D. S. Onley

A computer program for analysis of inelastic electron scattering from nuclei

Abstract A partial wave analysis of inelastic electron scattering is carried out for electric and magnetic multipole excitations of the nucleus. The results of this analysis which includes the effects of energy loss and Coulomb retardation have been programmed for the computer. The resulting FORTRAN IV program is capable of calculating inelastic electron scattering differential and total cross sections for a large range of incident electron energies and transitions of multipolarity 1 to 5. The methods of calculation and the limitations of the program are discussed in some detail.

Longitudinal response functions for 40Ca from quasi-elastic electron scattering

Abstract Longitudinal response functions were extracted from quasi-elastic electron scattering data on 40 Ca at angles of 45.5°, 90°, and 140° with bombarding energies ranging from 130 to 840 MeV and for constant three-momentum transfers of 300, 330, 370, 410 and 450 MeV/ c . Contrary to previously reported results, the present longitudinal response functions show no more than 20% missing strength when compared to the relativistic Fermi gas model. Calculations employing wavefunctions generated from a relativistic Hartree potential and using an effective momentum approximation yield results that are in much closer agreement with the experimental data and indicate essentially no longitudinal suppression.

A new technique for calculating virtual photon spectra

Abstract A first-order matrix differential equation in energy is used to propagate radial matrix elements arising in DWBA of relativistic electron scattering from nuclei. Given an initial set of matrix elements at some value of the energy, this equation permits the evaluation of the radial matrix elements over the complete energy transfer range. A computer code has been written for this new procedure and the virtual photon spectra accompanying electron scattering from a point nucleus is calculated as a function of photon energy for various multipoles, nuclear charges, and incident electron energies.

Radial integrals with finite energy loss for Dirac–Coulomb 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.

Matrix Elements of Relativistic Electrons in a Coulomb Field

Matrix elements for a radiative interaction between states of a Dirac electron in the presence of a Coulomb field are reduced to a closed analytic form in the limit of zero electron mass; corrections for finite electron mass are indicated. The application of these to inelastic electron scattering and radiation problems is discussed.

Relativistic Hartree study of deformed nuclei

Abstract Relativistic Hartree calculations are performed for axially symmetric solutions of deformed nuclei in the sd shell. Both even-even and selected odd- A nuclei are included. The systematic behavior of quadrupole moments and binding energies are reproduced; the deformations being solely determined by self-consistency. The states are expanded in a spherical basis of states obtained by solving the same or neighboring nucleus with a constraint to retain spherical symmetry. The continuum states are artificially discretized by applying a boundary condition; both the positive and negative energy states are included in the expansion. The effects of tensor coupling of the rho meson and of the pion are included. The contribution of the former are small in the nuclei studied here; however, the pion has a large effect on the magnetic moment of odd- A nuclei. The binding energies, quadrupole moments, magnetic moments and single particle spectra are presented and compared with similar calculations, both relativistic and non-relativistic.

Charge and current distributions in the Helm model

Abstract The convoluted forms of the transition charge and current distributions of the generalized Helm model make it particularly convenient for plane wave Born approximation calculations but difficult to compare with other models. We have derived explicit expressions for these distributions that can be compared with those used in distorted wave calculations. We also suggest more general forms for the transverse contributions.

Partial differential matrix equations for generalized hypergeometric functions

A method of handling a number of generalized hypergeometric functions in terms of first-order partial differential matrix equations is introduced. This method has many advantages in formal manipulations and in numerical integration. In particular, it allows investigation of the energy dependence of matrix elements arising in scattering problems in quantum mechanics.

Quasielastic electron scattering from {sup 40}Ca

Differential cross sections for quasielastic electron scattering on {sup 40}Ca have been measured at laboratory scattering angles of 45.5{degree}, 90{degree}, and 140{degree} with bombarding energies ranging from 130 to 840 MeV. Transverse and longitudinal response functions have been extracted for momentum transfers from 300 to 500 MeV/c. Contrary to some previously reported results, the total observed longitudinal strength agrees with the relativistic Fermi gas prediction to within {plus_minus}18{percent}. {copyright} {ital 1997} {ital The American Physical Society}

Quasielastic electron scattering from40Ca

Differential cross sections for quasielastic electron scattering on {sup 40}Ca have been measured at laboratory scattering angles of 45.5{degree}, 90{degree}, and 140{degree} with bombarding energies ranging from 130 to 840 MeV. Transverse and longitudinal response functions have been extracted for momentum transfers from 300 to 500 MeV/c. Contrary to some previously reported results, the total observed longitudinal strength agrees with the relativistic Fermi gas prediction to within {plus_minus}18{percent}. {copyright} {ital 1997} {ital The American Physical Society}