Inclusive Photoproduction of η\eta Mesons on Nuclei and the in-medium properties of the S11_{11} Resonance

A relativistic non-local model for the inclusive photoproduction of $\eta$ mesons from complex nuclei is introduced. The model is based on the dominance of the S$_{11}$(1535) resonance. We compare the results of our calculations with the available data on inclusive cross sections for the nuclei C, Al and Cu. Assuming the resonance propagates freely in the nuclear medium, we find that the calculated angular distribution and energy dependence of the cross sections reproduce the data in a reasonable fashion. The present non-local model allows the inclusion of density dependent mass and width in the calculations. Including these in the calculations reveals that the presently available data do not show clear preference for the inclusion of such modifications of the properties of the S$_{11}$(1535) in the nuclear medium.Comment: 15 pages, 8 figure

Relativistic Calculations for the Exclusive Photoproduction of Eta Mesons from Complex Nuclei

A relativistic model for the quasifree photoproduction of eta meson from complex nuclei is developed. The interactions between fields are introduced through effective Lagrangians. Contributions from several nucleon resonances as well as nucleon Born terms and vector meson exchange diagrams are included. Nucleon and eta wavefunctions are solutions of Dirac and Klein-Gordon equations, respectively. Final state interactions of the outgoing particles are included via optical potentials. The effects of these interactions on the cross sections and photon asymmetries are studied and are found to be large. Calculations indicate that at energies near threshold the exclusive reaction takes place mainly through formation of the S_{11}(1535) resonance. Comparisons with the non-relativistic calculations show differences between the two approaches both for the cross sections and photon asymmetries. We give some detailed predictions for the reaction observables for exclusive photoproduction on ^{12}C, ^{16}O and ^{40}Ca.Comment: Latex, 27 pages, 13 uuencoded postscript figures. Accepted for publication in Phys. Rev.

Relativistic calculations for photonuclear reactions; 2, nonrelativistic reductions and nuclear medium effects

The relativistic amplitude for the direct knock-out contribution to \left( \gamma, p \right) reactions on nuclei is reduced to a nonrelativistic form using an effective Pauli reduction scheme. The reduction is carried out to second order in the inverse nucleon mass. It is found that the interaction Hamiltonian appearing in the nonrelativistic amplitude has significant dependence, starting at second order, on the vector and scalar mean nuclear potentials. These strong medium modifications are absent in traditional nonrelativistic calculations. Detailed comparisons show that these modifications are crucial to understanding the differences between relativistic and nonrelativistic models. These differences are also examined through reduction of the relativistic amplitude via the Foldy-Wouthuysen transformation. Similar medium modifications are obtained in this case as well. We discuss the implications of these medium modifications for the consistency of existing nonrelativistic calculations

Nuclear Medium Effects in the Relativistic Treatment of Quasifree Electron Scattering

Non-relativistic reduction of the S-matrix for the quasifree electron scattering process $A\left(~e, e'p~\right)A-1$ is studied in order to understand the source of differences between non-relativistic and relativistic models. We perform an effective Pauli reduction on the relativistic expression for the S-matrix in the one-photon exchange approximation. The reduction is applied to the nucleon current only; the electrons are treated fully relativistically. An expansion of the amplitude results in a power series in the nuclear potentials. The series is found to converge rapidly only if the nuclear potentials are included in the nuclear current operator. The results can be cast in a form which reproduces the non-relativistic amplitudes in the limit that the potentials are removed from the nuclear current operator. Large differences can be found between calculations which do and do not include the nuclear potentials in the different orders of the nuclear current operator. In the high missing momentum region we find that the non-relativistic calculations with potentials included in the nuclear current up to second order give results which are close to those of the fully relativistic calculation. This behavior is an indication of the importance of the medium modifications of the nuclear currents in this model, which are naturally built into the relativistic treatment of the reaction.Comment: Latex, 26 pages including 5 uuencoded postscript figures. accepted for publication in Phys. Rev. C

Non-locality and Medium Effects in the Exclusive Photoproduction of Eta Mesons on Nuclei

