Approximate analytical expressions are derived for the ionization cross sections in the high- and low-collision-energy limits, using the improved impulse approximation based on the assumption that the electron-atom inelastic-scattering amplitude is a function only of the momentum transfer. Both cases of simultaneous excitation and de-excitation of one of the atoms are discussed. The formulas are applied to the collisions between two excited hydrogen atoms and are found very useful for estimating the cross sections in the wide range of collisions energies.

The adiabatic approximation in scattering theory is modified by allowing for the splitting and shifts of perturbed target-state energy levels. This energy-modified adiabatic approximation, derived from operator equations formally equivalent to close-coupling equations in the basis of perturbed target states, is shown to be qualitatively correct for threshold and resonance structures, for which the usual adiabatic theory is inadequate. In the case of electron-molecule vibrational excitation, it is shown that electronic threshold scattering structures should be associated with each vibrational threshold. A single electronic resonance becomes a manifold of multichannel vibrational excitation resonances. Vibrational excitation structures in $e^{-}-N_2$ scattering are computed as an example of the method.

Doubly differential cross sections of secondary electrons ejected from He by electron impact have been measured utilizing a crossed-beam method. The incident energies used were 50, 100, 200, and 300 eV. The energy and angular range of the secondary electrons measured were from half of the difference between incident energy and ionization energy to 1.0 eV and from 6° to 156°, respectively, with an emphasis on the measurements of low-energy secondary electrons. The present results have been placed on an absolute scale by using the ionization cross section at 100 eV. The results indicate a strong forward peak for lowenergy (< 5 eV) secondaries at angles less than 30°. There is good agreement among the measurements of the high-energy secondary electrons but considerable differences exist in the measurements of the low-energy secondary electrons.

A four-inch curved-crystal spectrometer has been used to investigate the internal resonance Raman scattering (IRRS) process in Si $K$ x-ray spectra induced by 1.5- and 2.0-MeV proton bombardment of thick targets. The IRRS process involves the scattering of characteristic target $K{\alpha }_{1,2}$ radiation off of the $L$ shell of a neighboring target atom. The scattered photons exhibit an edge-shaped structure at ∼ 1640.5 eV which tails off at low energies. A thick-target analysis has been used to obtain a partial scattering cross section for scattering within the observable energy range $1634\le E_f\le 1640.5$ eV, which is in reasonable agreement with our calculations based on second-order perturbation theory. Based on the partial cross section, we are able to estimate the total IRRS cross section for scattering into all angles and all allowed energies ($0\le E_f\le 1640.5$ eV) to be $(58\mathrm{}\pm 20)r_0^2$ or (4.6±1.6)${10}^{-24\mathrm{}}$ ${\mathrm{cm}}^2$.

The collision-induced polarization and momentum transfer are treated as the two components of a time-dependent complex variational parameter $\overrightarrow{\mathrm{p}}\mathrm{}\left(t\right)\mathrm{}$. The equation of motion derived from the Schrödinger Hamiltonian is investigated. Within the linear approximation the energy transfer to a bound electron is shown to be $\Delta E=\frac{{\left|\Delta \overrightarrow{\mathrm{p}}\right|}^2}{2m}$. The harmonic oscillator and the hydrogen atom are studied. To be consistent with the results of Bohr, Bethe, and Bloch, for fast collisions, the impulse approximation must be incorporated into the variational approach. Higher-order $Z$ corrections to electronic stopping are worked out. The problem of joining together distant and close collisions is avoided.

High-resolution projectile Auger spectra of singly and doubly core-excited oxygen ions are studied as a function of incident beam energy (2-18 MeV), exciter gas (helium, neon, argon, and krypton) or foil (carbon), incident charge state (1+ to 4+), and delay time. Auger-electron production from excited oxygen states varies considerably for collisions with different beam energies and exciter gases. A striking similarity in both the linewidths and relative Auger line intensities is observed for single-collision gas and multiplecollision foil excitation. The incident ion charge state does not appreciably affect the excitation cross sections and the charge state of the outgoing projectile. In order to assign the measured Auger peaks numerous excitation and Auger transition energies for singly and doubly core-excited states are calculated using semiempirical and ab initio methods. Calculated transition energies are compared with experimental line structures. Possible excitation and deexcitation mechanisms are suggested and discussed within a quasimolecular single-particle model.

