The two interspersed series of resonances experimentally observed in $e$-${\mathrm{H}}_2$ scattering at 11-13 eV are identified as ${{}_{}{}^2{}_{}{}^{}\Sigma _g^{}{}_{}{}^{}}^{+}$ (series I) and ${}_{}{}^2{}_{}{}^{}\Delta _g^{}{}_{}{}^{}$ (series II), both in the configuration $\left(1s{\sigma }_g\right){\left(2p{\pi }_u\right)}^2$. This interpretation leads to a natural explanation that series I is strong while series II is weak in the $X{{}_{}{}^1{}_{}{}^{}\Sigma _g^{}{}_{}{}^{}}^{+}$ and in the $B{{}_{}{}^1{}_{}{}^{}\Sigma _u^{}{}_{}{}^{}}^{+}$ channels, and that the two series are equally strong in the $c{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ channel. Angular distributions for these resonances are computed and compared with experiment. Some old expressions are corrected, and new expressions are given for decay into the $c{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ channel.

The exact elastic optical potential is compared with an analogous potential in the adiabatic approximation, which is shown to give a lower bound on the scattering length. A variational-bound procedure is formulated to estimate the scattering length and also the scattering phase shift near the elastic threshold.

The magnetic field dependence of the cross sections for the disorientation of $6{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ cesium atoms, induced in Cs-He collisions, has been studied using Zeeman scanning techniques. A Cs-He mixture, contained in a fluorescence cell which was located in a magnetic field variable from 0 to 10 kG, was irradiated with the circularly polarized 8943-Å component of cesium resonance radiation in a direction parallel to the field, and the polarization of the resonance fluorescence was monitored in the backward direction in relation to the helium pressure and to the magnetic field strength. The cross sections, which are in good agreement with the results obtained previously at high and low magnetic fields, exhibit a variation with the magnetic field, which is in accordance with theoretical predictions.

$M$— x-ray spectra from foil-excited iodine beams between 40 and 62 MeV have been studied using a bent-crystal spectrometer. The prompt spectrum is so rich as to defy analysis, but the delayed spectrum exhibits a number of resolved lines. Electric quadrupole $4s\to 3d$ transitions are observed from metastable systems in the Ni i, Cu i, and Zn i isoelectronic sequences. Electric dipole $4p\to 3d$ transitions from states in these isoelectronic sequences also appear downstream. Transition energies and quadrupole lifetimes have been measured and are compared with the results of both relativistic and nonrelativistic calculations.

We have used the beam-gas technique to make the first reported measurements of the radiative lifetimes of six terms of S ii using visible transitions. A gas-jet target and a doubly-differentially-pumped gas cell were used to populate the excited levels of fast ions in an ${\mathrm{S}}^{+}$ beam. The weighted averages of the lifetimes and the standard deviations of the means in nanoseconds are as follows: for $4p{}_{}{}^4{}_{}{}^{}D_{}^o{}_{}{}^{}$, 10.25±0.07; $4p{}_{}{}^4{}_{}{}^{}P_{}^o{}_{}{}^{}$, 8.95±0.03; $4p{}_{}{}^4{}_{}{}^{}S_{}^o{}_{}{}^{}$, 5.46±0.05; $4p^{\prime }{}_{}{}^2{}_{}{}^{}F_{}^o{}_{}{}^{}$, 10.20±0.09; $4d{}_{}{}^4{}_{}{}^{}F$, 4.83±0.04; and for $4d{}_{}{}^4{}_{}{}^{}D$, 5.23±0.05. Total uncertainties are estimated to be in the range 5-10%.

The coherent scattering of 25- to 75-keV filtered fluorescence $K\alpha$ radiation from thin Sn, Sm, Ta, Pt, and Au foils has been measured absolutely. Values of atomic scattering factors in the range of $q=\frac{sin\left(\frac{\theta }{2}\right)}{\lambda }$ from 0.5 to 5.5 ${\mathrm{\AA }}^{-1\mathrm{}}$ were obtained for five different incident energies with scattering angles ranging from 45° to 135°. Our results are compared with Cromer's recent relativistic Dirac-Slater calculations with and without anomalous dispersion corrections. When plotted against the ratio of the target $K$-edge energy to the incident energy, differences between measured and calculated scattering factors follow the same general trend for all these high-$Z$ elements. Before they are corrected for dispersion, the calculated scattering factors for incident energies below the target $K$-absorption edge exceed the measured values, with the difference increasing in magnitude as the $K$ edge is approached. After the dispersion correction, the calculated values are all lower than the measured values by about 1.3 units. For incident energies above target $K$ edges, differences are generally small; but uncorrected calculated scattering factors also exceed the experimental values in a rapidly increasing manner as the $K$ edge is approached. After they are corrected for dispersion, calculated values are lower than measured values by about 0.6 units. Improved agreement can be obtained over the whole energy range for each element by arbitrarily reducing the magnitude of the real part of the dispersion correction term to that of the principal anomalous term.

The correlation between Doppler and collisional broadening has been considered in detail for radiation in which the lower level of the transition is broadened by the resonance interaction. It is found that rather than a single Voigt profile, the profile of the radiation is essentially a sum of Voigt profiles. Although the widths of these profiles vary by some 40%, the over-all line shape is very close to the single Voigt shape obtained when correlation effects are neglected.

