Relativistic Coulomb Sum Rules for (e,e′)(e,e^\prime)

A Coulomb sum rule is derived for the response of nuclei to $(e,e^\prime)$ scattering with large three-momentum transfers. Unlike the nonrelativistic formulation, the relativistic Coulomb sum is restricted to spacelike four-momenta for the most direct connection with experiments; an immediate consequence is that excitations involving antinucleons, e.g., $N{\bar N}$ pair production, are approximately eliminated from the sum rule. Relativistic recoil and Fermi motion of target nucleons are correctly incorporated. The sum rule decomposes into one- and two-body parts, with correlation information in the second. The one-body part requires information on the nucleon momentum distribution function, which is incorporated by a moment expansion method. The sum rule given through the second moment (RCSR-II) is tested in the Fermi gas model, and is shown to be sufficiently accurate for applications to data.Comment: 32 pages (LaTeX), 4 postscript figures available from the author

Energy Dependence of the NN t-matrix in the Optical Potential for Elastic Nucleon-Nucleus Scattering

The influence of the energy dependence of the free NN t-matrix on the optical potential of nucleon-nucleus elastic scattering is investigated within the context of a full-folding model based on the impulse approximation. The treatment of the pole structure of the NN t-matrix, which has to be taken into account when integrating to negative energies is described in detail. We calculate proton-nucleus elastic scattering observables for $^{16}$O, $^{40}$Ca, and $^{208}$Pb between 65 and 200 MeV laboratory energy and study the effect of the energy dependence of the NN t-matrix. We compare this result with experiment and with calculations where the center-of-mass energy of the NN t-matrix is fixed at half the projectile energy. It is found that around 200 MeV the fixed energy approximation is a very good representation of the full calculation, however deviations occur when going to lower energies (65 MeV).Comment: 11 pages (revtex), 6 postscript figure

Total Cross Sections for Neutron Scattering

Measurements of neutron total cross-sections are both extensive and extremely accurate. Although they place a strong constraint on theoretically constructed models, there are relatively few comparisons of predictions with experiment. The total cross-sections for neutron scattering from $^{16}$O and $^{40}$Ca are calculated as a function of energy from $50-700$~MeV laboratory energy with a microscopic first order optical potential derived within the framework of the Watson expansion. Although these results are already in qualitative agreement with the data, the inclusion of medium corrections to the propagator is essential to correctly predict the energy dependence given by the experiment.Comment: 10 pages (Revtex 3.0), 6 fig

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

Channel Coupling in A(e⃗,e′N⃗)BA(\vec{e},e' \vec{N})B Reactions

The sensitivity of momentum distributions, recoil polarization observables, and response functions for nucleon knockout by polarized electrons to channel coupling in final-state interactions is investigated using a model in which both the distorting and the coupling potentials are constructed by folding density-dependent effective interactions with nuclear transition densities. Calculations for $^{16}$O are presented for 200 and 433 MeV ejectile energies, corresponding to proposed experiments at MAMI and TJNAF, and for $^{12}$C at 70 and 270 MeV, corresponding to experiments at NIKHEF and MIT-Bates. The relative importance of charge exchange decreases as the ejectile energy increases, but remains significant for 200 MeV. Both proton and neutron knockout cross sections for large recoil momenta, $p_m > 300$ MeV/c, are substantially affected by inelastic couplings even at 433 MeV. Significant effects on the cross section for neutron knockout are also predicted at smaller recoil momenta, especially for low energies. Polarization transfer for proton knockout is insensitive to channel coupling, even for fairly low ejectile energies, but polarization transfer for neutron knockout retains nonnegligible sensitivity to channel coupling for energies up to about 200 MeV. The present results suggest that possible medium modifications of neutron and proton electromagnetic form factors for $Q^2 \gtrsim 0.5 (GeV/c)^2$ can be studied using recoil polarization with relatively little sensitivity due to final state interactions.Comment: Substantially revised version accepted by Phys. Rev. C; shortened to 49 pages including 21 figure