Using the relative-flow technique elastic differential cross sections ${\sigma }_{\theta }\left(\mathrm{Ar}\mathrm{or}\mathrm{Kr}\right)$ for Ar and Kr relative to ${\sigma }_{\theta }\left(\mathrm{He}\right)$ have been measured at impact energies of 3, 5, 7.5, 10, 15, 20, 30, 50, 75, and 100 eV. The angular range covered is from 20° to 135°. These ratios have been multiplied by the recently measured values of ${\sigma }_{\theta }\left(\mathrm{He}\right)$ to obtain ${\sigma }_{\theta }\left(\mathrm{Ar}\mathrm{or}\mathrm{Kr}\right)$. The differential cross section curves for both Ar and Kr show deep minima. The positions of these minima have been obtained with an accuracy of ±2°. The cross sections in the angular regions lying between 0° and 20° and 135° and 180° could not be measured owing to instrumental limitations. In these regions estimates of the shapes of differential cross section (DCS) curves have been made by fitting the data obtained from 20° to 135° with a phase-shift analysis, while the normalization to the absolute scale was obtained by normalizing these fits to the relative flow measurements. From these estimates and the measured values of the differential cross section, integral and momentum-transfer cross sections have been obtained. The error limits for the differential, integral, and momentum-transfer cross sections have been estimated as 20, 30, and 30%, respectively.

Differential, integral, and momentum-transfer cross sections have been determined for the excitation of the 24 lowest electronic states of Kr (some of the transitions are unresolved). The inelastic-scattering cross sections were normalized to the absolute scale with the help of the elastic-scattering differential cross sections (DCS's) which in turn were normalized with respect to absolute He DCS's. The impact energies were 15, 20, 30, 50, and 100 eV and the DCS's were obtained over the range of 5°-135° scattering angles. The error limits associated with the differential, integral, and momentum-transfer cross sections have been estimated at 25%, 38%, and 46%, respectively.

Normalized, absolute differential cross sections have been measured for electron-impact excitation of 23 individual or composite electronic states of argon lying within 14.30 eV of the ground state. Incident electron energies are 16, 20, 30, 50, and 100 eV, and the range of scattering angles 5°-138°. The absolute differential cross sections are extrapolated to 0° and 180° and integrated to yield integral and inelastic-scattering momentum-transfer cross sections for the excitation processes. Errors in the differential cross section are grouped into the classes $A\mathrm{}(26\%)\mathrm{}$, $B\mathrm{}(31\%)\mathrm{}$, and $C\mathrm{}(45\%)\mathrm{}$, with slightly larger errors given to the integrated quantities owing to extrapolation uncertainties. Comparisons of the present data are made with previous measurements where available, and with results of several distorted-wave and Born calculations. Differential magnetic sublevel cross sections for the ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ and ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ levels are also obtained at 50-eV incident energy and 5° scattering angle using previously measured $\lambda$ parameters.

First-order many-body theory has been used to calculate the differential and integral cross sections for electron-impact excitation of the argon atom to the $4{}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}$, $4{}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$, $4{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$, and $4{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ electronic states, for incident electron energies of 16, 20, 30, 50, and 80.4 eV. The resulting cross sections are in good agreement with recent results extracted from electron energy-loss measurements on argon. Detailed calculations show that spin-orbit coupling must be included in the ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ wave function in order to describe the electron-impact excitation of the state properly.

Total excitation cross sections for electrons scattering from atomic hydrogen are calculated by using a complex optical potential. Distorted-wave propagators as well as free-particle propagators are used in computing the optical potential. It is found that using an attractive potential to generate the propagator results in poorer agreement with experiment than using a free-particle propagator. The effect of neglecting coupling between excited target states in computing the optical potential is also studied. It is concluded that it necessary to include coupling between excited target states if the calculation is to be reliable.

