Approximate Coulomb distortion effects in (e,e'p) reactions

In this paper we apply a well-tested approximation of electron Coulomb distortion effects to the exclusive reaction (e,e'p) in the quasielastic region. We compare the approximate treatment of Coulomb distortion effects to the exact distorted wave Born approximation evaluated by means of partial wave analysis to gauge the quality of our approximate treatment. We show that the approximate M\"oller potential has a plane-wave-like structure and hence permits the separation of the cross section into five terms which depend on bilinear products of transforms of the transition four current elements. These transforms reduce to Fourier transforms when Coulomb distortion is not present, but become modified with the inclusion of Coulomb distortion. We investigate the application of the approximate formalism to a model of 208Pb(e,e'p) using Dirac-Hartree single particle wave functions for the ground state and relativistic optical model wave functions for the continuum proton. We show that it is still possible to extract, albeit with some approximation, the various structure functions from the experimentally measured data even for heavy nuclei.Comment: 32 pages, 11 figures, 19 reference

Extraction of Structure Functions from Quasielastic Electron Scattering (e,e') from Medium and Heavy Nuclei

Using a relativistic mean-field single particle knock-out model for (e,e') reactions on nuclei, we investigate approximate treatments of Coulomb distortion effects and the extraction of longitudinal and transverse structure functions. We show that an effective momentum approximation (EMA) when coupled with a focusing factor provides a good description of the transverse contributions to the (e,e') cross sections for electron energies above 300 MeV on 208Pb. This approximation is not as good for the longitudinal contributions even for incident electron eneriges above 1 GeV and if one requires very precise extraction of longitudinal and transverse structure functions in the quasielastic region it is necessary to utilize distortion factors based on a nuclear model and a more accurate inclusion of Coulomb distortion effects.Comment: 5 pages, 7 figures, submitted to Phys. Rev.

On representation of mechanical behavior and stereological measures of microstructure

Macroscopic homogeneity of a heterogeneous body is defined from various points of view. The applicability of the principle of Delesse to a single macroscopically homogeneous body is discussed. It is then seen that a function derived from a consideration of the area fraction of a phase can serve as a measure of clustering of particles of that phase

Coulomb Distortion Effects for Electron or Positron Induced (e,e′)(e,e') Reactions in the Quasielastic Region

In response to recent experimental studies we investigate Coulomb distortion effects on $(e,e')$ reactions from medium and heavy nuclei for the case of electrons and positrons. We extend our previously reported full DWBA treatment of Coulomb distortions to the case of positrons for the $^{208}Pb(e,e')$ reaction in the quasielastic region for a particular nuclear model. In addition, we use previously reported successful approaches to treating Coulomb corrections in an approximate way to calculate the Coulomb distortion effects for $(e,e')$ reactions for both electrons and positrons for the case of a simple nuclear model for quasielastic knock-out of nucleons. With these results in hand we develop a simple {\em ad-hoc} approximation for use in analyzing experiments, and discuss methods of extracting the ``longitudinal structure function" which enters into evaluation of the Coulomb sum rule. These techniques are generally valid for lepton induced reactions on nuclei with momentum transfers greater than approximately 300 $MeV/c$.Comment: 18 pages, 6 figure

y-scaling in Quasielastic Electron Scattering from Nuclei

A relativistic single particle model is used to calculate the inclusive $(e,e')$ reaction from $A=$12, 40, 56, 197, and 208 nuclei in the quasielastic region. We have shown that this model provides a very good description of the available experimental cross sections when they are dominated by the quasielastic process. In this paper we use this model to investigate the dependence of $y$-scaling on electron kinematics, particularly the electron scattering angle, for a range of squared four momentum transfer $0.20-0.80$ (GeV/c)$^2$. In this kinematic domain, Coulomb distortion of the electron does not significantly affect scaling, but final state interactions of the knocked out nucleon do affect scaling particularly when the nucleons have lower energies. In general, we find that scaling works for this reaction, but at lower values of the four momentum transfer, the scaling function does have some dependence on the electron scattering angle. We also consider a modification of y-scaling to include small binding energy effects as a function of Z and A and show that there is some improvement in scaling.Comment: 21 pages, 11 figure

Studies in a transonic rotor aerodynamics and noise facility

The design, construction and testing of a transonic rotor aerodynamics and noise facility was undertaken, using a rotating arm blade element support technique. This approach provides a research capability intermediate between that of a stationary element in a moving flow and that of a complete rotating blade system, and permits the acoustic properties of blade tip elements to be studied in isolation. This approach is an inexpensive means of obtaining data at high subsonic and transonic tip speeds on the effect of variations in tip geometry. The facility may be suitable for research on broad band noise and discrete noise in addition to high-speed noise. Initial tests were conducted over the Mach number range 0.3 to 0.93 and confirmed the adequacy of the acoustic treatment used in the facility to avoid reflection from the enclosure