The two-photon ionization cross section for the neutral argon atom is calculated. A double perturbation expansion in the Coulomb correlations and the atom-radiation-field interaction is made. Contributions from intermediate states are obtained by direct summation over Hartree-Fock bound and continuum single-particle states. The effects of electron correlations and photon-radiative corrections are investigated. Comparison is made with previous theoretical methods.

A modification of the Born approximation is employed to compute the differential cross section for excitation of the $2s$ and $2p$ states of hydrogen by electrons at energies of 100, 200, 500, 1000, and 1500 eV. The modification consists of expanding the exact wave function of the total Hamiltonian in terms of Coulomb functions as opposed to plane waves in the normal Born approximation. The differential cross sections thus obtained are orders of magnitude larger at back angles and thus in much better agreement with experiment.

The x-ray production cross sections of the total $L$ shell and of the $L\alpha$, $L\beta$, $L\gamma$, $\mathrm{Ll}$, and $L\eta$ transitions have been measured for Au, Bi, and U for proton impact over the energy range from 1.0 to 4.5 MeV and for ${}_{}{}^3{}_{}{}^{}\mathrm{He}_{}^{+}{}_{}{}^{}$ impact from 3.0 to 9.0 MeV. The measured x-ray production cross sections and the ratios of the x-ray production for various transitions are compared with calculations based on the plane-wave Born approximation (PWBA) and the binary-encounter approximation (BEA). Generally, the PWBA is in better agreement with the observed results. Various correction factors to these simplified theories are also estimated and discussed. The ratios of the x-ray production for protoń impact to that for helium-ion impact, at equal velocities, deviate systematically from the theoretical ${\mathrm{Z}}_1^2$ dependence. This behavior is discussed in terms of the nuclear repulsion for the projectile, the change in binding energy of the target electrons, and the polarization of electron orbit. It is shown that the observed total $L$-shell ionization cross sections for various elements taken from the present work and other works can be represented by a single smooth curve, which at higher energies is in good agreement with the BEA curve of Garcia derived for the $K$-shell ionization, though the experimental values at lower energies are considerably higher than the theoretical predictions.

The method of moments is used to determine a functional form of the induced polarizability increment $\beta$, which gives rise to collision-induced light scattering from compressed C${\mathrm{F}}_4$. Based upon the zeroth and second moments, two expressions are found to be acceptable: $\beta \mathrm{}\left(x\right)=6\mathrm{}{\alpha }^2{\sigma }^{-3\mathrm{}}(x^{-3\mathrm{}}-2.85\mathrm{}{x}^{-4.05\mathrm{}})$ and $\beta \mathrm{}\left(x\right)=6\mathrm{}{\alpha }^2{\sigma }^{-3\mathrm{}}(x^{-3\mathrm{}}+0.757\mathrm{}{x}^{-8.51\mathrm{}})$, where $x=\frac{r}{\sigma }$. Both expressions result in calculated fourth moments consistent with the experimental estimate. This is the first experimental evidence in which a positive non-dipole-induced-dipole term is shown to be a possibility. In other respects, however, the results are similar to those obtained from rare-gas spectra.

Diffraction losses in the optical cavity of a He-Ne gas laser are experimentally studied for the $\mathrm{TE}{\mathrm{M}}_{q00\mathrm{}}$, $\mathrm{TE}{\mathrm{M}}_{q10\mathrm{}}$, and $\mathrm{TE}{\mathrm{M}}_{q01\mathrm{}}$ transverse modes by changing the size of a square aperture placed in front of one of the laser mirrors. By measuring the threshold oscillation current $I_s$ as a function of the aperture size $2a$, the total losses in the cavity can be determined. These losses are related to the electronic excitation rate of the He $2{}_{}{}^1{}_{}{}^{}S$ metastable state at the threshold of oscillation current and are used to evaluate the inelastic electron excitation cross section of the He $2{}_{}{}^1{}_{}{}^{}S$ state. The experimentally determined cross section is in very close agreement with the published absolute cross-section measurements.