Born-approximation calculations of various inelastic-scattering cross sections for collisions between ${\mathrm{U}}^{q+}$ ($q=1, 2, \mathrm{and} 4$) ions and Li atoms and ions are presented. The energies considered are in the 10-100-MeV/amu regime, with an emphasis on providing results useful in assessing the importance of various phenomena in heavy-ion, inertial-confinement-fusion reactor concepts for the case of ${\mathrm{U}}^{1+}$ beams of 10-20 GeV. Estimates of the ${\mathrm{U}}^{q+}$ electron-loss cross sections are given for collisions with lithium in all charge states; order-of-magnitude differences between Li atoms and ions are predicted. Calculations of the cross sections for the ionization of Li atoms and ions due to the impact of fast ${\mathrm{U}}^{q+}$ ions are also given. The lithium discrete-state and ionization contributions to the sum-rule asymptotic cross sections are computed for the cases of ${\mathrm{Li}}^0$ and ${\mathrm{Li}}^{2+}$. Ionization is the dominate contributor (> 50%) for these collisions, in contrast to the case of proton impact at similar speeds (≲ 10% for ${\mathrm{Li}}^0$). We also estimate the mean energies of the electrons produced in these ionizing collisions and obtain results more than an order of magnitude larger than in the case of proton impact.

The semiclassical impact-parameter method is extended to study the electronic excitation of molecules by electron impact. The formalism describes the molecular electrons quantum mechanically but treats the collision classically using straight-line trajectories. The expression for the integrated cross section satisfies reciprocity. The method is applicable to spin-allowed transitions at intermediate and high impact energies where electron exchange is negligible. Theoretical excitation cross sections are presented for the $X{{}_{}{}^1{}_{}{}^{}\Sigma _g^{}{}_{}{}^{}}^{+}\to B{{}_{}{}^1{}_{}{}^{}\Sigma _u^{}{}_{}{}^{}}^{+}$ transition in ${\mathrm{H}}_2$, $X{{}_{}{}^1{}_{}{}^{}\Sigma _g^{}{}_{}{}^{}}^{+}\to 1{{}_{}{}^1{}_{}{}^{}\Sigma _u^{}{}_{}{}^{}}^{+}$, $3{}_{}{}^1{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ in ${\mathrm{F}}_2$, and $X{{}_{}{}^1{}_{}{}^{}\Sigma _g^{}{}_{}{}^{}}^{+}\to b^{\prime }$, $c^{\prime }{{}_{}{}^1{}_{}{}^{}\Sigma _u^{}{}_{}{}^{}}^{+}$ in ${\mathrm{N}}_2$. Below 50-eV impact energies, the method gives more accurate integrated cross sections than the Born approximation.

The absolute cross sections for the double, triple, and quadruple ionization of ${\mathrm{Rb}}^{+}$ ions by electron impact have been measured from below their respective thresholds to approximately 3000 eV. This determination has been accomplished using a crossed-beam facility in which monoenergetic beams of ions and electrons are caused to intersect at right angles in a well-defined collision volume. The various charged-particle currents, energies, and beam-current density distributions represent the experimental data from which the desired absolute cross sections have been determined. The results obtained with this technique are compared with available theoretical predictions of the appropriate cross sections.

Conditions for self-breakdown are studied with a time-dependent one-dimensional model which includes effects of ionization by electrons, ions, and energetic neutrals, charge exchange, secondary-electron emission from the cathode due to impact of ions and neutrals, and backscattering of electrons from the anode. Theoretical predictions for the low-pressure branch of the Paschen curve are reported. $\mathrm{Pd}$ scaling is explicitly verified. In addition, the rates for current buildup above the critical pressure are calculated. The relative importance of various physical effects on the onset of self-breakdown are studied.

The projectile charge-state ($q$) dependence of characteristic $K$ x-ray production has been studied for a variety of collision systems, ${\mathrm{Cu}}^{q+}\to \mathrm{H}\mathrm{e},\mathrm{N}\mathrm{e},\mathrm{K}\mathrm{r},\mathrm{Z}\mathrm{n}$, and ${\mathrm{Br}}^{q+}\to \mathrm{Kr}$, at 0.87 and 1.40 MeV/amu. All targets were of gas or vapor type to provide single-collision conditions. An increase in the $K$-excitation cross sections occurs for projectiles having performed $2p$ vacancies, the absolute cross section increase per incoming $2p$ vacancy being orders of magnitude larger for near-symmetric than for asymmetric collision systems. We identify the difference in magnitude with the predominance of a different excitation mechanism in the two cases, contrary to the view put forward recently by Tserruya et al.

