(1966). Electron scattering and nuclear structure. Advances in Physics: Vol. 15, No. 57, pp. 1-109.

https://www.annualreviews.org/doi/pdf/10.1146/annurev.ns.25.120175.001553

Electron Scattering and Nuclear Structure

Electron scattering and nuclear structure.

Confluent Hypergeometric Functions.

Particle-hole excitations in 208Pb

This paper presents a review on the field of inclusive quasielastic electron-nucleus scattering. It discusses the approach used to measure the data and includes a compilation of data available in numerical form. The theoretical approaches used to interpret the data are presented. A number of results obtained from the comparison between experiment and calculation are then reviewed. The analogies to, and differences from, other fields of physics exploiting quasielastic scattering from composite systems are pointed out.

https://arxiv.org/pdf/nucl-ex/0603029.pdf

Inclusive quasielastic electron-nucleus scattering

We describe a calculation for the electron Coulomb distortion effects in ({ital e},{ital e}{prime}{ital p}) in the quasielastic region from medium and heavy nuclei. The bound nucleons are described by single-particle Dirac wave functions in the presence of scalar and vector potentials which are parametrized fits to relativistic Hartree potentials, while the wave function of the knocked-out nucleon is a solution to the Dirac equation with the relativistic optical potential. The electron wave functions are solutions to the Dirac equation in the presence of the Coulomb potential of the nucleus and the interaction with the selected nucleon is treated to first order. We examine the {sup 40}Ca({ital e},{ital e}{prime}{ital p}) reaction in both parallel and {omega}-{ital q} constant kinematics. We find that electron Coulomb distortion has a smaller effect in {omega}-{ital q} constant kinematics than in parallel kinematics. The principal effect in parallel kinematics is to shift the maximum and minimum of the reduced cross section which is consistent with the experimental data. Occupation numbers of about 70% to 80% are needed to normalize the distorted-wave Born approximation calculation to the {sup 40}Ca({ital e},{ital e}{prime}{ital p}) experimental data. We also calculate the reduced cross section for the 3{ital s}{sub 1/2}more » state in {sup 208}Pb and compare our results to experimental data and previous calculations. We find no significant difference in using relativistic, as compared with nonrelativistic, nuclear wave functions. We do find significant corrections to earlier methods of treating Coulomb distortion which, in turn, affect the occupation number extracted from experiment. We find an occupation number for this state of 71.4%.« less

Electron Coulomb effects in quasielastic (e,e'p) reactions.

Partial-wave analysis of the inelastic scattering of electrons by nuclei. iii. systematics of electric multipole excitation

We report a calculation of inclusive electron scattering from {sup 40}Ca in the quasielastic region where we use relativistic Hartree bound-state wave functions for the nucleons and use the same real potential for the final-state interaction which guarantees orthogonality of initial and final states, current conservation, and, hence, gauge invariance. This potential gives quite good agreement with the measured cross sections, especially for energy transfer above the quasielastic peak approaching the dip region; however, it still does not successfully reproduce the experimentally separated longitudinal and transverse structure functions. We use this simple model which gives a reasonable fit to the cross-section data to discuss possible problems involved in the experimental separation procedure, which might distort the extraction of the longitudinal structure function.

Single particle analysis of (e,e') and the value of separated structure functions.

We examine the question of whether the fourth and fifth structure functions (called ${\mathrm{W}}_{\mathrm{LT}}$ and ${\mathrm{W}}_{\mathrm{LT}\ensuremath{'}}$) defined by the plane wave Born approximation (PWBA) for the reaction (e,e\ensuremath{'}p) are still meaningful quantities in the presence of electron Coulomb distortion. For a heavy target (${\mathrm{Pb}}^{208}$), the apparent structure functions obtained in the presence of the electron Coulomb distortion have shapes (in terms of the number of maxima or minima) similar to those defined in PWBA; however, the magnitudes are changed greatly. For the fourth structure function, the distortion can change the magnitude, even for ${\mathrm{O}}^{16}$, by more than 15%. For proton knockout from (l\ifmmode\pm\else\textpm\fi{}12) spin-orbit doublet states, the changes caused by electron distortion have opposite effects, increasing the magnitude of the one while decreasing the other. The Coulomb effects on the fifth structure function depend on the out of plane angle used in the extraction. For a small angle (e.g., 10\ifmmode^\circ\else\textdegree\fi{}), the electron distortion can be more than 15% in ${\mathrm{O}}^{16}$. However, for certain kinematic choices, the Coulomb distortion effects on the fifth structure function can largely be removed. For proton knockout from spin-orbit doublet states the ratio of the fifth structure functions is of interest. We find that this ratio is nearly independent of the central part of the proton final state interaction and has the power of investigating the spin-orbit interaction of optical potentials.

Effects of Coulomb distortion and final state interaction on the fourth and fifth structure functions.

Analytic results for radial integrals over products of Dirac–Coulomb functions and the radial part of the electromagnetic Green’s function are expressed in terms of a matrix generalization of the gamma function. This matrix gamma function has many useful properties, including a recurrence relation similar to that of the gamma function, and provides a compact easily manipulated method of evaluating the Dirac–Coulomb radial integrals. These results can be used to calculate the virtual and real photon spectra associated with electron scattering from the nucleus.

D. S. Onley

Papers

Electron Coulomb effects in quasielastic (e,e'p) reactions.

Partial-wave analysis of the inelastic scattering of electrons by nuclei. iii. systematics of electric multipole excitation

Single particle analysis of (e,e') and the value of separated structure functions.

Effects of Coulomb distortion and final state interaction on the fourth and fifth structure functions.

Radial integrals with finite energy loss for Dirac–Coulomb functions