Faddeev equations for four-body problems are written in the momentum representation. Our choice of angular momentum separation allows us to make explicit the kernels of four-body equations in terms of two-, three-, and four-body equations with interactions by pairs for which results are given.

Solutions of the Faddeev equations for four-body problems in the case of Coulomb potentials are investigated. A method which is of practical use for solving these equations for bound-state energies is developed. As an example, the method is applied to the ${\mathrm{Li}}^6$ system in its fundamental state.

Differential cross sections for the production of ${\mathrm{D}}^{-}$ and ${\mathrm{D}}^0$ + ${\mathrm{D}}_2^0$ + ${\mathrm{D}}_3^0$ are given for electron-capture collisions into ${\mathrm{D}}_3^{-}$ and ${\mathrm{D}}_3^0$ repulsive states by bombardment of Cs with ${\mathrm{D}}_3^{+}$ ions in the energy range 1.5-7.5 keV. A theory is presented for the angular distributions of dissociation fragments in the special cases in which the dissociation (i) produces two fragments, or (ii) produces three fragments, one of which has a small energy in the molecular center-of-mass frame. In both cases a scaling law is predicted: ${\left({\gamma }_n{E}_i\right)}^{-1\mathrm{}}$ $\frac{d{\sigma }_n}{d\omega }=f\left({\gamma }_n{E}_i{\theta }_n^2\right)$, where $\frac{d{\sigma }_n}{d\omega }$ is the differential cross section for finding fragment $n$ at angle ${\theta }_n$, $E_i$ is the incident energy, and ${\gamma }_n$ is a mass ratio. The ${\mathrm{D}}^{-}$ distributions are observed to fit this scaling law. Peaks are found in both the ${\mathrm{D}}^{-}$ and ${\mathrm{D}}^0$ + ${\mathrm{D}}_2^0$ + ${\mathrm{D}}_3^0$ distributions for which $\frac{1}{2}{E}_i{\theta }^2\simeq 15$ keV ${\mathrm{deg}}^2$ and 14 keV ${\mathrm{deg}}^2$, respectively. A corresponding peak is also found in the neutral distribution for which $2E_i{\theta }^2\simeq 14$ keV ${\mathrm{deg}}^2$. The peaks indicate a repulsive state in ${\mathrm{D}}_3^{-}$ which decays into ${\mathrm{D}}^{-}$ + ${\mathrm{D}}_2^0$, and a repulsive state in ${\mathrm{D}}_3^0$ which decays into ${\mathrm{D}}^0$ + ${\mathrm{D}}_2^0$ and which has an energy surface close to that of the ${\mathrm{D}}_3^{-}$ repulsive state. An energy surface of a repulsive singlet state of ${\mathrm{D}}_3^{-}$ is presented which does decay into ${\mathrm{D}}^{-}$ and ${\mathrm{D}}_2^0$.

The total cross section for $e^{-}$-Hg scattering has been measured in the energy range between 0.1 and 500 eV. Absolute data taken at a few energies by means of a static target were used to normalize the relative cross sections, which were measured in the whole energy range by scattering from an atomic beam. This technique was used to help meet the high-angular-resolution requirements. The cross sections obtained are considerably larger than those obtained in most of the other measurements performed around 1930. Satisfactory agreement is found, however, with semiempirical cross sections (mainly based on recent measurements) and with a recent theoretical calculation. The most pronounced structure is a cross section maximum at 0.4 eV, which probably can be ascribed to a $\left(6\mathrm{}{s}^{2}6p_{\frac{1}{2}}\right){}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ shape resonance.

