The coincidence technique has been employed to determine the yield of $L$ x-rays emitted following ${\mathrm{Ar}}^{+}$ + Ar collisions of known incident energy $T_0$, scattering angle $\theta =14\mathrm{}°$, and scattered ion charge $m$. The range of $T_0$ studied, 50 to 575 keV, corresponds to a distance of closest internuclear separation $r_0$ from 0.18 to 0.03 Å. As in the case of our earlier ion-Auger-electron coincidence experiments on ${\mathrm{Ar}}^{+}$ + Ar over this range, the present work uncovers evidence for two different $L$-vacancy-creating processes. The first process has a threshold at $r_0=0.25\mathrm{}$ Å and is the result of the transfer of two electrons out of the $4f\sigma$ molecular orbital (MO). The second process, which appears when $r_0$ is made less than 0.13 Å, is due to rotational transitions of up to six electrons from the $3d\pi$ and $3d\sigma$ MO's into the $3d\delta$ MO. We find that there is a large increase in x-ray fluorescence associated with the $3d\pi ,3d\sigma \to 3d\delta$ transition, an increase which is considerably in excess of that expected from available estimates. A qualitative explanation of this phenomenon is offered that takes into account combinations of long-lived autoionizing states involving outer-shell electrons, preferential pumping of $L$ electrons up to the $3d$ radiative level, and finally, outer-shell-electron depopulation by prior Auger transitions. This interpretation is also consistent with the differing ion-charge x-ray-yield correlations that we find are characteristic of the $4f\sigma$ and $3d\pi ,3d\sigma$ processes.

Cross sections for the photoproduction of electron-positron pairs in the field of atomic electrons are calculated for all elements and photon energies above 10 MeV. A fit with an analytic formula provides a set of coefficients for each element from $Z=1\mathrm{}$ to $Z=100\mathrm{}$.

Relative beam-foil level excitations in hydrogen and helium have been studied as a function of the foil thickness using incoming beams of ${\mathrm{H}}^{+}$, $\mathrm{H}_2^{}{}_{}{}^{+}$, $\mathrm{H}_3^{}{}_{}{}^{+}$, ${\mathrm{D}}^{+}$, $\mathrm{D}_2^{}{}_{}{}^{+}$, $\mathrm{D}_3^{}{}_{}{}^{+}$, $\mathrm{HD}_2^{}{}_{}{}^{+}$, and He${\mathrm{H}}^{+}$, thus varying the average distance between the fragments at the exit of the foil. Large changes in level excitation are observed in many cases for molecular projectiles when using thin foils. For molecular-hydrogen projectiles the same enhancement of excitation is found for all hydrogen levels studied. However, a remarkable difference is found for the heteronuclear projectile He${\mathrm{H}}^{+}$. In that case, the uniform enhancement for different hydrogen levels vanishes. The results are discussed.

Inelastic-collision processes in fine-structure-changing collisions have been studied by selective stepwise excitation and observation of the resulting fluorescence. Hereby, the effect of ground-state rubidium atoms colliding with excited-state rubidium atoms was investigated. The ground-state density was changed by three orders of magnitude by performing the measurements over the temperature range of 75 to 200 °C. The cross section for fine-structure-changing collisions [i.e., $\mathrm{Rb}\left(6^2{D}_{\frac{5}{2}}\right)+\mathrm{Rb}\left(5^2{S}_{\frac{1}{2}}\right)\to \mathrm{Rb}\left(6^2{D}_{\frac{3}{2}}\right)+\mathrm{Rb}\left(5^2{S}_{\frac{1}{2}}\right)$] is ${\sigma }_{\mathrm{fs}}=(1.0\mathrm{}\pm 0.6)\times {10}^{-13\mathrm{}}$ ${\mathrm{cm}}^2$. The cross sections for transfer out of the fine-structure doublet [i.e., $\mathrm{Rb}\left(6^{2}D\right)+\mathrm{Rb}\left(5^2{S}_{\frac{1}{2}}\right)\to \mathrm{states}\mathrm{other}\mathrm{than}\mathrm{Rb}\left(6^{2}D\right)$] is ${\sigma }_{\mathrm{tr}}=(3.8\mathrm{}\pm 0.6)\times {10}^{-13\mathrm{}}$ ${\mathrm{cm}}^2$. It is demonstrated that for the intermediate excited rubidium states, both the fine-structure-changing and transfer cross sections are of the order of the geometrical cross section of the excited rubidium states.