Differential and integral electron scattering cross sections have been measured and calculated for the transitions $1{}_{}{}^1{}_{}{}^{}S\to 3{}_{}{}^1{}_{}{}^{}S, 3{}_{}{}^3{}_{}{}^{}S, 3{}_{}{}^3{}_{}{}^{}P$ and for the experimentally unresolved transitions $1{}_{}{}^1{}_{}{}^{}S\to 3{}_{}{}^1{}_{}{}^{}P, 3{}_{}{}^{1,3}{}_{}{}^{}D$ in helium. Measurements were made relative to both the $2{}_{}{}^3{}_{}{}^{}P$ and $2{}_{}{}^1{}_{}{}^{}P$ transitions at incident electron energies of 29.2 and 39.7 eV, and over the angular range 5-136°. The $n=3\mathrm{}$ relative differential cross sections (DCS) were normalized to the absolute scale by utilizing known normalized absolute DCS for the $2{}_{}{}^3{}_{}{}^{}P$ and $2{}_{}{}^1{}_{}{}^{}P$ transitions. The theoretical calculations were carried out in the first-order manybody theory of Csanak, Taylor, and Yaris. Comparisons are also made of the present measurements and calculations with other calculations carried out for the $3{}_{}{}^1{}_{}{}^{}S$, $3{}_{}{}^1{}_{}{}^{}D$, and $3{}_{}{}^1{}_{}{}^{}P$ states in the Born and several Ochkur-like approximations. The theoretical origins in several theories of the intriguing sharp minimum in the $1{}_{}{}^1{}_{}{}^{}S\to 3{}_{}{}^1{}_{}{}^{}S$ DCS are discussed.

The photoelectron asymmetry parameter $\beta$ in $\mathrm{LS}$ coupling is obtained as an expansion into contributions from alternative angular-momentum transfers $j_t$. The physical significance of this expansion of $\beta$ is shown to be that (i) the electric-dipole interaction transfers to the atom a characteristic single angular momentum $j_t=l_0$, where $l_0$ is the photoelectron's initial orbital momentum, whereas (ii) angular-momentum transfers $j_t\ne l_0$ indicate the presence of anisotropic (i.e., term-dependent) interaction of the outgoing photoelectron with the residual ion. For open-shell atoms the photoelectron-ion interaction is generally anisotropic; photoelectron phase shifts and electric-dipole matrix elements depend on both the multiplet term of the residual ion and the total orbital momentum of the ion-photoelectron final-state channel. Consequently, $\beta$ depends on the term levels of the residual ion and contains contributions from all allowed values of $j_t$. These findings contradict the independent-particle-model theory for $\beta$, which ignores the final-state electron-ion interaction and to which our expressions reduce in the limiting cases for which only $j_t=l_0$ is allowed, namely (a) spherically symmetric atoms (e.g., closed-shell atoms) and (b) open-shell atoms for which the electron-ion interaction is isotropic (e.g., very light elements). Numerical calculations of the asymmetry parameters and partial cross sections for photoionization of atomic sulfur are presented to illustrate the theory and to demonstrate the information on electron-ion dynamics that can be obtained from the theoretical and experimental study of $\beta$ for open-shell atoms.

$K$-shell x-ray production cross sections and $\frac{K\beta }{K\alpha }$ ratios have been measured for thin targets of Ti, V, Cr, Fe, Ni, Cu, Zn, Ga, As, Se, Rb, Sr, and Y for 0.5- to 2.5-MeV alpha particles. The experimental values are compared to the nonrelativistic plane-wave Born approximation (PWBA), the binary-encounter approximation, and the PWBA with binding energy and Coulomb deflection corrections. The PWBA with corrections provides the best agreement with the experimental cross sections.

A wide class of problems is considered involving the interaction of multilevel atoms with classical time-dependent fields switched on at a definite time. It is shown that the exact time-dependent Green's function can be written as the particular solution to an inhomogeneous differential equation involving derivatives with respect to the external field variables. Asymptotic expansions are discussed and analytic solutions found for several cases. The time and frequency distributions of radiation emitted by a field-perturbed atom are calculated by including the radiation field as a first-order perturbation.

