Bethe cross sections for the excitation of Na-like ions to the $3{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$, $3{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$, $4{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$, and $4{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ states from the ground state are computed from the relativistic Hartree-Fock wave functions. As the nuclear charge is increased, excitation cross sections to the ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ states are affected far more by relativistic effects than those to the ${}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ states. The asymptotic ionization cross sections for the neutral Na atom and ${\mathrm{Fe}}^{15+}$ ion are computed from a sum rule, i.e., by subtracting the sum of discrete excitation cross sections from the total inelastic-scattering cross section obtained from the sum rule. The ionization cross sections thus obtained are ${\sigma }_{\mathrm{ion}}\left(\mathrm{Na}\right)={\beta }^{-2\mathrm{}}\left(2.51\right\{\ln \left[\frac{{\beta }^2}{(1-{\beta }^2)}\right]-{\beta }^2\}+ 26.3)\times {10}^{-20\mathrm{}} {\mathrm{cm}}^2,$ ${\sigma }_{\mathrm{ion}}\left({\mathrm{Fe}}^{15+}\right)={\beta }^{-2\mathrm{}}\left(0.209\mathrm{} \right\{\ln \left[\frac{{\beta }^2}{(1-{\beta }^2)}\right]-{\beta }^2\}+1.64)\times {10}^{-20\mathrm{}} {\mathrm{cm}}^2,$ where $\beta$ is the incident electron or proton speed divided by that of light. The cross section for Na is in agreement with that calculated by McGuire, but not with the electron-impact experiment by McFarland and Kinney. The ionization cross section for ${\mathrm{Fe}}^{15+}$ is a factor of 2 to 3 larger than the Coulomb-Born results by Rudge and Schwartz and by Bely in the asymptotic region.

Differential cross sections for 25-, 50-, and 100-keV-proton excitation of helium to the $n=2\mathrm{}$ level have been determined for center-of-mass scattering angles from 0 to 1.2 mrad. The cross sections were obtained from an analysis of the angular distribution of the scattered protons which had lost an energy corresponding to the excitation of the helium target to its $n=2\mathrm{}$ level. The differential cross section is very sharply peaked in the forward direction and decreases by a factor of 45 in 1.0 mrad at 25 keV and by a factor of 650 in 1.0 mrad at 100 keV. The data are in excellent agreement with a recent multistate eikonal calculation.

We study the off-shell Jost function $f(k, q)$, introduced by Fuda, for the Coulomb, the Hulthén, and two modified Eckart potentials. A simple closed expression for the $l=0\mathrm{}$ Coulomb off-shell Jost function has been obtained. This function is discontinuous at $q=k$. Its on-shell limiting behavior is given by the singular factor ${\mathrm{}(q-k)\mathrm{}}^{-i\gamma }$, where $\gamma$ is the Sommerfeld parameter. We also discuss the off-shell Jost solution $f(k, q, r)$, which is an off-shell generalization of the Jost solution $f(k, r)$. We consider the Hulthén potential as a screened Coulomb potential, let the screening parameter $a$ go to infinity, and derive the limiting behavior of the Jost solution, the Jost function, the off-shell Jost function, and the half-shell $T$ matrix for the Hulthén potential as $a\to \infty$. We obtain discontinuities given by the singular factor $a^{i\gamma }$. For comparison, we introduce two modifications of an Eckart potential which can be considered to be a screened $r^{-2\mathrm{}}$ potential and derive a number of limiting relations in analogy to those for the Hulthén-Coulomb pair of potentials.

