The probability for either exciting or ionizing an electron from a given atomic orbital as the result of a sudden vacancy in one of the atomic shells, such as might occur with photoionization, has been calculated through the use of the sudden approximation. Calculations were made for each of the subshells of neon, argon, krypton, and xenon as a function of the location of the initial vacancy. The calculations were based on relativistic Hartree-Fock-Slater wave functions. The results were generalized in terms of the change in effective charge. For example, electron shake-off in the valence shell was found to be nearly independent of the location of the initial core vacancy, increasing slightly as one goes to the lower principal quantum numbers. The ionization potentials were also found to be nearly independent of the location of the core vacancy. The results of the electron-shake-off calculations were also used to obtain an evaluation of the relaxation energy arising from the promotion of a single vacancy, and compared with values obtained from binding-energy calculations. Results of the electron-shake-off calculations are applicable to any process that leads to a sudden creation of a vacancy in an atom. However, particular emphasis is given to photoelectron spectroscopy in discussing the results.

The Kohn-Feshbach variational method in scattering is simplified such that the most difficult integrals one encounters are completely avoided. This greatly enhances the feasibility of the variational method in multichannel problems. Two model calculations are presented to illustrate this method. Excellent triplet $p$-wave phase shifts are obtained for electron-hydrogen elastic scattering.

Differential and total cross sections are calculated for elastic scattering and also for rotational and vibrational excitation when an atom and a diatomic molecule collide at keV energies. Explicit calculations for vibrational excitation are here limited to the first vibration state only, although the method can easily be extended to higher vibrational states. The results are valid for small-angle scattering at keV energies, for which the motion of the nuclei can be treated in the Born approximation, while the electronic motion is treated in the adiabatic approximation. The cross sections are obtained as analytic expressions, the exact solutions which follow from a realistic potential form with several adjustable parameters. These parameters can be adjusted to fit the proposed potential form to the potential appropriate to the desired collision reactants. The potential form includes the long-range $R^{-6\mathrm{}}$ van der Waals interaction as well as the steep repulsive potential at short ranges and is a function also of the orientation angle between the molecular axis and the incident direction. Hydrogen-atom-hydrogen-molecule scattering is presented as an example. The potential for three hydrogen atoms is obtained by adjusting the parameters in the analytical expression for the potential to the ab initio calculation of the ${\mathrm{H}}_3$ energy surface of Shavitt et al., and numerical values for the differential and total cross sections are obtained. In the case of other collision reactants, for which no ab initio energy-surface calculations are available, the results of the present work conversely permit the parameters (and, therefore, the energy surface) to be determined by experimental cross-section measurements at keV energies.

Differential cross sections are derived from a multistate impact-parameter treatment of heavy-particle collisions. Various approximations are suggested and their relationship with previous expressions are discussed. The equivalence between the differential cross sections in the impact-parameter and wave versions of the Born approximation is established for elastic and inelastic scattering and is illustrated explicitly for the $1s$, $2s$, $2p_0$, and $2p_{\pm 1}$ excitations of atomic hydrogen by proton and hydrogen-atom impact.

A semiquantal description of neutral-neutral collisions is applied to the examination of electron loss from $\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ moving in the rare gases He, Ne, Ar, Kr, and Xe. Cross sections for ionization of $\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ are calculated for relative speeds $v$ in the range $0.2\le v\le 20$ a.u. Simultaneous transitions in both target and projectile atoms are acknowledged and the relative contribution that arises from collisions in which the electronic state of the rare-gas atom remains unaffected increases from 37% for He to 95% for Xe. Good agreement with previous Born-wave results is obtained.

Excitation of helium atoms by electron impact is studied for intermediate- and high-energy electrons. Calculations of the differential cross sections for the $1S-2{}_{}{}^1{}_{}{}^{}S$ transition are made by use of a one-dimensional integral representation of the scattering amplitude obtained in the Glauber approximation. Comparisons with the Born approximation and with measurements between 22 and 600 eV are presented. Several sets of ground-state and excited-state wave functions are used. The results are a distinct improvement over the Born approximation at all energies considered and are in good agreement with the measurements above $\sim 90$ eV. At lower energies the Glauber predictions reproduce the qualitative features of the data. The results also show that the more-general one-dimensional integral expression for charged-particle—atom scattering amplitudes, derived earlier, can be used to perform calculations with relative ease.

