The equation describing scattering of a fast ion by a $K$-shell electron, $\frac{i\hslash v\partial S_I}{\partial Z}=\exp \left(\frac{i{\tilde{H}}_{e}Z}{\hslash v}\right)V(\overrightarrow{\mathrm{r}}, \overrightarrow{\mathrm{R}})\exp (-\frac{i{\tilde{H}}_{e}Z}{\hslash v})S_I$, where ${\tilde{H}}_e\left(\mathcal{r}\right)=-\left(\frac{{\hslash }^2}{2m_e}\right){\nabla }_{\mathcal{r}}^2-\left(\frac{{\hslash }^2}{m_e}\right)\left[\frac{\partial \ln {\chi }_0\left(\mathcal{r}\right)}{\partial \mathcal{r}}\right]\frac{\partial }{\partial \mathcal{r}}\equiv \mathrm{FT}+\mathrm{BT}$, is solved in the Glauber approximation by setting ${\tilde{H}}_e$ to zero and in the Cheshire approximation by setting the binding term (BT) to zero. In this paper we solve for $S_I$ including both the freely recoiling term (FT) and BT but neglecting their commutator. A divergence found with this method in a previous investigation of hydrogenlike atoms is removed as long as $\frac{Z_S{e}^2}{\hslash v}<1\mathrm{}$. This limit represents a natural "threshold" in the method since for lower velocities the target electron is moving faster than the projectile. We apply the method in its lowest-order approximation to $K$-shell ionization by differently charged projectiles. A substantial improvement in the fit to the ratio ${\mathcal{r}}_{12}$ given by ${\mathcal{r}}_{12}=\frac{\sigma \left(Z_2\right)Z_2^2}{\sigma \left(Z_2\right)Z_1^2}$, $Z_1>Z_2$, is found in comparison with the Glauber and Cheshire results. More experiments are needed with $Z_S\lesssim 20$ and at energies such that $\frac{Z_S{e}^2}{\hslash v}<1\mathrm{}$ to test this new theory. The method has immediate applicability to any scattering problem in which the projectile has a classical trajectory.

The relative apparent electron-excitation cross sections $\frac{\sigma \mathrm{}\left(v\right)\mathrm{}}{\sigma \mathrm{}\left(0\right)\mathrm{}}$ for vibrational levels $1\le v\le 4$ of the ${\mathrm{N}}_2^{+}$ $B{}_{}{}^2{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ state were measured over the temperature range of 300-900 K using an electron beam of 10-keV energy. Enhancement was observed for all temperatures investigated for the values of $\frac{\sigma \mathrm{}\left(v\right)\mathrm{}}{\sigma \mathrm{}\left(0\right)\mathrm{}}$ for $v=2, 3, \mathrm{and} 4$ relative to the values predicted using emission band strengths and excitation Franck-Condon factors. The values of $\frac{\sigma \mathrm{}\left(1\right)\mathrm{}}{\sigma \mathrm{}\left(0\right)\mathrm{}}$ agreed with calculated values to within experimental uncertainty. The apparent cross sections were determined for the N ii levels $2p\left({}_{}{}^2{}_{}{}^{}P_{}^o{}_{}{}^{}\right)3p$, $2p\left({}_{}{}^2{}_{}{}^{}P_{}^o{}_{}{}^{}\right)3d$, and $2p\left({}_{}{}^2{}_{}{}^{}P_{}^o{}_{}{}^{}\right)4f$ and the $2p^2\left({}_{}{}^3{}_{}{}^{}P\right)4p$ level of N i. To the accuracy of the measurement no temperature dependence of the atomic cross sections was observed.

