R. A. Bonham

Elastic Electron Scattering Amplitudes for Neutral Atoms Calculated Using the Partial Wave Method at 10, 40, 70, and 100 kV for Z = 1 to Z = 54

Elastic electron scattering amplitudes for neutral atoms were calculated using the partial wave expansion method for 10‐, 40‐, 70‐, and 100‐kV incident electrons. The partial wave phase shifts were calculated by numerical intergration using the phase amplitude method until the results converged to values obtained using the WKBJ and first Born approxmations, which were then used in the remainder of the partial wave sum.The static potential field of the target atoms was represented by an analytical expression involving a sum of Yukawa terms. Potential field parameters for the expression were obtained by a least‐squares fit of the radial electron distribution function, D (r), using Hartree—Fock and relativistic wavefunctions for all the neutral atoms from Z=1 to Z=54. For the smaller atoms from Z=1 to Z=21, Clementi Hartree—Fock wavefunctions were used and for the atoms from Z=22 to 54 Liberman—Waber—Cromer D (r) curves calculated using the Dirac Hamiltonian incorporating a j—j coupling scheme and the Slater...

Analytical Expressions for the Hartree—Fock Potential of Neutral Atoms and for the Corresponding Scattering Factors for X Rays and Electrons

Approximate analytical expressions for the Hartree—Fock potential of neutral atoms to Z=36 have been obtained by fitting the radial electron density with an analytical expression by least squares. The expression for the radial density corresponds to the following form of the screening factor: Zp(r)Z= ∑ i=12aγiexp(−aλir)+r ∑ j=1mbγjexp(−bλjr), where m=2 for Z=2 to Z=18 and m=3 for Z=19 to Z=36. The corresponding expressions for the mean radius, the mean square radius, the diamagnetic susceptibility, and the atomic scattering factors for x rays, and for electrons according to the first Born approximation are given. The accuracy of the approximate expressions is discussed in relation to results obtained by numerical calculations from the Hartree—Fock wavefunctions for the atoms.

Analytical Expressions for Potentials of Neutral Thomas—Fermi—Dirac Atoms and for the Corresponding Atomic Scattering Factors for X Rays and Electrons

Approximate analytical expressions for the electrostatic potentials of neutral Thomas—Fermi—Dirac atoms have been obtained by fitting a sum of three exponential terms to the tabulated values by least‐squares methods. The six different parameters used for each atom are expressed as functions of the atomic number. The corresponding expressions for the radical electron density, the mean‐square radius, the diamagnetic susceptibility, the atomic scattering factors for x rays and the atomic scattering factors for electrons according to the first Born approximation are given. The accuracy of the approximate expressions are discussed in relation to results obtained from the tabulated values of the electrostatic potential and from the corresponding electron density.

On the Calculation of Multicenter Two‐Electron Repulsion Integrals Involving Slater Functions

Integral transforms are used to evaluate many‐center two‐electron repulsion integrals involving Slater s‐type functions. The reduction of a general four‐center integral of this type to a form convenient for computational purposes is presented. The technique described has the important advantage that all lesser many‐center and one‐center integrals can be obtained from the four‐center case by proper choice of constants. The form of the result is such that simple single‐precision numerical techniques yield rapid and accurate evaluations of many‐center integrals. Several numerical examples are presented.

Inelastic Scattering from Atoms at Medium Energies. I. Bound States

The problem of computing differential scattering cross sections for the inelastic scattering of 10–80 kv electrons from atoms is treated. Expressions for the electron scattering factor for the excitation of bound states of atoms for small excitation energies are presented using the first Born approximation. The scattering factor and differential cross section for argon at 40 kv have been calculated neglecting spin and polarization effects. Both Hartree—Fock and Slater central‐field wave functions were used in these calculations. Selection rules for electron excitation of bound states of atoms and the behavior of the total inelastic scattering intensity at small scattering angles are discussed. Approximate formulas for the first Born approximation total cross sections have also been derived.