A relativistic model for the quasifree exclusive photoproduction of $\eta$ mesons on nuclei is extended to include both non-local and medium effects. The reaction is assumed to proceed via the dominant contribution of the S$_{11}$(1535) resonance. The complicated integrals resulting from the non-locality are simplified using a modified version of a method given by Cooper and Maxwell. The non-locality effects are found to affect the magnitude of the cross section. Some possibilities reflecting the effects of the medium on the propagation and properties of the intermediate S$_{11}$ resonance are studied. The effects of allowing the S$_{11}$ to interact with the medium via mean field scalar and vector potentials are considered. Both broadening of width and reduction in mass of the resonance lead to a suppression of the calculated cross sections.Comment: 19 pages, 7 figure

Systematic study of Coulomb distortion effects in exclusive (e,e'p) reactions

A technique to deal with Coulomb electron distortions in the analysis of (e,e'p) reactions is presented. Thereby, no approximations are made. The suggested technique relies on a partial-wave expansion of the electron wave functions and a multipole decomposition of the electron and nuclear current in momentum space. In that way, we succeed in keeping the computational times within reasonable limits. This theoretical framework is used to calculate the quasielastic (e,e'p) reduced cross sections for proton knockout from the valence shells in $^{16}$O, $^{40}$Ca, $^{90}$Zr and $^{208}$Pb. The final-state interaction of the ejected proton with the residual nucleus is treated within an optical potential model. The role of electron distortion on the extracted spectroscopic factors is discussed.Comment: 45 pages, 10 encapsulated postscript figures, Revtex, uses epsfig.sty and fancybox.sty, to be published in Physical Review

Relativistic calculation of nuclear transparency in (e,e'p) reactions

Nuclear transparency in (e,e'p) reactions is evaluated in a fully relativistic distorted wave impulse approximation model. The relativistic mean field theory is used for the bound state and the Pauli reduction for the scattering state, which is calculated from a relativistic optical potential. Results for selected nuclei are displayed in a Q^2 range between 0.3 and 1.8 (GeV/c)^2 and compared with recent electron scattering data. For Q^2 = 0.3 (GeV/c)^2 the results are lower than data; for higher Q^2 they are in reasonable agreement with data. The sensitivity of the model to different prescriptions for the one-body current operator is investigated. The off-shell ambiguities are rather large for the distorted cross sections and small for the plane wave cross sections.Comment: 8 pages, 3 figure

Relativistic mean field approximation to the analysis of 16O(e,e'p)15N data at |Q^2|\leq 0.4 (GeV/c)^2

We use the relativistic distorted wave impulse approximation to analyze data on 16O(e,e'p)15N at |Q^2|\leq 0.4 (GeV/c)^2 that were obtained by different groups and seemed controversial. Results for differential cross-sections, response functions and A_TL asymmetry are discussed and compared to different sets of experimental data for proton knockout from p_{1/2} and p_{3/2} shells in 16O. We compare with a nonrelativistic approach to better identify relativistic effects. The present relativistic approach is found to accommodate most of the discrepancy between data from different groups, smoothing a long standing controversy.Comment: 28 pages, 7 figures (eps). Major revision made. New figures added. To be published in Phys. Rev.

Inclusive electron scattering in a relativistic Green function approach

A relativistic Green function approach to the inclusive quasielastic (e,e') scattering is presented. The single particle Green function is expanded in terms of the eigenfunctions of the nonhermitian optical potential. This allows one to treat final state interactions consistently in the inclusive and in the exclusive reactions. Numerical results for the response functions and the cross sections for different target nuclei and in a wide range of kinematics are presented and discussed in comparison with experimental data.Comment: 12 pages, 7 figures, REVTeX

Relativistic versus Nonrelativistic Optical Potentials in A(e,e'p)B Reactions

We investigate the role of relativistic and nonrelativistic optical potentials used in the analysis of ($e,e'p$) data. We find that the relativistic calculations produce smaller ($e,e'p$) cross sections even in the case in which both relativistic and nonrelativistic optical potentials fit equally well the elastic proton--nucleus scattering data. Compared to the nonrelativistic impulse approximation, this effect is due to a depletion in the nuclear interior of the relativistic nucleon current, which should be taken into account in the nonrelativistic treatment by a proper redefinition of the effective current operator.Comment: Added one new figure, the formalism section has been enlarged and the list of references updated. Added one appendix. This version will appear in Phys. Rev. C. Revtex 3.0, 6 figures (not included). Full postscript version of the file and figures available at http://www.nikhefk.nikhef.nl/projects/Theory/preprints