Nuclear-spin-independent relative probabilities for quenching-induced transitions between the Zeeman sublevels of the $6{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ and $6{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ states of Cs have been measured in a new application of optical pumping. The results for Cs-${\mathrm{N}}_2$ collisions at 15 °C are $K_1({}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}\to {}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}, \Delta m_J=0)=0.5\mathrm{}\pm 0.06$, and $K_2({}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}\to {}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}, \Delta m_J=\pm 1)=0.44\pm 0.06$. The theoretical analysis includes a full treatment of the effect of the hyperfine interaction on relative quenching probabilities, yielding probabilities for $|F^{\prime }, m_{F^{\prime }}〉\to |F, m_F〉$ transitions parametrized in terms of $K_1$ and $K_2$. Full solutions to the pumping equations require knowledge of individual populations of excited-state sublevels: Appropriate analytic solutions for these populations have been calculated in the weak-pumping limit. The experimental results indicate that quenching collisions modify atomic de-excitation probabilities in ways which enhance the efficiency of optical pumping.

Expressions are derived for double-vacancy Auger transition rates, specifically for the noble-gas Auger satellite spectra. It is found that in the most general case, when both initial and final states are in intermediate coupling, there can be interference between final-state terms. When the final state is not in intermediate coupling, the interference vanishes and the transition rate can be written as a linear combination of transition rates in $\mathrm{LS}$ coupling. Expressions are given for the $\mathrm{dp}\to s{p}^2$ and $\mathrm{dp}\to p^3$ Auger transition rates in $\mathrm{LS}$ coupling.

Asymmetric charge-transfer total cross sections have been calculated for the reaction $X^{+}+\mathrm{Alk}\to X^{*}+{\mathrm{Alk}}^{+}$, where $X$ represents Ar, Kr, or Xe and Alk represents K, Rb, or Cs. The calculations were performed at low velocities, $v\sim 1\times {10}^6$ cm/sec, using a modified method of Demkov and semiempirical coupling matrix elements. The Ar results are compared with the experimental data of Peterson and Lorents and agreement is found in the total cross-section shape, but there is an increasing underestimation of the cross section with the higher-atomic-weight alkali-metal atoms. This problem is attributed to the importance of rotational coupling to the $p$-state levels of the excited noble-gas products, suggesting more accurate cross sections for Kr and Xe, where the contribution from the $p$ states will be of lesser importance. Large cross sections are predicted for direct production of the metastable noble gas in the lowest-lying ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ state for the reactions ${\mathrm{Ar}}^{+}$ + Rb, ${\mathrm{Kr}}^{+}$ + Rb, and ${\mathrm{Xe}}^{+}$ + Cs.

The $M$-shell x-ray production cross sections in Au, Bi, and U were measured with a Si(Li) detector for proton and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-ion bombardments over the energy range 1.0-4.5 MeV and 3.0-9.0 MeV, respectively. Absolute ionization cross sections are derived and compared to the predictions of the binary-encounter approximation (BEA) and the plane-wave Born approximation (PWBA). Systematic deviation of the experimental results from the scaled universal curve of the BEA is found. It is shown that this deviation can be understood by taking into account the velocity distribution function for the $3d$ electrons. Good agreement between the PWBA calculation of Choi and the experimental results is obtained for the $M$-shell ionization of Au. The ratios of the ionization cross sections for proton bombardment to those for helium-ion bombardment, at equal velocities, deviate substantially from the theoretical $Z_1^2$ dependence and show so-called crossover behavior, which has been found for the $K$- and -shell ionization.

The problem of the modification of the atomic structure of a hydrogenlike atom or ion as it is channeled through a thin single crystal is formulated. For high-velocity channeling there is an approximate decoupling of the internal atomic motion and the solid state. This allows a single-particle equation to be written for the modified hydrogen atom. The effective potential in the equation is absorptive because of the ionization of the atom due to collisions with the solid. Effects of both single-particle and collective excitations are discussed. An approximate Schrödinger equation is derived for the atom, and solved approximately for the distorted states.