Correction of Electron Diffraction Data for Failure of the Born Approximation

A simple objective method for correcting electron diffraction data for the effects of the imaginary part of the atomic electron scattering factor is presented. Expressions for the phase shifts of the form: η(s,z)=a(z)+b(z)s+c(z)s2, valid for s up to 50 at 40 kv and z up to 98 are given. This analytical form was chosen since it provides a close fit (less than 2% average deviation) to tabulated values of η(s, z), calculated by Ibers and Hoerni, over the useful range of s and thus makes the inclusion of the cos[η1(s)—η2(s)] term in theoretical molecular intensity curves a routine matter. The Fourier transform of the complete constant coefficient molecular intensity curve including the cosine phase shift term has been obtained and simple analytical expressions for peak splittings and corrections to vibrational amplitudes are presented.

A pulsed electron beam time of flight apparatus for measuring absolute electron impact ionization and dissociative ionization cross sections

A new electron impact spectrometer has been constructed that utilizes a variable energy (4–500 eV) pulsed electron source with time‐of‐flight detection of electrons and ions. The apparatus can be used in a beam‐beam scattering mode or in a constant pressure mode suitable for absolute measurements. A newly designed data processing system is described that uses standard CAMAC modules (LeCroy model 4208 TDCs) and allows up to 32 separate detectors to be used simultaneously in a single hit mode or up to four separate detectors in a multihit mode with each detector capable of recording up to eight hits in the same experiment. The dead time between experiments is 9.2 μs which allows up to 100 000 experiments/s for experimental flight times not exceeding 1 μs at 1 ns timing resolution. Longer flight times, up to 8.3 ms in duration, can be accommodated but with reduced timing resolution. The determination of the partial ionization cross sections for Ar+, Ar2+, and Ar3+ from threshold up to 500 eV is used as an il...

Simple Correlated Wavefunctions for the Ground State of Heliumlike Atoms

A number of correlated wavefunctions of simple form were investigated for heliumlike atoms. Instead of the usual Hylleraas expansion the wavefunctions considered contained exponential correlation functions with nonlinear variational parameters. Wavefunctions of this type are usually avoided because of the nonlinear parameters. However, this type of function was chosen to try to determine some simple but relatively good wavefunctions for use in computing atomic properties. Results for atomic numbers 1 through 3 are presented.

Bethe surface, elastic and inelastic differential cross sections, Compton profile, and binding effects for H2 obtained by electron scattering with 25 keV incident electrons

Electron impact spectra for H2 have been obtained at scattering angles of 1°, 1.5°, 2°, 3°, 4°, 5°, 7°, and 10° using 25 keV incident electrons. The measured intensities were converted to generalized oscillator strengths and placed on an absolute scale at each scattering angle by the use of the Bethe sum rule for the generalized oscillator strength distribution. The cross section differential with respect to both solid angle and energy loss of the scattered electron was corrected for relativistic and exchange effects and integrated over energy loss to obtain the inelastic differential cross sections. In addition the elastic cross section differential with respect to solid angle was measured. The results are all in excellent agreement with theoretical calculations. The total elastic cross section was determined using additional data from another source. The Compton profile was determined from the 7° scattering data and was found to agree well with the previous x‐ray results. Consistent generalized optical ...

Effect of Bond Formation on Electron Scattering Cross Sections for Molecules

Total differential scattering cross sections were obtained experimentally for molecular hydrogen, nitrogen, and oxygen. The cross section for helium was also measured and compared with a calculated cross section to calibrate the apparatus. The calculation of the binding energy from the data was carried out and compared with previous results. It was found that the scattering method with presently available experimental and theoretical techniques cannot give values comparable in accuracy to other methods for obtaining the binding energy itself but it is useful as a test of scattering theory. The binding energy obtained for hydrogen was in good agreement with the spectroscopic value. The binding energies which were obtained for nitrogen and oxygen were considerably higher than the accepted values. The experimental uncertainties were quite large but even so the results suggest that there may be significant deviations from the simple theory. Information about the molecular densities was obtained which may serv...