Crossed beams of electrons and ${\mathrm{Hg}}^{+}$ ions have been employed to measure absolute cross sections for 165.0-nm emission, corresponding to the transition ${\mathrm{Hg}}^{+}\left(6p{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^0{}_{}{}^{}\right)\to {\mathrm{Hg}}^{+}\left(6s{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}\right)$. The emission cross section, which is nearly identical to the excitation cross section for ${\mathrm{Hg}}^{+}\left(6p{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^0{}_{}{}^{}\right)$ near threshold, has a value of about 1.2 × ${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ at the 7.51-eV threshold, rises to a maximum of 2.26 × ${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ at 13 eV, and falls to 0.64 × ${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ at 274 eV. The cross section exhibits considerable structure in the energy region from threshold to the onset of the first cascade ($7s{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$) at 11.9 eV; this structure is likely due to interference from autoionizing states of neutral Hg. The total uncertainty at a "good" confidence level is about 18%, taken as the quadrature sum of random uncertainty (5% at 90% confidence level) with systematic uncertainties (17% at a level equivalent to 90% confidence level). At threshold, the Gaunt-factor formula of Seaton predicts a value of about 3 times that measured, but the two converge to within about 15% for electron energies ranging from 13 to 274 eV. The results are also in reasonable agreement with a semiclassical Gryzinski-type calculation for energies above several times threshold. The data give an emission cross section of (2.8 ± 0.5) × ${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ at 6.8 eV for 194.2 nm ($6p{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^0{}_{}{}^{}\to 6s{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$). Analysis of data taken with some metastable $6s^2{}_{}{}^2{}_{}{}^{}D$ ions in the target beam indicates that the mean cross section for excitation of the $6s{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^0{}_{}{}^{}$ level from the $6s^2{}_{}{}^2{}_{}{}^{}D$ metastable states is larger than that for excitation from the $6s{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ ground state. Additional measurements of 398.4-nm emission ($6p{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^0{}_{}{}^{}\to 6s^2{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}$) yield a cross section of about 6 × ${10}^{-19\mathrm{}}$ ${\mathrm{cm}}^2$ near threshold, and a branching ratio $\frac{({}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\to {}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{})}{({}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\to {}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{})}$ of $\frac{350}{1}$.

Experimental x-ray production cross sections for Ne projectiles impinging on thick Al foils and Ar projectiles on Si foils reveal that in asymmetric atom-atom collisions, $K$-shell vacancies are created in both collision partners. Only in the almost adiabatic collision regime at very low velocities, corresponding to projectile energies $E_1<20\mathrm{}$ keV/amu, are all of the vacancies created in the collision partner with the lower atomic number, as predicted by the electron-promotion model of Pauli excitation. At higher energies, $E_1>25\mathrm{}$ keV/amu, the ratio of the $K$-shell x-ray production cross section of the heavier collision partner to that of the lighter collision partner increases approximately as the square of the incident ion energy, and can exceed unity. It provides experimental evidence for Pauli excitation of both $K$ shells under nonadiabatic conditions.

Ionization in Ar+Ar collisions is studied at beam energies of 2.00, 2.50, and 3.00 keV over an angular range from 2.0° to 12.0°. The ionization probability ($P_1$) shows a threshold for $\tau \approx 5$ keV deg and a second rise for $\tau \approx 25$ keV deg. The scattered ion beam is energy analyzed at selected energies and angles. For $2<\mathrm{}\tau <12\mathrm{}$ keV deg the ion energy-loss spectra show a double-peaked structure, at an 18-eV and at a 29-eV energy loss. At larger $\tau$ there is predominately one peak in the spectra at 43 eV. The energy losses and $\tau$ dependence of $P_1$ suggest that the 29- and 43-eV processes involve excitation of autoionizing states. Additional results at beam energies of 0.50, 0.75, 1.00, and 1.50 keV show $P_1\left(\tau \right)$ to be velocity dependent at these lower energies.