A microwave-afterglow mass-spectrometer apparatus has been used to determine the dependence on electron temperature $T_e$ of the recombination coefficients $\alpha$ of the hydronium-series ions ${\mathrm{H}}_3{\mathrm{O}}^{+}·{\left({\mathrm{H}}_2\mathrm{O}\right)}_n$. For $n=1-3\mathrm{}$, we find $\alpha \left({37}^{+}\right)=(2.5\mathrm{}\pm 0.5)\times {10}^{-6\mathrm{}} {\left[\frac{300}{T_e} \right(\mathrm{K}\left)\right]}^{0.08}$, $\alpha \left({55}^{+}\right)=(3.0\mathrm{}\pm 0.6)\times {10}^{-6\mathrm{}} {\left[\frac{300}{T_e} \right(\mathrm{K}\left)\right]}^{0.08}$, and $\alpha \left({73}^{+}\right)=(3.6\mathrm{}\pm 0.7)\times {10}^{-6\mathrm{}} {\left[\frac{300}{T_e} \right(\mathrm{K}\left)\right]}^{0.00}$ ${\mathrm{cm}}^3$/sec over the range $300-400 \mathrm{K}\le T_e\le 6000-8000 \mathrm{K}$ and $T_{\mathrm{gas}}=T_{+}=300-400\mathrm{}$ K. For $n=4\mathrm{} \mathrm{and} 5$, $\alpha \left({91}^{+}\right)\simeq \alpha \left({109}^{+}\right)\sim 5\times {10}^{-6\mathrm{}}$ ${\mathrm{cm}}^3$/sec, with no apparent dependence on $T_e$. These results for the higher hydrates differ somewhat from those obtained by Leu, Biondi, and Johnsen. The very weak dependence of $\alpha$ on $T_e$ is quite similar to the behavior noted for the $\mathrm{N}{{\mathrm{H}}_4}^{+}·{\left(\mathrm{N}{\mathrm{H}}_3\right)}_n$ cluster ions.

Energy partitioning among accessible product excited states has been spectroscopically studied in a beam apparatus for ${\mathrm{He}}^{+}$ and ${\mathrm{H}}^{+}$ collisions with Na and K atoms in the kinetic energy range 10-800 eV. The dominant observable inelastic channel in all collision systems was found to be collision-induced excitation yielding resonance radiation. While excited states of ${\mathrm{K}}^{+}$ formed by charge exchange were also observed, no analogous ${\mathrm{Na}}^{+}$ emissions were detected; the absence of ${\mathrm{Na}}^{+}$ emissions is attributed to inefficient energy conversion. Comparison of data from one-electron and two-electron processes supports the propensity rule which states that the former are generally favored.

The Glauber amplitude for rotational excitation of molecules by electron scattering for the pure quadrupole anisotropic potential is set up. Explicit expressions are presented both for the Glauber amplitude which is reduced to a two-dimensional integral and for a series-expansion amplitude which is reduced to a singledimensional integral. The selection rules for the Glauber amplitude are given and numerical examples of differential cross sections are presented for ${\mathrm{N}}_2$ targets.

Absolute cross sections for the single ionization of ${\mathrm{Rb}}^{+}$ ions by electron impact have been measured as a function of electron energy from below threshold to approximately 2000 eV. Measurements were made in a crossed-beam facility having modulated beams. Numerous consistency checks were performed to evaluate possible sources of experimental error. Comparisons were made with other available results.

The coupling between electron spin and collisional angular momentum has been studied for ${\mathrm{He}}^{++}$-He, Ne, ${\mathrm{H}}_2$, and ${\mathrm{O}}_2$ collisions (4-600 eV) by observing radiation resulting from double electron capture into excited states of Hei and comparing the triplet and singlet emissions. The two-electron targets provide a rigid test of the spin-conservation rule, but of these only ${\mathrm{H}}_2$ yields data in accord with the rule. The apparently anomalous ${\mathrm{He}}^{++}$-He results are attributed to the domination of short-range effects. These short-range effects are not restricted to double-electron capture, but can apply in any process which involves spin flip.

The information-theoretic maximal-entropy procedure for the analysis of collision processes is derived as a consequence of the dynamics, be they quantal or classical. The method centers attention on the minimal number of operators (the "dynamic constraints") whose expectation values are both necessary and sufficient to completely characterize the collision dynamics. For a given Hamiltonian and initial state, the constraints required to obtain an exact solution of the equations of motion are determined by a purely algebraic procedure. It is furthermore found possible to derive equations of motion for the conjugate Lagrange parameters. Immediate applications are noted, e.g., a family of similar reactions is shown to have a common set of dynamic constraints and simple illustrative applications are provided. The determination of the scattering matrix is discussed, with examples. The general formalism consists in solving the scattering problem in two stages. The first is purely algebraic. At the end of this stage one obtains the functional form of, say, the scattering matrix or of the density matrix after the collision expressed in terms of parameters whose number equals the number of dynamic constraints. The end result of this algebraic stage suffices to analyze the scattering pattern for any initial state. The second stage is the predictive procedure. Explicit coupled first-order nonlinear differential equations are obtained for the parameters.

