculated in a nonrelativistic approach based on the impulse approximation. Results are presented and discussed for different nuclei in different kinematical conditions. Coulomb distortion gives two different effects. The first one is to change the momentum transfer into an effective momentum transfer. This effect is dominant for light nuclei and decreases by increasing incident electron energy. The second one is the focusing of the electron wave in the nuclear Coulomb field. This effect, almost energy independent, is sizeable in medium and heavy nuclei. It increases the cross section and in some cases becomes very large.

The two-step charge-exchange contribution coming from a direct (γ, p) reaction followed by a (p, n) transition due to isospin dependence of the optical-model potential is studied for photonuclear reactions. The charge-exchange mechanism appears to be substantial: its contribution is strongly dependent on the rather uncertain isospin term in the phenomenological optical-model potential, but is still insufficient to make the size of the (γ, n) cross section comparable with the (γ, p) one as found experimentally.

The quasi-free nucleon knockout by the electron is studied in the general case of both polarized beams and polarized targets. The coincidence cross section involves nine structure functions which give detailed information on the nuclear current operator. However, their measurement requires out-of-plane experiments. Results on 7 Li and 39 K obtained within the nonrelativistic DWIA framework indicate that some structure functions, very sensitive to final state interactions, are probably too small to be separated. On the other side, cross sections, asymmetries and electron polarization ratios in coplanar kinematics have measurable size. They add complementary information to the unpolarized quasi-free nucleon knockout because of their sensitivity to spin degrees of freedom which are averaged out without target polarization. In the particular case of a nucleon ejected along the direction of the momentum transfer from a target with spin oriented in the same direction (superparallel kinematics) only three structure functions survive and can be simply separated.

Medium energy (γ, p0) reactions are investigated with the purpose of finding how far a direct knockout mechanism holds. Final state interactions are included in a cross section where the hole spectral function is not factorized. The approximate factorized formula gives large differences (a priori out of control). The choice of different optical model potentials and bound state wave functions is discussed and results are compared with experimental data for 12C, 16O and 40Ca. The sensitivity to the optical potential is confirmed. The direct mechanism appears able to reproduce the experimental cross sections up to photon energies corresponding to a recoil momentum larger than 2 fm−1.

The measurement of recoiling nucleus momentum distributions in (e,e'p) reactions has been performed for p-hole states in 12 C and 16 O under extended kinematical conditions. The analysis of the experimental data has been performed without requiring the usual factorization of the cross section. The sensitivity of the data and of the analysis for deducing bound and scattering proton states is discussed.

The use of polarized electrons for the quasi-free knockout of nucleons is considered by taking advantage of the effective polarization of the target nucleus resulting from final-state interaction. The coincidence cross section is written in terms of five structure functions, four of which are involved in the case of unpolarized electrons. The fifth structure function, ⨍' 01 , entirely dependent on the presence of final-state interactions, is related to the interference between the nuclear charge and the transverse nuclear current. Its behaviour in the reaction 16 O(e, e'p) 15 N is studied for the p 1 2 and p 3 2 holes with different combinations of bound states and distorting optical potentials. The possible observation of ⨍' 01 is also discussed.

The relevance of different approximations usually adopted in the description of direct knockout of nucleons in photoreactions at medium energies is investigated. Orthogonality between initial and final states in DWIA and antisymmetrization of the outgoing particle are studied in the presence of recoil terms arising from a correct treatment of the c.m. motion. The different effects are discussed in the specific example of the 12 C target nucleus for different combinations of bound and scattering states. Whereas orthogonality and antisymmetrization appear to play a rather relevant role only at backward angles, the recoil term is particularly important for the (γ, n) reaction and cannot be simulated by the use of multipole energy-independent effective charges.

We discuss the problem of the lack of orthogonality between continuum final states obtained by the use of an optical potential and the initial bound states in the description of knockout reactions. Orthogonality is in general lost whenever the description is restricted to a model space with other channels suppressed. The use of suitable effective operators may correct for the orthogonality defect. We obtain an orthogonality condition and evaluate the importance of the orthogonality defect for knockout reactions induced by electromagnetic probes. For (e, e'p) reactions this effect is found irrelevant. For (γ, p) reactions the use of an unfactorized cross section overcomes the difficulty, whereas a large spurious electric dipole effect is found in the usual factorized approximation.

Spin-orbit distortion of the emerging nucleon in quasi-free electron scattering is considered in the frame of a program aiming at examining the approximations involved in the theoretical treatment. The imaginary part of the spin-orbit coupling in the optical-model potential felt by the knocked out nucleon appears here to have a significant role. Its consequences in the case of the reaction 12 C(e, e′p) 11 B are discussed.

The coincidence cross section for quasi-free electron scattering is written in terms of four structure functions. Two of them represent the longitudinal and transverse response. The other two are interference terms. Their behaviour in the reaction 16O(e, e'p)15N is studied for the p 1 2 and p 3 2 holes. The influence of the bound state and of the distorting optical potential is investigated. Possible kinematical situations are considered in order to determine the structure functions with the available experimental set-up.

In the one-photon exchange approximation the coincidence cross section of the quasifree (e, e′p) reaction can be written in terms of four structure functions, which represent the response of the nucleus to the various components of the electromagnetic interaction. The role of Coulomb distortion of electrons on the separation of these structure functions is investigated. The distorted-electron wave functions are given by an expansion in powers of Z α, whose validity is discussed. The effect of electron distortion on the separation of longitudinal and transverse responses in parallel kinematics is considered, taking 40 Ca and 208 Pb as study cases. The effect is found to be significant. However, whereas for 40 Ca it can be eliminated, with a good degree of accuracy, by correcting the cross section through effective momentum transfer, in 208 Pb also large contributions due to the focusing of the electron wave must be carefully subtracted. The determination of longitudinal-transverse interference structure function in coplanar perpendicular kinematics is also discussed.

The (γ, p) and (γ, n) reactions with polarized photons at intermediate energies are discussed under the hypothesis of a direct knockout mechanism with final state distortion. As in this frame the behaviour of the cross sections is quite different, the experiment is proposed as a crucial test of the direct emission in photoreactions.

A detailed analysis has been made on the recent (e,e'p) experiment on 16 O for the p-shell protons. The absorption factors and the occupation numbers can be largely influenced by the effect of spin orbit components in the optical potential. Different kinematical conditions have been studied experimentally and theoretically on 12 C and 16 O to see the influence of final state interaction and factorization of the cross section.