An analytic model is derived for long-range coupling in inner-shell excitation processes of ion-atom collisions using a two-state wave function with Bates and McCarroll translation factors. The result we derive for the sharing ratio reduces to the Demkov result in the low-velocity limit. At higher velocities, we predict a sharing ratio which drops below the Demkov curve. As the velocity increases, a maximum is reached and the sharing ratio then decreases with further increase in velocity. Numerical calculations using translation factors in a molecular orbital basis have shown such a falloff. The effect has been previously attributed to phasing between interaction regions due to a multistate configuration. We show that the effect is due to the inclusion of translation factors. The modification we derive to the analytic model of Demkov resolves discrepancies with the experimental data which were previously attributed to fluorescence yield problems. In addition, we find that without making adiabatic assumptions in treating the solutions of the equations of motion, we can recover the exact Born result in the high-velocity limit.

Numerical solutions of Boltzmann's equation are obtained for the distribution of electrons in gaseous Ar in the presence of a dc electric field and a laser field. The calculations are performed at field strengths below those either of electrical or optical gas breakdown in order to study the effect of the radiation on dc-field-induced electron mobilities. The isotropic component of the electron distribution function oscillates with energy as a result of the discrete nature of free-free absorption and stimulated emission. Similar structure has been observed in previous studies at laser-field strengths close to optical breakdown with no dc field present. The radiative processes cause the mobility to increase by roughly the same amount as that obtained by use of the classical model of microwave electron heating, or by removing the laser and increasing the temperature to a thermal energy close to one laser photon. Thus, the energy oscillations in the distribution are not significantly probed by the $e$,Ar mobility. These findings suggest the use of molecular gases, having vibrationally inelastic-threshold energies in the region of oscillations, to find mobilities more sensitive to the discrete nature of the radiative processes.

A study is made of the range of applicability of various versions of the low-frequency approximation for electronatom scattering in a laser field. A key physical parameter—the ratio of the electron-field interaction energy to the photon energy—is identified and a distinction is drawn between two regimes, corresponding to values of this ratio of order unity (intermediate coupling) and values large compared to unity (strong coupling). Separate derivations are given which are appropriate to one or the other of these regimes, with proper account taken of the possibility of resonances or composite bound-state poles in the field-free scattering amplitude. The strong-coupling case is characterized by the emission or absorption of large numbers of virtual soft photons in initial and final states. The analogy with the problem of spontaneous infrared radiation which this physical picture suggests is put into more precise form here through the derivation of sum rules for the total cross section and for the average energy transferred to the field. The strong-coupling approximation is closely related to the approximate treatment, due to Keldysh and others, of multiphoton ionization as a tunneling process. This relation is demonstrated explicitly here by recognizing that ionization may be thought of as the second half of an induced resonance reaction and applying, to the amplitude obtained in this way, some of the approximation techniques developed for the scattering problem.

The stopping power of matter for deuterons at extreme relativistic energies is calculated by including the effects of the deuteron's electric and magnetic form factors as well as $S$ and $D$ states. The contributions of these effects reduce the mass stopping power by over 20% at the highest energies considered here. A table of stopping powers of aluminum, copper, and lead is presented.

A consistent prescription is given for constructing semiquantized Hamiltonians in generalized coordinates. The method extends the classical path approximation and deals directly with a generalized form of the quantized kinetic-energy operator to derive simplified quantum-mechanical wave equations for multidimensional dynamical systems exhibiting both quantal and classical features.

The conventional quantum-mechanical formulation of near-adiabatic collision theory is known to have a number of defects. These defects arise because the usual description does not account for the displacement of electronic states with moving nuclei, or for the change of momentum of the electron as it jumps from one moving nucleus to the other. The purpose of this series of papers is to develop an improved theory, in which such effects are taken into account. In this paper, we show that displacement and momentum-transfer effects can be incorporated into the theory in a very simple way, provided that the wave function is expanded in terms of electronic states that have single-center character. (Linear combinations of single-center states are also permitted.) A particular form of such an expansion is proposed, and it is shown that this expansion leads to equations in which fictitious displacement couplings are eliminated and momentum-transfer terms are included. The work of this paper and of others on this subject leads to revised notions about the definition and meaning of nonadiabatic couplings.