Elastic and inelastic collisions in the symmetric He-He, Ne-Ne, Ar-Ar, and Kr-Kr systems are investigated experimentally and theoretically at low keV energies (0.5-4 keV). Standard techniques, employing electrostatic energy analysis for ions and time-of-flight methods for neutrals, are used in energy-loss measurements. The characteristic energy spectra of the scattered beams generally show three peaks corresponding to elastic scattering and collisions resulting in one- or two-electron excitations. Of particular significance is the dominance of the lowest-lying $p$ levels in the inelastic scattering. Differential cross sections are determined at select energies and the interpretation of the results is made in the framework of the electron-promotion model. Ab initio calculations are performed for the Ne and Ar cases. The primary mechanism in the inelastic scattering always involves one- or two-electron transitions from a promoted incident molecular orbital by rotational coupling for He-He, and by radial coupling in the Ne-Ne and Ar-Ar cases. Predictions based on the assumed model are compared with results of related experiments.

Angular distributions have been measured and polarization fractions determined for target and projectile x rays emitted in collisions of 3-MeV protons on argon and 33-MeV fluorine ions on argon and helium. The near isotropy in target x-ray emission that follows $K$-shell ionization is not unexpected; however, the anisotropic emission of projectile x rays contradicts the assumptions that are made in the analysis of x-ray cross sections. The polarization of ∼ 23% in this characteristic $K$-shell radiation can be understood qualitatively from the alignment of excited states populated by electron capture in atomic collisions.

The conservation of spin angular momentum during inelastic collisions of spin-oriented metastable $\mathrm{He}\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S\right)$ atoms with contaminated surfaces and a variety of gaseous targets, including Ar, ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, CO, C${\mathrm{O}}_2$, and ${\mathrm{N}}_2$O, has been investigated. The metastables are contained in a flowing helium afterglow and are oriented by optical pumping. The electrons produced during subsequent chemi-ionization and surface-ejection reactions are extracted and spin analyzed by Mott scattering. Spin angular momentum is found to be fully conserved for all the reactions studied, with the possible exception of the chemi-ionization of CO. The experimental results are discussed in the light of existing theories and models for chemi-ionization. The results also suggest that secondary electron ejection from chemically cleaned surfaces occurs through chemi-ionization of adsorbed species.

An optically pumped flowing helium afterglow is evaluated as a potential source of polarized electrons. Spin angular momentum conservation in chemi-ionization reactions involving optically oriented $\mathrm{He}\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S\right)$ atoms has been exploited to yield microampere electron beams with 30% polarization and energy spread ≤ 0.5 eV. The beam emittance is on the order of 10 mrad cm at 500 V extraction potential. This source appears well-suited for most spin-dependent scattering experiments that have been proposed.

The solution of the transport equation by the Laplace-transform method, introduced by Landau and modified by Vavilov and others, is compared with the solution of that equation by what we term a convolution method. An energy-loss cross section determined for solid aluminum has been used as input to the calculations. For very small values of absorber thickness, the straggling distribution is dominated by peaks at multiples of the Al plasmon frequency. At intermediate values, these peaks are a small structure superimposed on a broad energy-loss distribution which is not described well by any of the Laplace-transform theories. At larger values, the straggling distribution consists of one peak which is well described by the Vavilov theory.

In low-energy atomic scattering theory it is well known that the accuracy of the familiar target eigenstate expansion or "close coupling" methods cannot be totally relied upon unless all open channels of the target system are included in the expansion. We show that the same methods, as applied to low-energy scattering by a molecular target, converge even though all open channels above a certain energy level may be truncated in the target eigenstate expansion. The result is applicable only in the energy regime where rotational channels are open but vibrationally and electronically excited state channels are closed.

Cross sections, differential in ejection energy and angle, for electron emission from methane, ethane, ethylene, acetylene, and benzene molecules following proton impact have been measured for protons of 0.3-, 1.0-, and 2.0-MeV energy, in an attempt to observe a variation in the electron yield attributable to the chemical form or molecular binding of the target atoms. The results indicate that emission cross sections for electrons ejected with energy greater than about 10 eV show no effects related to the molecular structure within this group of molecules. When the results are compared with similar data for molecular hydrogen however, one observes a significant difference in the angular dependence of the emission cross sections between the hydrocarbons as a group and hydrogen; the emission from the hydrocarbons is more isotropic than from hydrogen. This observation indicates that the amount of ionization produced by energetic charged particles may be different in different gaseous mixtures containing hydrogen and hydrocarbon gases. The double-differential cross sections for the group of hydrocarbons are found to be scalable in terms of the number of weakly bound electrons in the molecule.