We show that a measurement of the anisotropy in the angular distribution of the quenching radiation emitted by metastable hydrogen and deuterium atoms in an electric field can be used to determine the Lamb shift to an accuracy of at least ±0.1%. The method can be extended to the hydrogenic ions, where it offers several advantages over the quench-rate technique used in earlier measurements. The experiment is interpreted by means of a nonperturbative theory of the quenching process, which includes hyperfine structure and time-dependent effects. In the limit of zero field strength, the anisotropies of H and D are measured to be 0.139 01 ± 0.000 12 and 0.141 21 ± 0.000 14, while the theoretical values are 0.139 078 and 0.141 30, respectively. The corresponding Lamb shifts are 1057.3 ± 0.9 MHz and 1058.7 ± 1.1 MHz.

The time development of the normally ordered generating functional of a light beam interacting linearly with a collection of two-level atoms is determined exactly. Rigorous conclusions on changes of the statistical properties of the beam are drawn. It is shown that the field after the interaction appears to be the superposition of a thermal field and of a field statistically similar to the initial one.

We consider the photon-counting statistics with polarized thermal light having arbitrary rational spectral profile. The method is illustrated for a light beam having a two-peak symmetric Lorentzian spectrum. The associated integral equation is converted into a differential equation and the eigenvalues are determined. Using the standard techniques of contour integration, an explicit expression is obtained for the generating function valid for an arbitrary value of the counting interval.

A class of molecular two-photon processes, occurring under transient or steady-state conditions, is analyzed exactly for certain cases using a density-matrix formalism. Our results are relevant to the recently observed phenomena of transient coherent Raman beats and steady-state two-photon absorption of oppositely directed laser beams. Lowest-order perturbation theories have shown that these processes are insensitive to the Doppler effect, and consequently the linewidth is unaffected by Doppler broadening and by elastic collisions that change molecular velocity. The solutions presented here are of the same form for the Raman and two-photon problems and reveal significant power-dependent frequency shifts and line broadening that correct the ideal Doppler-free solutions. For the transient case, we assume a molecular three-level quantum structure that can be switched in or out of optical resonance with cw laser radiation by means of a pulsed dc Stark field, but the solutions also apply when resonant optical pulses are introduced. During the resonant condition when the Stark pulse is on, the three levels are prepared in coherent superposition, and during the nonresonant condition following the Stark pulse, the laser field(s) stimulates the coherently prepared sample in a transient two-photon process. One of these processes, the Ramanbeat effect, has been observed in forward scattering, but the second one, transient two-photon emission, should be observable in backward scattering. Bloch-like equations are derived for this three-level problem that facilitate an exact pulse solution for state preparation. Following the pulse, transient decay is well-approximated by a perturbation calculation. For the steady-state case, an exact solution is also obtained and is of interest for continuous-wave spectroscopy or for transient experiments requiring an initial preparation of quantum states, prior to Stark switching. These solutions exhibit a power-dependent line broadening and a frequency shift of magnitude $\sim \frac{\Delta ({\alpha }^2-{\beta }^2)}{({\Delta }^2+\frac{1}{T_2^2})}$, in agreement with our earlier estimate, where $\alpha$ and $\beta$ are the Rabi flopping frequencies for the two intermediate transitions and $\Delta$ is the off-resonance tuning behavior for one of them.