In a drift experiment, results have been obtained on the energy dependences of the rate coefficients for the forward and reverse reaction ${\mathrm{Ar}}^{+}\left({}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\right)+\mathrm{N}\underset{k_r}{\stackrel{k_f}{\rightleftarrows }}\mathrm{Ar}+{{\mathrm{N}}_2}^{+}$ ($v=0\mathrm{}$ and $v\ne 0$). The forward reaction predominantly proceeds via an endoergic channel, resulting in the ionic product ${{\mathrm{N}}_2}^{+}(X,v\ne 0)$, and $k_f$ increases from 1×${10}^{-11\mathrm{}}$ ${\mathrm{cm}}^3$ ${\sec }^{-1\mathrm{}}$ to 7×${10}^{-10\mathrm{}}$ ${\mathrm{cm}}^3$ ${\sec }^{-1\mathrm{}}$ in the energy range from thermal up to ${\mathrm{E}}_{\mathrm{c}.\mathrm{m}}$ ∼3 eV. In the reverse direction the reaction is fast in the entire energy range investigated (a few tenths of an eV up to about 6 eV) for vibrationally excited ${\mathrm{N}}_2^{+}$, for which the reaction is exoergic, but it shows a strong energy dependence in the case of ${{\mathrm{N}}_2}^{+}\mathrm{}(v=0\mathrm{})\mathrm{}$, reflecting the endoergicity of this reaction path.

The results are presented of a study of the forward and reverse rate coefficients ($k_f$ and $k_r$) at thermal energies for the reaction ${\mathrm{Ar}}^{+}\left({}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\right)+{\mathrm{N}}_2\underset{k_r}{\stackrel{k_f}{\rightleftarrows }}\mathrm{Ar}+{{\mathrm{N}}_2}^{+}(\nu =0,1)$. The data were obtained in a selected ion flow tube. It is shown that at 300 K the forward reaction proceeds predominantly via the ${{\mathrm{N}}_2}^{+}(\nu =1)$ product channel and at 80 K via the ${{\mathrm{N}}_2}^{+}(\nu =0)$ channel. $k_r$ is large for ${{\mathrm{N}}_2}^{+}(\nu =1)$ which probably explains the anomalies in previous studies of $k_f$ in afterglows in which Ar and ${\mathrm{N}}_2$ coexisted.

We have determined the net ionization cross section for total slow-ion or slow-electron charge production in rare-gas targets by passage of a fast projectile both experimentally and theoretically. We have experimentally studied ionization in these targets by C, Fe, Nb, and Pb projectiles with energies ranging from 310 keV/amu to 4.75 MeV/amu and for charge states in the range of + 4 to + 54. Theoretical calculations employing the classical-trajectory Monte Carlo method are used to calculate ionization cross sections in the rare gases for projectiles at collision energies of 1-5 MeV/amu with charge states + 5 to + 80. Experiment and theory generally agree within a factor of 2 over this wide range of conditions. For a given rare-gas target, the cross sections for net ionization reduce to a common curve when plotted as cross section divided by charge state versus energy per nucleon divided by charge state.

Differential cross sections are presented for the production of ${\mathrm{H}}^{+}$ and ${\mathrm{H}}^0$ fragments produced in collisions of ${\mathrm{H}}_2^{+}$ with He at collision energies 0.5, 1.0, 2.0, and 3.0 keV. The results are interpreted in terms of direct collisional excitation of the $1\sigma u$ repulsive state of ${\mathrm{H}}_2^{+}$ and charge exchange into the ${}_{}{}^3{}_{}{}^{}\Sigma _u^{}{}_{}{}^{}$ repulsive state of ${\mathrm{H}}_2^0$. The angular distributions of ${\mathrm{H}}^0$ fragments which arise from the ${\mathrm{H}}_2^0$ repulsive state are given by the angular distribution for (½)$({\mathrm{H}}^0-{\mathrm{H}}^{+})$. The results are in agreement with those of previous experiments and extend the earlier work down to lower collision energies. The measured angular distributions fit a scaling law $\left(\frac{1}{E_{\mathrm{inc}}}\right)\frac{d\sigma }{d\omega }=N\left(E_{\mathrm{inc}}\right)f_i\left(E_{\mathrm{inc}}{\theta }^2\right)$, where $i$ indicates the dissociation fragment.