The vibrational excitation of ${\mathrm{N}}_2$O by electrons in the energy range 1-4 eV has been studied with a crossed-beam apparatus using an energy resolution of 22 meV and an observation angle of 40°. The scattering in the middle of this energy range is dominated by the ${}_{}{}^2{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$ shape resonance which contributes to the excitation of about 20 vibrational modes. The vibrational modes belong to four series, namely, the $n00\mathrm{}$, $n10\mathrm{}$, $n01\mathrm{}$, and $n02\mathrm{}$ series with the quantum number $n$ ranging from 0 to 7. The energy dependence of the differential vibrational cross sections is bell shaped and exhibits no fine structure. At the center of the ${}_{}{}^2{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$ resonance (2.3 eV), the $n00\mathrm{}$ series is most intensely excited and has a cross section of (9.6 ± 3.5) × ${10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$/sr for $n=1\mathrm{}$ and an exponentially decreasing magnitude for successively higher $n$. A similar trend of the branching ratio has also been observed in the $n01\mathrm{}$ series. The present experiment combined with a calculation of Dubé and Herzenberg demonstrates that the impulse picture which was originally proposed for the case of vibrational and rotational excitation in ${\mathrm{H}}_2$, is applicable to this triatomic molecule as well. The width $\Gamma$ for the ${}_{}{}^2{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$ shape resonance of ${\mathrm{N}}_2$O has been found to be 0.7 eV in the center of the Franck-Condon region, and it decreases for larger internuclear separations.

${\mathrm{N}}_2$O is a linear triatomic molecule. Electron scattering shows a ${}_{}{}^2{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$ shape resonance at ∼ 2.3 eV. The lifetime turns out to be so short, 0.9 × ${10}^{-15\mathrm{}}$ sec, that one has an impulse picture, in which the nuclei acquire velocity but suffer little displacement during the residence of the projectile electron. The nuclear wave equation at the resonance is solved in the impulse approximation, and is shown to give a good account of the excitation of more than 20 vibrational states observed by Azria, Wong, and Schulz.

We present calculations of the cross section ${\sigma }_{01}$ for the vibrational excitation of ${\mathrm{H}}_2$ by proton impact with several interaction potentials. The calculation with a long-range anisotropic potential shows features very similar to the calculation with the ${\mathrm{H}}_3^{+}$ potential surface, but both calculations fail to account for the observed persistence of the cross section at high velocities (proton energy range from 200 to 1000 eV). A trajectory-dependent potential is introduced semiempirically, and it is found that the main features of the observed cross section can be explained by its short-range parts ($r\lesssim 2$ Å). The significance of this potential is discussed. The approximation scheme involves first-order time-dependent perturbation theory and considers only rectilinear trajectories. Therefore, for the case reported here, the calculation is valid for energies higher than about 200 eV, where the trajectories are essentially rectilinear. The semiempirical deduction of the trajectory-dependent potential was greatly simplified by representing the time-dependent potential by a Gaussian pulse. The results are compared with a previous calculation.

