Critical Assessment of the Polarized-Orbital Method in Atomic Scattering

The method of polarized orbitals used in calculating electron-atom scattering amplitudes has two obvious flaws: the wave function is discontinuous, and the method is not variationally based. These are corrected in a somewhat arbitrary manner, and it is found that the results then depend upon a parameter of the theory sufficiently strongly that there are serious doubts about the predictive nature of the theory

Rapid Calculation of Electron Scattering Factors

The phase amplitude method is used to reduce the radial Schrödinger equation to two separate differential equations, one for the phase and one for the amplitude. These functions are both smooth as opposed to the rapidly oscillating solution of the radial Schrödinger equation for electron energies in the kilovolt range. The partial-wave phase shifts were obtained rapidly by integrating the differential equations for the phase and amplitude numerically. Hartree-Fock and Thomas-Fermi-Dirac fields were used in the calculation. Results for argon and uranium are given in order to compare with previous results. It was found that the WKBJ approximation to the partial-wave phase shift is a good approximation for the energies used in electron diffraction. This rapid method of computing electron-scattering factors will make routine analysis of electron diffraction data more rapid as well as more exact

Survival Probability in Dissociative Attachment

The survival probability in dissociative attachment is investigated with special attention to the (e, H2 ) system. It is shown that the simple expression for the dissociative-attachment cross section, as given by the product of a capture cross section and a survival probability, is equivalent to the s -wave approximation for the g → g dissociative attachment. This expression, however, does not constitute an approximation for the g → u dissociative attachment, since the parity of the initial rotational states of H2 is always opposite to that of the relative angular momentum states of H and H- and the capture cross section appearing in the simple expression is identically zero. According to the Kronig selection rules and the symmetry requirements, only odd partial waves of the incident electron may contribute to the g → u dissociative attachment in the (e, H2 ) system. Consequently, the lowest contributing partial wave is not the s wave but the p wave of the incident electron. This, then, destroys the simple proportional dependence of the cross section on the survival probability. However, one may still express the cross section as a sum of products of a capture cross section and a survival probability for the various contributing angular momentum states of the constituent nuclei. The dependence of the survival probability on the angular momentum states of the constituent nuclei is also investigated for the (e, H2) system. It is observed that for the g → u dissociative attachment the survival probability depends strongly on the angular momentum states. This arises because the g → u dissociative attachment occurs at such a low energy that variations in the centrifugal barrier become comparable with the breakup energy of the constituent atoms. This then suggests a strong temperature dependence for the g → u dissociative attachment in the (e, H2) system. For the g → g dissociative attachment, such dependence is much weaker since here the process significant at a somewhat higher energy and the variation in centrifugal energy is overshadowed by the larger break-up energy of the constituent atoms. The validity of the commonly adopted approximation for survival probability (involving the auto-ionization width and relative velocity of the nuclei) is also examined

Associative Detachment: H+Hˉ→₂\u3csup\u3e*\u3c/sup\u3e+e

The process of associative detachment in the (H,H-) collision system is investigated at energies below 12 eV. In this energy region, the interaction potential between H and H- has recently been determined. The energy dependence of the cross section is calculated with explicit allowance for the production of hot hydrogen molecules. It is observed that associative detachment provides a possible mechanism for generating an inverted population of the residual molecule such as H2

Eikonal Distorted-Wave Calculation for the Excitation of H by He

The eikonal distorted-wave Born approximation developed recently by Chen, Joachain, and Watson is applied to hydrogen excitation by helium impact in the intermediate-energy range. The differential and total cross sections for the excitation of the hydrogen atom to the 2s, 2p±, or 2p0 state by helium impact are presented. These results are compared to experiment and previous calculations. The differential cross section for the excitation of hydrogen to the 2s state compares well with the experimental data of Thomas and Sauers in shape and slope, but has a discrepancy in magnitude

Eikonal Approximation Applied to Atom-Atom Excitation at Intermediate Energies: Excitation of H by H

The eikonal distorted-wave Born approximation (DWBA) developed recently by Chen, Joachain, and Watson is applied to atom-atom excitation in the intermediate energy range. In this paper the excitation of a hydrogen atom to the 2s, 2p±, or 2p0 state by hydrogen impact is considered. Differential cross sections are presented. Total cross sections are presented and compared to previous calculations. It is shown that the eikonal DWBA results for the total cross section approach the two-state distortion-approximation results in the limit of high energy and very-small-angle scattering

Theory of the Effect of Temperature on the Electron Diffraction Patterns of Diatomic Molecules

The effect of temperature on the electron diffraction pattern of a diatomic molecule is considered from the standpoint of the simple kinematic scattering theory utilizing a quartic vibrational potential. The potential is obtained by an expansion of ħ2J( J+1)/2μr2+D exp[-2a(r-re)]-2D exp[-a(r-re)] about its minimum value r0. The second-order wavefunction for the nth vibrational and 7th rotational state of the system has been obtained, and expressions for the electron diffraction quantities rg, le 2, and M (s) have been computed. General results for the quantity M (s) utilizing the approximate eigenfunctions of the complete Morse potential and incorporating an approximate treatment of the effect of centrifugal stretching are also presented. Explicit expressions for M (s) for the first three vibrational states as derived by this treatment are given. Appropriate sums over all the vibrational and rotational states have been carried out to obtain the temperature dependence for the above quantities. Estimates of the effect of temperature on the parameters rg and Ie 2 at 300° and 1500°K for representative diatomic molecules are given

Interaction Potential between the Ground States of H and Hˉ

An investigation of the interaction potential for H and H- in both ungerade and gerade modes is carried out by a semiempirical method in which the recently observed isotope effect in dissociative attachment of electrons to hydrogen molecules is used. The interaction obtained is complex, and the imaginary parts of the interaction account for electron emissions during the course of the interaction. A comparison of the present result with other calculations is presented. The isotope effect in dissociative attachment is also discussed. It is shown that the ratios of the survival probabilities alone do not provide an adequate approximation for the isotope effect

Doppler Shift in Frequency in the Transport of Electromagnetic Waves through an Underdense Plasma

In an earlier publication, the validity of the radiation transport theory was studied for the calculation of multiple scattering of electromagnetic waves by a turbulent plasma. In the present paper, we extend the transport theory to include a description of the Doppler shift in frequency caused by electron motion

Theoretical Treatment of Electron-Impact Ionization of Molecules

There is currently no reliable theory for calculating the fully differential cross section (FDCS) for low energy electron-impact ionization of molecules. All of the existing experimental FDCS data represent averages over all molecular orientations and this can be an important theoretical complication for calculations that are computer intensive. We have found that using an averaged molecular orbital is an accurate approximation for ionization of ground states. In this paper, we will describe the approximation, discuss its expected range of validity and show some FDCS results using the approximation for ionization of H2 and N