The polarization and angular distribution of fluorescence radiation subsequent to inner-shell photoionization in atoms are presented here in the important special case that dynamic amplitudes are calculated in $\mathrm{LS}$ coupling taking full account of anisotropic electron-ion interactions. The resulting formulas require for their evaluation no more dynamical information than is usually obtained in an $\mathrm{LS}$-coupling calculation of the photoionization cross section. Exact geometrical relationships which are obscured in more general treatments become apparent in an $\mathrm{LS}$-coupling formulation. Thus it is shown that in $\mathrm{LS}$ coupling the fluorescence resulting from photoionization of an $s$ subshell in an atom having an initial orbital angular momentum $L_0=0\mathrm{}$ has an analytically known constant polarization. Analytic predictions for the linear polarization of fluorescence radiation resulting from ionization of atoms with $L_0=0\mathrm{}$ by unpolarized light are given and illustrated explicitly for nitrogenlike atoms. Experimental measurements of fluorescence polarizations which deviate from these theoretically exact predictions in $\mathrm{LS}$ coupling are thus a sensitive probe of relativistic and certain weak electron correlation interactions.

We have measured the partial cross sections for ionizing neutral helium to ${\mathrm{He}}^{+}$ in the $2s$ and $2p$ levels from threshold to 130 eV. Near threshold the data favor the close-coupling calculations of Jacobs and Burke rather than the many-body calculations of Chang, in contrast to the total $N=2\mathrm{}$ cross section. We have also made a detailed study of the autoionizing resonances leading to the $N=3\mathrm{}$, $N=4\mathrm{}$, and $N=5\mathrm{}$ thresholds. We present resonance parameters for the $N=3\mathrm{}$ series. The energies of the resonances agree well with calculated and experimental values, but the widths show substantial disagreement with calculations.

We point out several possible observable features of quadrupole contributions to intermediate- and low-energy photoelectron angular distributions $\frac{d\sigma }{d\Omega }$, including zeros (Cooper minima) in the quadrupole-matrix elements. These features result in deviations from the dipole symmetry of $\frac{d\sigma }{d\Omega }$ about 90° (under $\theta \to \pi -\theta$) and include an oscillation with energy in distributions which vary from peaking forward and backward of 90°. The quadrupole contribution to photoelectron angular distributions can remain significant even for outer shells in the low-energy region, particularly when there are zeros (Cooper minima) in the dominant dipole-matrix elements. As an example we discuss the photoelectron angular distribution from the $5s$ subshell of tin and estimate the magnitudes of the deviations from symmetry which would be the experimental signatures of these features.

When a beam of spin-polarized metastable ${\mathrm{He}}^{+}2s_{\frac{1}{2}}$ ions is quenched by an electric field $\overrightarrow{\mathrm{E}}$, the emitted radiation intensity contains an asymmetry term proportional to $\left(\hat{k}·\hat{E}\right)(\overrightarrow{\mathrm{P}}·\hat{k}\times \hat{E})$ where $\overrightarrow{\mathrm{P}}$ is the spin-polarization vector and $\hat{k}$ is the direction of observation. The resulting asymmetry is nearly proportional to the level width of the $2p_{\frac{1}{2}}$ state in ${\mathrm{He}}^{+}$. The experiment provides the first observation of the asymmetry. The measured asymmetry is (0.007 69±0.000 10) in agreement with the theoretical value 0.007 618 and corresponds to a lifetime ${\tau }_{2p}=(0.988\mathrm{}\pm 0.013)\times {10}^{-10\mathrm{}}$ sec.

The anticrossing spectra of the $n=6,7,8\mathrm{} {}_{}{}^1{}_{}{}^{}D-{}_{}{}^3{}_{}{}^{}D$ states of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ have been observed. From these measurements precise values of the electrostatic singlet-triplet separation of these states have been obtained and are found to differ systematically from the accepted values of the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ singlet-triplet separation by approximately 34 MHz. We have investigated mass-dependent contributions to both the energy-level structure and the magnetic-tuning characteristics of the states of interest. We have found no mechanism that can explain such a large difference in the electrostatic-energy separation of the singlet and triplet $D$ states between the two helium isotopes.

Muonic x-ray intensity ratios [$\frac{I\left(\mathrm{Ki}\right)\mathrm{}}{I\left(K\alpha \right)}$] have been measured for 21 pure elements in the range $4\le Z\le 48$. The cyclic variation of these ratios with $Z$ is clearly seen to follow the pattern of the periodic table of the elements over this range. The product of $\frac{I\left(K\beta \right)}{I\left(K\alpha \right)}$ and nearest-neighbor distance in the pure-element lattices varies approximately linearly with $Z$ within each period.