Ab initio potential-energy calculations have been performed on the $C{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ state of $\mathrm{He}\left(2\mathrm{}{}_{}{}^1{}_{}{}^{}S\right)+\mathrm{He}\left(2\mathrm{}{}_{}{}^1{}_{}{}^{}S\right)$ and on the $B{}_{}{}^1{}_{}{}^{}\Pi _g^{}{}_{}{}^{}$ state of $\mathrm{He}\left(2\mathrm{}{}_{}{}^1{}_{}{}^{}P\right)+\mathrm{He}\left(1\mathrm{}{}_{}{}^1{}_{}{}^{}S\right)$; the $L_y$ rotational-coupling matrix elements were also calculated. The potential curves were found to cross at $R=3.89\mathrm{}{a}_0$, where $L_y=0.68\mathrm{}$. Close-coupled calculations were then used to predict the cross sections for collision energies $E\le 100$ eV. The excitation total cross section was found to rise rapidly from the threshold at $E=0.60\mathrm{}$ eV to values greater than 1 × ${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ at collision energies $E\gtrsim 4$ eV. The inelastic- scattering total cross section for the reverse reaction, deexcitation of $\mathrm{He}\left(2\mathrm{}{}_{}{}^1{}_{}{}^{}P\right)$ by $\mathrm{He}\left(1\mathrm{}{}_{}{}^1{}_{}{}^{}S\right)$, was found to be greater than 1 × ${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ at thermal energies and yields a Boltzmann-averaged rate of $k\left(300\mathrm{}°\mathrm{K}\right)=2.9\mathrm{}\times {10}^{-12\mathrm{}}$ ${\mathrm{cm}}^3$/sec. At energies $E\lesssim 3$ eV, sharp peaks are found on the inelastic-scattering total cross sections and are attributed to quasibound states present at these low energies. The inelastic-scattering differential cross sections are forwardly peaked with most of the scattering appearing at reduced angles $\tau =E\theta \lesssim 250$ eV deg.

Differential and integral cross sections for the $1s-2p$ excitation of the hydrogen atom at impact energies of 0.81, 1.00, 1.21, 1.44, 2.25, and 4.00 Ry are calculated from the most accurate available ab initio calculations and tabulated.

A 1-${\mathrm{cm}}^3$ Ge(Li) $\gamma$-ray detector was placed directly in a beam of thermal neutrons where the ${}_{}{}^{72}{}_{}{}^{}\mathrm{Ge}(n, \gamma ){}_{}{}^{73}{}_{}{}^{}\mathrm{Ge}$ reaction produced 254-eV ${}_{}{}^{73}{}_{}{}^{}\mathrm{Ge}$ recoil atoms in the detector. The primary capture $\gamma$ rays from the reaction were detected in a 7.6-cm × 7.6-cm NaI(Tl) detector placed at 90° to the incident beam. In addition to singles measurements a coincidence between the primary capture $\gamma$ ray and the $\gamma$ ray or conversion electrons from the decay of the 68.75-keV ${}_{}{}^{73}{}_{}{}^{}\mathrm{Ge}$ third excited state was used to search for directional effects in the stopping and to check the value of the recoil energy deduced from the feeding of the 68.75-keV level. The level energy was remeasured and a value of 68.755 ± 0.005 keV was found, which when combined with the results of previous work gives a value of 68.7535 ± 0.0043 keV. The amount of energy lost to ionization in the stopping of the 254-eV ${}_{}{}^{73}{}_{}{}^{}\mathrm{Ge}$ atom is found from the energy shift in the peak position for the 68.75-keV level. Our measurement of this shift gives a value of 39.2 ± 5.5 eV, which is then the energy loss to ionization by the stopping of the 254-eV ${}_{}{}^{73}{}_{}{}^{}\mathrm{Ge}$ recoil atom. This result is (27 ± 3)% higher than the theoretical estimate made from an extrapolation of the Lindhard theory to this energy region. An attempt to observe a dependence of the ionization loss on the recoil direction in the Ge crystal was made, but no positive effect was observed.

We use a perturbative approach to analyze the diffusion equation for the atomic quasiprobability function derived by Narducci, Coulter, and Bowden, and demonstrate explicitly that the first-order correction contributes to the atomic moments only to order $\frac{1}{N}$, where $N$ is proportional to the cooperation number.

The quantum-electrodynamic frequency shifts of a two-level system in spontaneous emission and in an intense quantized radiation field are given up to eighth order in the coupling parameter, using the recursive perturbation method developed previously by one of the authors. The first six orders of the latter agree with the semiclassical result of Shirley and thus disagree with Chang and Stehle's calculation. The eighth-order term agrees with a recent semiclassical calculation by Ahmad and Bullough. The transition from the quantum mechanical case (the number of photons small) to the classical case (the number of photons very large) is also exhibited in our approach.