We report the characteristic $\mathrm{Ke}$-shell x-ray production cross sections for Al ions (500 keV to 40 MeV) incident on thin, solid Al targets and for Ni ions (10-63 MeV) incident on thin, solid Ni targets. In these energy regions the transition from predominately quasimolecular excitation to predominantly Coulomb excitation occurs. For incident Al-ion energies up to ∼ 10 MeV the experimental cross sections are predicted reasonably well by deuteron-deuteron cross sections, scaled according to a recipe provided in a model of Briggs and Macek. For higher incident Al-ion energies the reported cross sections fall below the predicted results given by the modified plane-wave Born approximation and probably reflect the dependence of the x-ray cross section on the charge of the incident ion.

The energy dependence of the cross section for charge transfer into the $\mathrm{H}\mathrm{}\left(3s\right)\mathrm{}$ and $\mathrm{H}\mathrm{}\left(4s\right)\mathrm{}$ states for ${\mathrm{H}}^{+}$ and ${\mathrm{D}}^{+}$ incident on ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, and ${\mathrm{O}}_2$ exhibits deviation from the form $\sigma =A{e}^{-Ka\frac{\left|\Delta E\right|}{h\nu }}$ predicted by the adiabatic criterion in the range 1.2-8.2 keV. Analysis of the present data and other previously reported cross sections for protons incident on Ar, He, and Ne reveal some secondary maxima in the $2s$, $3s$, and $4s$ cross sections. Correlations between the structure in these cross sections and maxima in the total and $2p$ cross sections suggest intermediate-state coupling as an explanation for the observed structure.

Many standard applications of the Born approximation to $K$-shell vacancy production apply first-order perturbation theory to the interaction between a projectile and an atomic target represented by a product wave function. It is shown that these standard Born predictions need not be restricted to one-electron ionization, but should be compared to experimental observations summed over all states corresponding to single-$K$-vacancy production to include multiple-vacancy production in other shells. These results are applicable to all targets in which the $K$ shell is weakly perturbed even though the other shells may be strongly perturbed.

The evaluation of a Feynman path integral is discussed for a scattering problem in which some degrees of freedom of the system are treated classically, while others are treated quantum mechanically. The path integral is of the type $K(0, t^{\prime \prime }; 0, t^{\prime })$, and is of interest in a multichannel semiclassical collision theory previously developed by Pechukas. It is shown that this path integral can be evaluated precisely in practice, despite the presence of noncausal terms in the integrand.

It is observed that a number of phase-shift rules can be deduced from properties of the Jost function. The simplest of these is $\int 0^{\infty }\left(\frac{d\epsilon }{\pi }\right)\left[{\delta }_l\right(\epsilon )-{\delta }_l^{1B}(\epsilon \left)\right]=\Sigma n^{}{\epsilon }_{\mathrm{nl}}$ where ${\delta }_l\left(\epsilon \right)$ is the phase shift, ${\delta }_l^{1B}\left(\epsilon \right)$ is the first Born approximation to the phase shift, and ${\epsilon }_{\mathrm{nl}}$ is the $n\mathrm{th}$ bound-state energy with angular momentum $l$.

The energy dependence near the ionization threshold of the electron-scattering cross section of ${\mathrm{H}}_2$ has been investigated. Two series of structures which proceed across the ${\mathrm{H}}_2^{+}$ threshold have been observed which can be correlated with structures observed previously in the ionization efficiency function. These results suggest that in the threshold region a significant portion of the ionization process by electron collision proceeds via the various decay modes of temporary ${\mathrm{H}}_2^{-}$ states. Furthermore, these structures can also be correlated with some structures in the photoionization cross section. Those ${\mathrm{H}}_2^{-}$ states that decay to autoionizing levels of ${\mathrm{H}}_2$ and then to ${\mathrm{H}}_2^{+}$ may account for the correlation with some of the photoionization data. To differentiate experimentally between one-and two-electron decay modes of ${\mathrm{H}}_2^{-}$ leading to ${\mathrm{H}}_2^{+}$ formation, coincidence experiments between ${\mathrm{H}}_2^{+}$ ions and electrons with specific energy losses will be necessary.