The relative populations of the $M_J$ magnetic substates of ${\mathrm{Ar}}^{-}$ formed by electron capture from ${\mathrm{O}}^{-}$, ${\mathrm{H}}^{-}$, and ${\mathrm{D}}^{-}$ are analyzed in terms of the $M_L$ populations. The analysis correlates a dip in the $J=\frac{3}{2},M_J=\frac{1}{2}$ population with a peak in the $J=\frac{3}{2},M_J=\frac{3}{2}$ population. Above 2.5-keV incident-ion energy the populations formed by capture from ${\mathrm{H}}^{-}$ are in accord with the hypothesis of spin independence in the formation of the states, but 10% departures are noted below 2.5 keV.

We report measurements of the following spontaneous-emission rates in atomic thallium: $A(6\mathrm{}{D}_{\frac{3}{2}}-7P_{\frac{1}{2}})=(5.97\mathrm{}\pm 0.78)\times {10}^5{\mathrm{s}}^{-1\mathrm{}}$, $A(7\mathrm{}{P}_{\frac{1}{2}}-7S_{\frac{1}{2}})=(1.71\mathrm{}\pm 0.07)\times {10}^7{\mathrm{s}}^{-1\mathrm{}}$, $A(7\mathrm{}{P}_{\frac{3}{2}}-7S_{\frac{1}{2}})=(2.37\mathrm{}\pm 0.09)\times {10}^7{\mathrm{s}}^{-1\mathrm{}}$, and $A(8\mathrm{}{P}_{\frac{3}{2}}\to \mathrm{all})=(9.2\mathrm{}\pm 1.0)\times {10}^6{\mathrm{s}}^{-1\mathrm{}}$. These results are compared to predictions of theoretical models and lend support to calculations of the recently measured parity-nonconserving circular dichroism of the $6P_{\frac{1}{2}}-7P_{\frac{1}{2}}$ forbidden $M1\mathrm{}$ transition in thallium.

Considering Stark-effect applications in atomic physics and especially in plasma spectroscopy, we established several formulas for spectral line intensity, energy level, and ionization rate. In particular, by means of the systematic numerical check on an intermediate formula [Eq. (36d) in the text], we show that the ionization rate may be expressed completely in terms of the energy level according to $\Gamma (n_1,n_2,m,\lambda )=\frac{1}{2\pi }\frac{\partial E(n_1,n_2,m,\lambda )}{\partial n_2}\exp [-K(n_1,n_2,m,\lambda \left)\right],$ where $\lambda ={(n_1+n_2+m+1)}^3\frac{F}{4Z^3}$, and $K(n_1,n_2,m,\lambda )=\frac{1}{6\lambda }+\ln \frac{{\lambda }^{2n_2+m+1\mathrm{}}{n}_2!(n_2+m)!}{2\pi }+3(n_2-n_1)-\frac{1}{6}\int 0^{\lambda }\left[n^3\frac{\partial E(n_1,n_2,m,{\lambda }^{\prime })}{\partial n_2}-1+6(2\mathrm{}{n}_2+m+1){\lambda }^{\prime }\right]\frac{d{\lambda }^{\prime }}{{\lambda }^{\prime 2}}.$ The two factors on the right-hand side of (i) are interpreted, respectively, as the atomic-electron-collision frequency and transmission coefficient through the potential barrier created by the electric field $F$. By using the ninth-order perturbation series for resonance energy $E(n_1,n_2,m,\lambda )$ it is found that (i) is in fairly good agreement with the most recent numerical solutions of the Schrödinger equation. A discussion follows in connection with other analytical and empirical formulas.

Recently the measured proton-induced C $K$-shell ionization probability was found to vary significantly near the 0.461-MeV $j=\frac{1}{2}+$ elastic resonance in ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$. Since the resonance was so wide that time-delay effects on $K$-shell ionization should be very small, it was hypothesized that this effect was due to the exchange of angular momentum between the projectile motion and electron. Assuming a potential description of the nuclear scattering, we make a completely quantum-mechanical calculation of the ionization probability in the distorted-wave Born approximation and show that angular momentum effects do not account for these results. We also show how the amplitude for monopole excitation is augmented by the "shake-off" or "sticking" term found in the semiclassical theory of Ciocchetti and Molinari, and display the formal correspondence between the semiclassical and quantum-mechanical theories. Numerical calculations of the ionization probability show only a slight dip at the minimum in the $p-\mathrm{C}$ elastic cross section, opposite in sign and of much smaller magnitude than the reported variation.