Retarded dispersion forces are calculated at finite temperature in the theory of classical electrodynamics with classical electromagnetic zero-point radiation. Expressions are given at all separations for the forces between a polarizable particle and a conducting wall and between two polarizable particles where the particles are represented by electric dipole oscillators immersed in thermal radiation. Also given are the simple expressions holding in the unretarded short-distance limit, and in the asymptotic large-distance limit. At any finite nonzero temperature $T$, the asymptotic large-distance Van der Waals force between two polarizable particles separated by a distance $R\gg \frac{\hslash c}{\mathrm{KT}}$ is given by the potential $U\left(R\right)=-\frac{3{\alpha }^2\mathrm{KT}}{R^6}$ rather than the Casimir-Polder form for zero temperature, $U\left(R\right)=-\left(\frac{23}{4\pi }\right)\frac{{\alpha }^2\hslash c}{R^7}$, where $\alpha$ is the static polarizability of each particle. Also the $R^{-6\mathrm{}}$ form holds at high temperatures for any fixed separation. The finite-temperature analysis presented follows directly from earlier classical work at zero temperature since within the classical theory, classical zero-point radiation and classical thermal radiation are treated on the same footing. The classical calculations are easier than those of quantum-electrodynamic perturbation theory but have been shown generally to reproduce the quantum results for dipole-oscillator systems. The forces in the high-temperature limit are shown to agree with the results of classical statistical mechanics and with the use of the Rayleigh-Jeans law for the thermal radiation spectrum. The new results for polarizable particles fit nicely with earlier work by other authors on the finite-temperature corrections to the Casimir effect, the force between uncharged conducting parallel plates. It is emphasized that the force between conducting plates may be regarded as due to the classical boundary conditions at the conductors rather than to any discrete quantum aspects; the Rayleigh-Jeans spectrum also leads to a force between conducting plates and this force is in agreement with the high-temperature limit of previous calculations including zero-point radiation.

Optical harmonic generation and mixing in the gas phase has been proposed as a technique for the generation of coherent radiation in the vacuum ultraviolet and soft x-ray spectral region. At the high field strengths required by these processes the interaction between atoms and the electromagnetic field shows intensity-dependent resonances. In this paper we modify harmonic generation theory to include the effect of these frequency shifts. Closed-form expressions for generated dipole moment, absorption probability, and coherence length are presented. The most important consequences of frequency shifts on resonantly enhanced processes are that the pump laser must be tuned away from the small-field resonance frequency, that the conversion efficiency may saturate, and that the dispersion of the medium may change sign. As an example, the generation of 198-Å radiation by a five-photon mixing process in ${\mathrm{Li}}^{+}$ is considered.

It has been shown recently that molecular gas samples excited with coherent light can display a variety of transient phenomena, similar to those found in nuclear magnetic resonance. This article elucidates how these coherence effects can be used to isolate or unfold molecular collision mechanisms that normally remain hidden within the optical line shape. Elastic collisions, for example, are easily detected here in two-pulse photon echo experiments for a ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$${\mathrm{H}}_3$F vibration-rotation transition. The echo-decay function which provides a signature for the velocity-changing collision diffusion mechanism, is not just a simple exponential in time but exhibits an $\exp (-K{t}^3)$ contribution for short times and an $\exp (-\Gamma t)$ decay for long times. This behavior, which is unknown heretofore, contrasts with spin echoes in molecular liquids where Brownian motion leads only to the cubic decay law. An $\exp (-K{t}^3)$ behavior can be understood in terms of a solution of the Fokker-Planck equation which describes the effect of Brownian motion on echo decay. Such a treatment is valid for small phase excursions; in the case of a gas, this implies the Doppler phase factor $k\Delta u\tau \ll 1$, where $\overrightarrow{\mathrm{k}}$ is the propagation vector of light, $\Delta u$ is a characteristic velocity jump for a binary collision, and $\tau$ is the echo-pulse delay time. When $k\Delta u\tau \gg 1$ as in the long-time regime, the Fokker-Planck solution fails. We, therefore, present a new solution to the Boltzmann transport equation using a weak collision model and find agreement with the entire echo time dependence observed. The echo measurements indicate very small changes in longitudinal velocity per ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$${\mathrm{H}}_3$F-${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$${\mathrm{H}}_3$F collision, i.e., $\Delta u=85\mathrm{}$ cm/sec, thereby justifying the weak-collision model. The total elastic collision cross section is 430 ${\mathrm{\AA }}^2$. It follows that elastic collisions lead to velocity thermalization in a time of ∼5 sec when the ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$${\mathrm{H}}_3$F pressure is 1 mTorr. A comparison is also made of the ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$${\mathrm{H}}_3$F dephasing time ${\tau }_2$ in a coherent Raman beat decay, which is independent of velocity-changing collisions, with the longitudinal decay time $T_1$. Here, $T_1$ represents the molecule-optical interaction time, due largely to jumps in molecular rotation ($J$) and orientation ($M$) state, and is obtained from a delayed nutation measurement. The fact that the pressure dependent part of ${\tau }_2=T_1$ shows that $T_1$ is also independent of velocity diffusion. Futhermore, when a hole is burned in the Doppler distribution, population recovery must be due to inelastic rather than elastic collisions. Optical Carr-Purcell echoes, multiple pulse echoes, provide a direct measure of the ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$${\mathrm{H}}_3$F transverse dephasing time $T_2$ without the effect of elastic collisions while being sensitive to "phase interrupting collisions." Again, we find that $T_2=T_1$ so that phase interruptions are negligible. Had such a process dominated the two-pulse echo, an $\exp (-\frac{t}{T_2})$ damping would have been noticed with no $\exp (-K{t}^3)$ contribution. Thus, the present study covers several new aspects of molecular collisions. It represents the first detailed examination of velocity-changing collisions by coherence methods and without the complication of Doppler broadening.