Three different measurements on the structure of the ${\mathrm{H}}_3^{+}$ molecular ion are reported. The measurements all make use of a new technique—the foil-induced dissociation of a fast molecular-ion beam. It is shown that the structure is equilaterally triangular in shape. The most probable length of side of the triangle is determined by the three measurements to be 0.97 ± 0.03 Å, 0.95 ± 0.06 Å, and 1.2 ± 0.2 Å, respectively.

We have performed Dirac-Fock calculations for a variety of muonic atoms. The muon is explicitly included in the self-consistent field theory, and electron exchange is treated exactly. Wave functions and energies are obtained for a variety of sample systems ranging from light to heavy ions, using finite models of the nucleus. The problem of angular momentum coupling schemes for muonic atoms is discussed. Results presented include comparison of Dirac-Fock and Dirac-Slater models, the effect of the inclusion of the Breit operator and the Lamb shift as perturbations, contributions of electron screening and relaxation to muon transition energies, and the dependence of screening on muonic angular momentum.

Approximate solutions to the time-dependent Schrödinger equation can be sought in terms of time-dependent parameters. In this work, a reasonable definition of the "best" values for these parameters is given by requiring that the time integral of the deviation of the approximate solution from the exact solution be minimized. A procedure for specifically evaluating the parameters to optimize the approximate solution is given in terms of equations analogous to Hamilton's equations of classical mechanics, which produce a minimum-deviation integral in analogy to Hamilton's principle. A comparison of this technique with previous approaches is made, both in terms of general principles, and in terms of a simple hypothetical example of a system subjected to a time-dependent perturbation.

A variationally optimized effective-potential model is used for calculation of the Compton profiles for atomic Ne, Ar, and Kr. The profiles were calculated from the one-electron wave functions obtained from the optimized potential by using a novel method for calculating Fourier transforms. For Ne, the agreement with Hartree-Fock results is excellent; overall the agreement is better than that with other local potential results.

A simple analytic expression for the Coulomb-Glauber-Ochkur amplitudes is derived for the exchange scattering of electrons from hydrogenic ions. The exchange amplitude is combined with the direct Coulomb-Glauber amplitude, derived by Thomas and Franco, to calculate the exchange-corrected cross section for the process $e+{\mathrm{He}}^{+}\mathrm{}\left(1s\right)\mathrm{}\to e+{\mathrm{He}}^{+}\mathrm{}\left(2s\right)\mathrm{}$. The results are compared with other theoretical calculations and experimental data.

The triple-differential cross section for electron-impact ionization of argon has been investigated for the primary electron energies near 100 eV and scattering angle 15°. The in-plane and out-of-plane measurements show that the forward lobe has a true minimum in the full three-dimensional sense when the ejected electron energy is 5 eV. However, such a minimum is not observed when the ejected electron energy is 20 eV. The cross section has much more structure than that of helium. No simple symmetry has been found common to all the cases for argon.

The nuclear deorientation of ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$(5/$2_1^{+}$, 197 keV) has been measured for highly stripped fluorine ions recoiling in He, ${\mathrm{N}}_2$, Ne, Ar, Kr, and Xe at 35 MeV and in ${\mathrm{N}}_2$ and Ar at 55 MeV at gas pressures between ${10}^{-3\mathrm{}}$ and 100 Torr. The nuclear alignment was found to decay quasiexponentially. The extracted nuclear deorientation cross sections are interpreted in a microscopic ion-atom collision model. The dominance of electronic charge-exchange transitions in producing the ionic states of strong hyperfine interactions is demonstrated. Collisional deexcitation of metastable states in heliumlike F is shown to contribute significantly.

Absolute total cross sections for electron scattering from He have been measured over the energy range from 1 to 50 eV with an accuracy of 3% or better. A novel method employing time-of-flight monochromatization and energy determination of electrons from a pulsed secondary-emission source in transmission through a gas cell has been used. This method is contrasted with conventional ones and a comprehensive error discussion is given. The reported results are then compared to existing experimental and theoretical results. Discrepancies in existing experimental data are resolved and good agreement is obtained with some recent theoretical results.