Auger-electron spectra have been measured following excitation of 100-500-keV phosphorus ions by thin carbon foils. The spectra are rich in structure mostly due to Augersatellite transitions. The composition of the Auger spectrum is interpreted with the aid of nonrelativistic Hartee-Fock calculations. In the low-energy portion, several lines could be identified. Based on calculated energies for groups of Auger transitions, the high-energy part can also be interpreted. We observe a general increase of the highenergy feature—distinct peaks as well as the gross structure—with decreasing projectile velocity. Two processes may be responsible for this variation: the enhanced production of double $L$ vacancies and the increased capture of target electrons into excited levels of the projectile ions.

In this work the electron cyclotron maser oscillator interaction is analyzed in an open resonator configuration with a magnetostatic field along the resonator axis. One of the salient features of this configuration for generating high-power short-wavelength radiation is its ability to mode select. Both the linear and the nonlinear analysis are developed for an arbitrary value of the refractive index $n=\frac{\mathrm{kc}}{\omega }$. Specializing to luminous waves, $n\to 1$, it is shown that the linear-gain curve is symmetric about synchronism and that instability can occur even at exact synchronism, for appropriate initial beam distributions. The nonlinear integrals of the motion are obtained, indicating that the total energy is available for conversion. The nonlinear evolution is described by a single differential equation, and the nonlinear efficiency is shown to depend on only four combinations of the beam, field, and resonator parameters. Nonlinear efficiencies up to 15% can be achieved. For a relativistic beam, a substantial frequency upshift is possible, with efficiencies up to 10%. Efficiency enhancement is possible, e.g., by the introduction of a two-stage resonator. In such a configuration, efficiencies exceeding 30% are calculated. Finally, the requirements for beam temperature and mode selectivity are found not to be particularly restrictive.

A novel mechanism is proposed for optical bistability by utilizing the effect of interference which occurs when two levels are coupled by a one-photon resonance and by a two-photon resonance. The resulting bistability does not require atomic saturation, so the bistability can be observed at relatively low incident intensities, and the mechanism is essentially Doppler free, since it occurs by a two-photon process involving absorption of counterpropagating beams of the same frequency. A significant feature is that two-photon bistability can be controlled not only by the magnitude of the field of the one-photon resonance but also by its phase, and an oscillation or amplification of the field of the two-photon resonance can be observed under certain conditions by the mechanism of the parametric interaction of the field of the one-photon resonance and the field of the two-photon resonance through a nonlinear medium.

Basic features of stimulated Čerenkov radiation are investigated by means of two different quantum-mechanical approaches: (a) a solution of the Klein-Gordon equation in the presence of a plane wave in a refractive medium, and (b) a classical current interacting with a quantized radiation field, with recoil corrections introduced by hand. Both approaches lead to identical results. The electron energy spread is obtained in perfect agreement with earlier classical calculations which have been indirectly verified by a recent experiment. The relation between gain and spread turns out to be more favorable than for the conventional free-electron laser.

A theory of modulation of optical bistability of a main (signal) beam by an additional (control) beam is presented. It is supposed that the mirrors composing a Fabry-Perot cavity are highly reflective to the signal beam but transparent to the control beam. We show that the property of a medium in the cavity, and hence the transmission of the signal beam through the cavity, is modulated by the control beam which changes the dielectric susceptibility of the intracavity medium. Amplification of the signal beam occurs in the limit of a strong control beam. The process can be viewed as a parametric transfer of energy between the signal beam and the control beam with the nonlinear medium providing the nonlinear susceptibility that couples the beams. In addition, multibistability in the transmission characteristics of the signal beam is predicted and attributed to the saturation effect of the multiphoton processes.

The canonical partition function for classical many-body systems is transformed so that the temperature-independent packing statistics and the thermal excitations are uniquely separated. This requires classification of particle configurations according to multidimensional potential-energy minima that can be reached by steepest-descent paths ("quenches"). Such classifications have been constructed for several starting configurations in the solid, fluid, and coexistence phases of the two-dimensional Gaussian core model. These quenches reveal a remarkable degree of polycrystalline order hidden within the fluid phase by "vibrational" distortion, and that order appears to have a large correlation length. The results suggest that melting hinges upon defect softening in the quenched packings, and a crude "theory" of melting for the Gaussian core model is developed in the Appendix.