A method is presented for improving the phase of the semiclassical radial functions obtained from the average approximation. It yields improved phases for problems possessing localized regions of strong coupling, for example, in curve-crossing problems. For problems without such regions, the method yields essentially the same results as the average approximation. Results are presented for atomic-scattering situations in both close-coupling and distorted-wave theory.

Using the "equivalent-quadrature" relationship between diagonalization of the $s$-wave kinetic energy $H^0$ in a Laguerre-type basis and Chebyschev quadrature of the second kind, a procedure is given by which potential-scattering phase shifts may be constructed from approximation to the Fredholm determinant constructed using only square-integrable ($L^2$) functions. For the problem of electron-hydrogen scattering in the static approximation, highly accurate phase shifts are obtained over a continuous range of energies from a single major computational step.

High-resolution studies of aluminum $K\alpha$ x rays produced by O, F, and Cl beams at beams energies ≳ 1 MeV/amu have been performed with a crystal spectrometer. Fluorescence yields are calculated for the various single $K$-shell, multiple $L$-shell vacancy configurations. A simple model of the ionization process has been assumed that allows determination of average $2s$ and $2p$ ionization probabilities from the experimental x-ray yields using the calculated fluorescence yields.

A number of peaks appear in the spectrum of electrons produced by collisions of ${\mathrm{Cl}}^{-}$ ions with helium- and hydrogen-gas targets. These features can be attributed to doubly excited autodetaching states of ${\mathrm{Cl}}^{-}$. Assignment of approximate electron configurations is possible for states appearing at 8.53, 9.15, and 9.97 eV, but ambiguities remain in the assignments for the other states lying between 10.47 and 12.44 eV.

An investigation of doubly excited states of the negative chlorine ion using the method of configuration interaction has located several Feshbach autodetaching resonances in the energy region 8.5-12.6 eV. Dominant two-particle excitations considered include $3p^2\to 4s^2$, $4s4p$, $4p^2$, and $5s^2$. The results obtained are useful in interpreting the recent experimental structure observed in the electron spectrum resulting from collisions of ground-state ${\mathrm{Cl}}^{-}$ ions with helium- and hydrogen-gas targets.

Bethe-Goldstone continuum equations for the scattering of electrons from helium are solved variationally in the energy range between the $n=2\mathrm{}$ and $n=3\mathrm{}$ thresholds. Polarization and correlation effects are included in the calculations by allowing for virtual excitation of the $2s$ electron. Shape resonances are found above the $2{}_{}{}^3{}_{}{}^{}S$ threshold, in substantial agreement with close-coupling calculations of Burke, Cooper, and Ormonde. Structures observed immediately below the $3{}_{}{}^3{}_{}{}^{}S$ threshold in experimental cross sections for metastable formation are attributed to several Feshbach resonances whose energies and widths are computed. Cross sections are presented for elastic and inelastic scattering involving the ground state and $n=2\mathrm{}$ states of helium. Cusp behavior, expected at various inelastic thresholds and found in the variational calculations, accounts for several prominent structural features in the scattering cross sections. The present computed results are compared with previous theoretical studies and, wherever possible, with experimental data.