A new straightforward method for the evaluation of the rearrangement-scattering amplitude has been proposed to study the following reactions: ${\mathrm{H}}^{+}+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}\to \mathrm{H}\mathrm{}\left(\mathrm{nlm}\right)+{\mathrm{H}}^{+}$; $e^{+}+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}\to \left(e^{+}{e}^{-}\right)\mathrm{}\left(\mathrm{nlm}\right)+{\mathrm{H}}^{+}$, $2\le n\le \infty$ and $l=0,1\mathrm{}$, in the first Born approximation embodying the full interacting potential. A contour-integral representation has been used for the Laguerre polynomial that occurs in the final-state wave function. The amplitude containing only the electron-nucleus interaction has been evaluated analytically. But the amplitude for the projectile nucleus interaction involves a contour integration on a circular path, and this integral can easily be evaluated numerically. To provide an estimate of the asymptotic cross section, expressions for the transition amplitudes when $n\to \infty$ have also been given. It is shown explicitly that the charge-exchange cross sections asymptotically obey the inverse $n$-cube law irrespective of the incident energy. In proton-hydrogen collisions our computed results for the low-lying discrete states show excellent agreement with the earlier theoretical values of Mapleton and those of Band as well. For positronium (Ps) formation all the reported results, except for the $2s$ excitation, are quite new. Zeros of the angular distributions are seen to be almost independent of the principal quantum number $n$, but dependent only on the projectile energy. $n^3\sigma$ shows regular smooth behavior with increasing $n$, and the results for $n=18\mathrm{}$ and $n\to \infty$ agree within 0.5% throughout the energy range considered.

Resonant Raman x-ray scattering on molybdenum was studied using a Mo-anode x-ray tube and a LiF crystal monochromator. Beside the usual resonant Raman peak corresponding to the fluorescent $K\alpha$ lines, another peak with a smaller energy loss was found. It is attributed to resonant Raman scattering with a final-state $M$-shell vacancy corresponding to the fluorescent $K\beta$ lines. Both contributions are shown to be independent of the scattering angle. Absolute cross sections have been determined and compared with theoretical predictions.

The mean life of the $4s{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ resonance level in Al i has been measured at seven different vapor densities using a tunable dye laser for excitation and a method of delayed coincidence for detection. The lifetime values, obtained by exciting the level with radiation at the resonance wavelength of 3944.01 Å and observing its decay by means of the transition at 3961.52 Å, increase with increasing vapor density. This vapor-density dependence was interpreted as being due to the imprisonment of the 3962-Å radiation. Imprisonment theory at low densities was applied to the experimental data to yield the following results: ${\tau }_0=6.78\mathrm{}\pm 0.06$ ns, $f_{3944}=0.115\mathrm{}\pm 0.001$, and $f_{3962}=0.116\mathrm{}\pm 0.001$. Experimental and theoretical results of other workers are presented for comparison with the results of the present work.

The decay rates of Li $2s^{2}2p$ and $1s2s^2$ were calculated using many-body perturbation theory with $\mathrm{LS}$-coupled intermediate states. The double-electron Auger rate to $1s^2\mathrm{kp}$ and the radiative decay rate were also calculated for the $2s^{2}2p$ level. The ratio of the double-electron Auger rate to the single-electron Auger rate was calculated to be $\frac{1}{1256}$, and the ratio of the double electron Auger rate to the radiative rate was calculated as 6.44.

Dirac-Fock calculations for the photoionization of Ne $2s$, Ar $3s$, Kr $4s$, and Xe $5s$ have been performed in pure $j-j$ coupling. The asymmetry parameter $\beta$, which characterizes the photoelectron angular distribution, is found to deviate from $\beta =2\mathrm{}$ owing to the anisotropic spin-orbit interaction. It is found that the deviation increases with increasing $Z$ owing to the increase in the spin-orbit force. The influence of exchange is also examined and its energy dependence discussed.

We have studied the electric field ionization of excited states of K and have found that it is similar in its gross features to the field ionization of Na. However, there are clear differences which are particularly important for applications. We attribute the differences to the coupling of states of different $\left|m_l\right|$ in high electric fields by the spin-orbit interaction of the K $p$ states.