A method for producing population inversion in a plasma for use as an x-ray or vacuum-ultraviolet lasing medium is described. The process involves a method for removal of the lower quantum levels of an ion, based upon their velocity, which results in an inversion between them and various upper levels. A possible device and its operating characteristics are also discussed.

A general theoretical treatment of multichannel photodetachment is presented, with application to ${\mathrm{Cs}}^{-}$ photodetachment from 14 800 to 15 600 ${\mathrm{cm}}^{-1\mathrm{}}$. The sharp and strong resonances near the first ${}_{}{}^2{}_{}{}^{}P$ states of the Cs atom, observed by Patterson et al., were reproduced by fitting eight physically meaningful parameters of a general theoretical framework. Predictions are also made concerning the branching ratios, the angular distribution, and the spin orientation of the detached electrons as well as the orientation of the excited neutral Cs atoms.

Bounds for contributions to transport coefficients in systems with convective mode coupling described by nonlinear Langevin equations are obtained by moment-theory summation of perturbation series. The results are illustrated with long-time tails in two-dimensional simple fluids and anomalous transport in binary critical solutions.

Existing experimental data on the compressibility, chemical potential, specific heat, and critical opalescence of C${\mathrm{O}}_2$ are analyzed to determine a parametric, scaling-law representation for the critical region. A representation of the form of the linear model of Schofield is found to be consistent with these data for scaling-law amplitudes $a=22\mathrm{}$, $b^2=g=1.30\mathrm{}$, exponents $\beta =0.347\mathrm{}$, $\gamma =1.22\mathrm{}$, $\alpha =0.09\mathrm{}$, and for a slowly varying (nondivergent) background. This representation corresponds approximately to the use of the mean range of local density correlations and of the macroscopic order as fundamental (parametric) variables to locate positions in thermodynamic space. The representation thus obtained is used to predict effects of gravity and the shape of contours of equal wave scattering close to the critical point. The predictions are investigated experimentally by studying the dependence of the scattering of laser light on chemical potential (height) and temperature. Satisfactory agreement is found to within the precision of the measurements. In addition, it is verified experimentally that contours of equal opalescence have the same shape as contours of equal mean relaxation time of local density fluctuations. This demonstrates that the relaxation time and the correlation length obey equivalent scaling-law homogeneity relationships close to the critical point. Some discrepancies among existing experiments and between experiment and theory are noted and discussed briefly. In particular, there remain unexplained discrepancies between the values of the critical-point exponents found here and those predicted by the Ising model.