The formation and decay of excited ${\mathrm{Hg}}_2$ molecules formed in Hg-${\mathrm{N}}_2$ mixtures irradiated with 2537-Å Hg resonance radiation, has been investigated using methods of delayed coincidences. The vapor-gas mixtures contained in a quartz fluorescence cell were excited with pulses of light and the resulting decay spectra of the 3350- and 4850-Å molecular fluorescent bands were studied in relation to ${\mathrm{N}}_2$ pressure. Both bands exhibited identical decay patterns which included a slower and a faster component, the latter being identical with that for the decay of the 2537-Å afterglow. Analysis of the decays indicates that the molecular ${}_{}{}^3{}_{}{}^{}1_u^{}{}_{}{}^{}$ state (which is associated with the 3350-Å band) is formed in a $\mathrm{Hg}\left({}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}\right)+\mathrm{Hg}\left({}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\right)+{\mathrm{N}}_2$ triple collision and the ${}_{}{}^3{}_{}{}^{}0_u^{-}{}_{}{}^{}$ state (associated with the 4850-Å band) is produced by subsequent molecular collisions of ${\mathrm{Hg}}_2\left({}_{}{}^3{}_{}{}^{}1_u^{}{}_{}{}^{}\right)$ with ${\mathrm{N}}_2$. The experiments yielded, in addition to the lower limit of the lifetime $\tau \left({}_{}{}^3{}_{}{}^{}0_u^{-}{}_{}{}^{}\right)>\mathrm{}4.5\mathrm{}$ msec, the following total cross sections and rate constant: $Q({}_{}{}^3{}_{}{}^{}0_u^{-}{}_{}{}^{}\to {}_{}{}^3{}_{}{}^{}1_u^{}{}_{}{}^{})=5.5\mathrm{}\times {10}^{-21\mathrm{}}$ ${\mathrm{cm}}^2$; $Q({}_{}{}^3{}_{}{}^{}1_u^{}{}_{}{}^{}\to {}_{}{}^3{}_{}{}^{}0_u^{-}{}_{}{}^{})\approx 3\times {10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$; $k({}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}\to {}_{}{}^3{}_{}{}^{}1_u^{}{}_{}{}^{})\approx {10}^{-30\mathrm{}}$ ${\left({\mathrm{cm}}^{-3\mathrm{}}\right)}^{-2\mathrm{}}$ ${\sec }^{-1\mathrm{}}$.

Data obtained as energy-loss spectra at angles from 0 to 7.3×${10}^{-3\mathrm{}}$ rad (c.m.) with typical energy-loss resolution of 0.7 eV and angular resolution of 2×${10}^{-3\mathrm{}}$ rad (c.m.) were used to calculate average differential cross sections ${〈\frac{d\sigma }{d\Omega }〉}_{\mathrm{av}}$ for elastic scattering, direct excitation of the individual $\mathrm{He}\mathrm{}(n=2\mathrm{})\mathrm{}$ states, and direct excitation of the ${\mathrm{He}}^{+}\mathrm{}(n=2\mathrm{})\mathrm{}$ states. The total cross section for excitation of the $\mathrm{He}\mathrm{}(n=2\mathrm{})\mathrm{}$ states obtained by integrating the differential cross sections was found to be 20×${10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$ at 25 keV (lab) decreasing to 7×${10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$ at 140 keV. At incident lab energies below 100 keV the $\mathrm{He}\left(2\mathrm{}{}_{}{}^2{}_{}{}^{}S\right)$ and $\mathrm{He}\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}P\right)$ states dominate the $\mathrm{He}\mathrm{}(n=2\mathrm{})\mathrm{}$ structure at angles close to zero, while the $\mathrm{He}\left(2\mathrm{}{}_{}{}^1{}_{}{}^{}P\right)$ state dominates at larger angles. The contribution of the $\mathrm{He}\left(2\mathrm{}{}_{}{}^1{}_{}{}^{}S\right)$ state remains below 25% at all angles and energies.

The results of close-coupling calculations for electron-helium scattering at incident electron energies between 40 and 70 eV are reported. The calculations were carried out by including in the expansion terms representing both the singly and doubly excited electronic states of the target. The results confirm the suggestion by Fano and Cooper that the narrow resonances at about 57.2 and 58.3 eV can be associated with formation of autoionizing states of ${\mathrm{He}}^{-}$ with dominant configurations $\left(2\mathrm{}{s}^{2}2P\right){}_{}{}^2{}_{}{}^{}p_{}^o{}_{}{}^{}$ and $\left(2s2p^2\right){}_{}{}^2{}_{}{}^{}D_{}^e{}_{}{}^{}$, respectively. The results for total excitation cross sections of the $2{}_{}{}^3{}_{}{}^{}S$ state agree qualitatively with recent measurements, but a discrepancy of a factor of 2 between theory and experiment remains at this time unexplained. The calculated total cross section for scattering by the gound state agrees quite well with experiment. The effect of the resonances on the total cross section and their possible correlation with other resonances observed in electron-helium excitation functions is discussed.