The photoelectron angular distribution for the $4f$ subshell of mercury, along with the photoionization cross section, has been calculated in Hartree-Fock and Hartree-Slater approximations. The angular distributions in the various approximations are in good agreement but the cross sections differ by as much as a factor of 2.

The Auger single $3d$ vacancy and satellite spectrum for Kr is calculated. It is shown for the single-vacancy $M_{4,5}-NN$ spectra that the calculations are in good agreement with experiment only if certain levels in Kr Iii are reassigned. The level at 171 997 ${\mathrm{cm}}^{-1\mathrm{}}$ attributed in Moore's tables to ${\mathrm{}\left(4p\right)\mathrm{}}^3{}_{}{}^2{}_{}{}^{}D\mathrm{}\left(4d\right)\mathrm{}{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ is assigned to the missing ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ term, and the ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ is located at 196 500 ${\mathrm{cm}}^{-1\mathrm{}}$. These reassignments are consistent with expected configuration-interaction effects. As a result the low-energy doublet in the Kr $M_{4,5}-NN$ spectrum is identified as the $M_{4,5}-N_1{N}_1$ transition, in agreement with recent energy calculations. Calculations were made to reproduce the observed satellite spectra $\mathrm{}\left(3d\right)\mathrm{}\left(4p\right)\mathrm{}\to {\mathrm{}\left(4p\right)\mathrm{}}^3$ and $\mathrm{}\left(3d\right)\mathrm{}\left(4p\right)\mathrm{}\to \mathrm{}\left(4s\right)\mathrm{}{\mathrm{}\left(4p\right)\mathrm{}}^2$, with both a statistical distribution of shakeoff and Auger decay of $3p$ vacancies, as population mechanisms for the $\mathrm{}\left(3d\right)\mathrm{}\left(4p\right)\mathrm{}$ configuration. It was found that the $\mathrm{}\left(3d\right)\mathrm{}\left(4p\right)-{\mathrm{}\left(4p\right)\mathrm{}}^3$ calculations with an initial $\mathrm{}\left(3d\right)\mathrm{}\left(4p\right)\mathrm{}$ population distribution from Auger decay of $3p$ vacancies were in excellent agreement with experiment, while the statistically distributed shakeoff hypothesis leads to relatively poor agreement. For the $\mathrm{}\left(3d\right)\mathrm{}\left(4p\right)\mathrm{}\to \mathrm{}\left(4s\right)\mathrm{}{\mathrm{}\left(4p\right)\mathrm{}}^2$ neither calculation is in agreement with experiment, because of the neglect of configuration interaction. The summed calculated intensity appears to agree with the summed measured intensity for an initial $\mathrm{}\left(3d\right)\mathrm{}\left(4p\right)\mathrm{}$ population produced by Auger decay of $3p$ vacancies. Statistically distributed shakeoff leads to a summed intensity far in excess of the summed measured intensity. We conclude that statistically distributed shakeoff must have a probability significantly less than 5%, in contrast to recent calculations indicating 10% shakeoff.

A matrix variational calculation has been done for electron scattering by atomic O, which includes $2s^{2}2p^4$, $2s2p^5$, and $2p^6$ target configurations and all possible single excitations of the $2p$ orbital. Integral and differential cross sections are reported for elastic and inelastic scattering for energies up to the first $n=3\mathrm{}$ excitation threshold. The full effects of long-range polarization and short-range correlation appear to be nearly completely accounted for. No low-lying resonances are observed.