We have discovered an interference which results in the vanishing of some electric dipole transition amplitudes. A transition-matrix element $T$ between certain $S$ and $P$ sublevels with the same value of $M_F$ vanishes when an applied magnetic field satisfies $X_s+X_p=-2\mathrm{}{M}_F$, where $X={\mu }_B{g}_J\frac{B}{A}$, and $A$ is the hfs constant. There must be an avoided crossing between the two states of the same $M_F$ which can only occur when one of the hyperfine manifolds has an inverted Zeeman effect. These conditions imply $M_F<0\mathrm{}$ and $I>J$. We observed the vanishing of $T$ in ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$ for one of the $\Delta M_F=0\mathrm{}$ optical transitions of the $3S_{\frac{1}{2}}\mathrm{}(F=1\mathrm{})\mathrm{}\to 3P_{\frac{1}{2}}\mathrm{}(F=1\mathrm{})\mathrm{}$ manifold. Absorption of cw laser light was monitored by observing total fluorescence perpendicular to both the atomic and laser beams, and absorption vanished near an applied field of 155 G. $T$ vanishes for a large number of cases including rf and microwave frequencies and is a rather general consequence of angular momentum selection rules and perturbation theory. This phenomenon may have application in optical pumping, Lamb-shift measurements, and atomic weak neutral-current experiments.

We have made careful absolute measurements of the collisionless multiphoton energy deposition in S${\mathrm{F}}_6$ for C${\mathrm{O}}_2$ laser pulses of varying duration and energy fluence. Likewise, we have also measured the absolute dissociation yields. An experimental plot of yield versus energy deposition shows that the energy distribution function is nearly thermal, becoming somewhat broader than thermal for the longer pulse durations. A "bottlenecking effect" of molecules in the discrete level region is held responsible for this smearing of the population distribution function.

The ${\beta }^{\prime }$ and ${\beta }^{\prime \prime }$ satellites in the measured Cu $K{\beta }_{1,3}$ emission spectrum are shown to be due to the double-vacancy transitions $1s3p^{6}3d^{91,3}D\to 1s^{2}3p^{5}3d^{91,3} \mathrm{PDF}$. This assignment is consistent with an earlier analysis of a highly resolved Cu $K{\alpha }_{1,2}$ spectrum. The $M_2$ and $M_3$ level widths are estimated to be 1.68 eV, in agreement with 2.0±0.3 eV and 1.6±0.3 eV, respectively, from photoelectron spectroscopy, and a calculated width of 2.0 eV. Comparison of the calculated double-vacancy transition array with the neighboring elements $30\le Z\le 32$ suggest a similar identification to the ${\beta }^{\prime }$ and ${\beta }^{\prime \prime }$ satellites in their $K{\beta }_{1,3}$ spectra.

High-resolution $M_{4,5}{N}_{2,3}{N}_{4,5}$, $M_{4,5}{N}_{4,5}{N}_{4,5}$, and $M_{4,5}{N}_{4,5}O$ Auger spectra from ${\mathrm{I}}_2$ vapor and from Xe gas have been measured using electron-beam excitation. In order to reduce satellite backgrounds, the $M_{4,5}{N}_{4,5}{N}_{4,5}$ spectra were also taken using primary-beam energies just below the core-ionization energy of the $M_3$ levels of iodine and xenon. The relative line energies and intensities for all of the xenon spectra and for iodine $M_{4,5}{N}_{4,5}{N}_{4,5}$ spectra have been calculated in the mixed-coupling scheme. The agreement between theory and experiment is excellent for the $M_{4,5}{N}_{4,5}{N}_{4,5}$ spectra of both xenon and iodine. The agreement for the xenon $M_{4,5}{N}_{2,3}{N}_{4,5}$ spectrum is less good, but is close enough to indicate the approximate validity of the independent-electron model. This result is in contrast to that for one-hole states involving the $N_{2,3}$ shell; such a model fails completely to account for the xenon $4p$ photoemission spectrum. The independent-electron model will not account for the $M_{4,5}{N}_{2,3}{N}_{4,5}$ spectrum of iodine. Reasons for the success of this model for xenon and its failure for iodine are presented. The observed inherent linewidths of the Auger lines are considerably broader in molecular iodine than in xenon. The photoelectron spectra and core-ionization energies of the $3d$, $4s$, $4p$, $4d$, $5s$, and $5p$ levels of ${\mathrm{I}}_2$ have been measured. The role of extra-atomic relaxation in the observed Auger energies is discussed.