The evolution of electron density, electron temperature, and population of excited states is measured in a cesium afterglow (pressure range ${10}^{-3\mathrm{}}$-2 × ${10}^{-2\mathrm{}}$ torr). These are compared with the predictions of a collisional-radiative model. For electron densities between ${10}^{13}$ and ${10}^{11}$ ${\mathrm{cm}}^{-3\mathrm{}}$ and electron temperatures in the range 700-2000°K, the recombination coefficient is found to be in good agreement with theoretical values. It is proportional to ${T_e}^{-\gamma }$ with $\gamma =4.2\mathrm{}\pm 0.4$. The model is shown also to predict accurately the evolution of the electron temperature and excited-state populations. In the late afterglow a change in the ambipolar-diffusion coefficient is observed and is interpreted to be due to a change in the majority ion.

In the enormous magnetic fields anticipated at the surface of neutron stars, the geometry of a scattering event involving charged particles is drastically altered. A number of familiar concepts, including the cross section, and collision frequency, are redefined in consequence following a one-dimensional multichannel approach. Separate collision frequencies are defined for each Landau level, displaying a strong oscillatory behavior as a function of the electron's energy. For electrons energetically confined in the lowest Landau orbital only backward-scattering events contribute to the collision frequency. New analytic expressions are obtained for the Coulomb matrix elements in the magnetic field. The results are used to study the effect of electron-ion scattering on the properties of electrons occupying low-lying Landau levels.

Estimates of the total ionization and multi-ionization high-energy-electron collision cross sections have been obtained for krypton and its ground-state ions. The total cross sections were computed within the framework of the Bethe-Born high-energy-approximation theory using the semiclassical projection-operator technique of Hahn and Watson and the independent-particle model for atoms due to Green, Sellin, and Zachor. Both direct continuum ionization and inner-shell excitation followed by Auger ionizing transitions were taken into account. Multiple-ionization cross sections were then estimated using experimental information on electron emission following ejection of inner-shell electrons in neutral krypton and a simplified model of Auger cascading in ions. The results, applied to a calculation of the cumulative ionization produced by a relativistic electron ring beam interacting with a krypton pressure pulse, indicate that Auger processes have a significant influence in speeding up ionization rates in such a system.

The method presented in the first paper of this series for computing distributions in steady-state effusive flows was applied to beam-scattering chambers of especially simple geometry having identical long, narrow slits of negligible channel length. The results are presented as correction factors $\alpha$ which, when multiplied by the chamber length, give the effective length of scattering path through an attenuating medium of uniform density equal to that in the scattering-gas source. Predictions of the calculations compare well with scattering measurements made with a chamber of variable length.

The dynamics of an infinite one-dimensional system of hard rods is generalized to include the effects of a random background. Each rod follows a trajectory which is described by a generalized random function and when two rods collide they interchange velocities (and trajectories). An exact solution is obtained for the distribution $f_s(x,v,\frac{t}{v^{\prime }})$ which is the probability of finding a particle at $x$ with velocity $v$ at time $t$ that was at $x=0\mathrm{}$ with velocity $v^{\prime }$ at $t=0\mathrm{}$. The most interesting result is that in the long-time limit $p(x,t)\mathrm{}$, which is the probability of finding a particle at $x$ at time $t$ that was at $x=0\mathrm{}$ at $t=0\mathrm{}$, is of the form $t^{-\frac{1}{4}}\exp (-\frac{x^2}{t^{\frac{1}{2}}})$. Thus, the spatial distribution does not become Gaussian and Fick's law is not valid. It is suggested that this qualitative behavior might be expected whenever single-file effects become important and that it is not dependent on the details of the one-dimensional hard-rod collisions which have been used in the derivation.