Cl $K$ x-ray-production cross sections have been measured in single collisions of 0.1-1.5-MeV/amu Cl ions with gas targets of He, ${\mathrm{N}}_2$, Ne, Si${\mathrm{H}}_4$, ${\mathrm{H}}_2$S, HCl, Ar, Kr, and Xe. Cross sections for Ne $K$, Si $K$, S $K$, Ar $K$, Kr $L$, and Xe $L$ x-ray production and yields for Xe $M$ x rays were also obtained. Similar measurements for both Cl and S ions were made at one velocity as a function of projectile charge state $q$ for $5\le q\le 11$. Except at the highest energies, projectile $K$ x-ray-production cross sections are nonmonotonic as a function of target atomic number $Z_2$. Anomalously high target and projectile cross sections occur in the symmetric region: $Z_2\simeq 17$. For all x-ray lines, the cross sections show an increase with increasing $q$ at constant projectile velocity, with the rate of increase being greatest in the symmetric region. The experimental results indicate the importance of one-step molecular processes suggested by Meyerhof in producing $K$ vacancies. The $2p\sigma -2p\pi$ transition may be of importance when initial $2p$ vacancies are carried into $K$-vacancy-producing collisions. The large cross sections for both target and projectile in nearly symmetric collisions gives evidence for $K$-vacancy transfer between collision partners.

Triple- and double-photon inelastic and elastic scattering is observed from diamond upon the passage of intense picosecond laser pulses. The spectrum and intensity of the nonlinear scattering is measured. The triple-photon scattering is interpreted in terms of the hyper-Raman and hyper-Rayleigh effects. The value for the three-photon Raman hyperpolarizability is estimated from the experiment.

A detailed theoretical calculation is carried out for the photoionization of lithium at low energies within the framework of Brueckner-Goldstone perturbational approach. In this calculation extensive use is made of the recently developed multiple-basis-set technique. Through this technique all second-order perturbation terms, plus a number of important classes of terms to infinite order, have been taken into account. Analysis of the results enables one to resolve the discrepancies between two previous works on this subject. The detailed calculation also serves as a test on the convergence of the many-body perturbation-expansion approach.

In recent work, the existence of stationary bounds on bound-state matrix elements for rather broad classes of quantum-mechanical operators was used to obtain a stationary upper bound on the scattering length for the collision of positrons with atoms whose target wave functions are not precisely known. This was done by obtaining calculable stationary bounds on the unknown matrix elements which appear in the formal expression for the bound on the scattering length. This method is extended in the present paper to electron-atom scattering for which it is necessary to obtain-in addition to bounds of the previous type-stationary bounds on the various exchange integrals. These latter cannot be obtained by means of techniques previously described. New techniques are presented for deriving such bounds, which are then used to obtain rigorous stationary upper bounds on the scattering length for the collisions of electrons with helium and with atoms heavier than helium.

We have calculated the locations of the Regge poles for an actual interatomic potential by following the semiclassical formulation. For negative energies, this formulation is equivalent to the Bohr-Sommerfeld quantization condition. For positive energies there are three complex turning points; use of linear and parabolic connection formulas yields a semiclassical quantization condition for the poles. The poles are found to lie symmetrically along lines in the first and third quadrants of the angular-momentum plane. The locations of the poles at a given energy and the motion of these poles as the energy changes are presented. Remler has shown that Regge poles provide a convenient way of parametrizing experimental differential cross sections. We discuss the relation between this parametrization and the present results.

The $2s$ and $2p$ excitation cross sections for electron scattering on hydrogen in the energy range from threshold to 50 eV are calculated by two similar methods. The distorted-wave method using Hartree-Fock continuum wave functions in the frozen-core approximation is applied. The effect of calculating the distorted waves in the potential of the initial or final state is investigated. The imaginary part of the optical potential, or self-energy of the single-particle Green's function, is also calculated in lowest order by the use of many-body diagrams. Comparison is made with recent experimental results.