Doppler-free two-photon transition between the $3s$, $J=2\mathrm{}$ metastable state and the $4d^{\prime }\left(\frac{5}{2}\right)$, $J=3\mathrm{}$ excited state of neon has been performed with a monomode cw dye laser. We have measured the hyperfine constants of the $4d^{\prime }\left(\frac{5}{2}\right)$, $J=3\mathrm{}$ state of ${}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}$ to be $A=-235.9\mathrm{}\pm 0.6$ MHz and $B=11\mathrm{}\pm 9$ MHz. The isotopic shifts for this two-photon transition are $E\left({}_{}{}^{22}{}_{}{}^{}\mathrm{Ne}\right)-E\left({}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}\right)=2780.0\mathrm{}\pm 2.5$ MHz and $E\left({}_{}{}^{21}{}_{}{}^{}\mathrm{Ne}\right)-E\left({}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}\right)=1452\mathrm{}\pm 6$ MHz. From these results, the possibility of a slight departure from the mass formula cannot be rejected.

A realistic model for resonant two-photon ionization of an atom is developed which can be solved exactly to give the ionization probability as a function of time, photon intensity, and a few atomic parameters. The exact solutions are compared to various commonly used perturbation results in order to ascertain the regions of validity of the perturbation calculations. It is shown that there are combinations of the parameters for which ionization rates cannot accurately describe the correct results, and that one commonly used perturbation development is not generally applicable to resonant two-photon ionization. Extension of the model to $\mathrm{}(n+m)\mathrm{}$-photon ionization having an $m$-photon resonance is discussed. The model is applied to two- and three-photon ionization in Cs.

The highly forbidden single-photon transition rate between the $2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ and $1{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ states of Hei has been measured in a radio-frequency He discharge. The population of metastables in the $2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ state was determined by Fabry-Perot interferometric profiles of absorption from the $2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ to the $4{}_{}{}^3{}_{}{}^{}P_{0,1,2}^{}{}_{}{}^{}$ states. High spectral resolution and precision ultraviolet radiometry were used to determine the brightness of the emission feature observed at 625.54 ± 0.05 Å, compared to the theoretical value of 625.56 Å. Because of the very low transition rate, this feature is weak, but it is shown that it is due to the $2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-1\mathrm{}{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ transition. The value for the radiative transition rate obtained in these experiments was 1.10 × ${10}^{-4\mathrm{}}$/sec, with a $2\sigma$ uncertainty of ± 30%. A comparison to the theoretical value of 1.27 × ${10}^{-4\mathrm{}}$/sec is given. The relevance of this work to the beam-foil experiments which have measured the $2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-1\mathrm{}{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ transition rate for high-$Z$ He-like ions is also discussed.

The predissociation in the $B\to A$ system of the deutroxyl radical has been reinvestigated. The experimental line shapes $P17\mathrm{}$, $P18\mathrm{}$, $R18\mathrm{}$, $P20\mathrm{}$, and $P21\mathrm{}$ of the (0,9) band of the system are analyzed in the framework of the Mahaux-Lejeune theory. The $P18\mathrm{}$ and $R18\mathrm{}$ transitions contain a $Q$ component. This lends support to existing calculations that a ${}_{}{}^4{}_{}{}^{}\Pi$ repulsive state is responsible for the predissociation. The transition probability to the continuum is not contant, but varies as the predissociated half-width.

We discuss some implications of the description of spontaneous emission of radiation which has been offered by Jaynes and his collaborators in their "neoclassical" extension of semiclassical electrodynamics. In particular, we examine the thermal-equilibrium condition of radiation interacting with a tenuous gas of atoms. We argue that rate equations may be used to describe the interaction of such atoms with the chaotic thermal radiation field. For this situation the neoclassical spontaneous emission rate is incompatible with the well-secured laws of Boltzmann and Planck. Experimental evidence bearing on the accuracy of those laws as well as on the accepted level population dependence of the induced emission rate is reviewed.

The neoclassical theory of the interaction of radiation with matter, introduced by its authors as a potentially viable alternative to quantum electrodynamics, is examined in the case of a multilevel atom interacting with blackbody radiation. The stationary statistical states of the atom and the field are derived, and two independently untenable results emerge. First, the stationary blackbody law turns out to be that of Rayleigh and Jeans, rather than that of Planck. Second, the mean energy of a harmonic oscillator, which interacts with the field only near a single frequency, turns out to be infinite. These results are discussed in the light of the neoclassical description of spontaneous emission.

The ${}_{}{}^3{}_{}{}^{}F$ metastable states of the $5d^2$ configuration of neutral barium have been observed in an atomic beam. As far as can be determined from the literature, these states have not been observed previously. Their $g$ factors have been measured, and the transmission characteristics of the apparatus indicate a lifetime of at least ${10}^{-3\mathrm{}}$ sec.

Time-resolved studies of the vacuum-uv emissions from neon and helium-neon mixtures were made using a single-photon counting technique. Excitation of the atoms was provided by a pulsed beam of 250-keV electrons. Measurements in neon were carried out at the wavelengths of the resonance states $\mathrm{Ne}\left({}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$, and $\mathrm{Ne}\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$. Collision coefficients for the destruction of $\mathrm{Ne}\left({}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$, $\mathrm{Ne}\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$, and $\mathrm{Ne}\left({}_{}{}^2{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$ atoms in neon were determined. The two-body collision coefficient for deexcitation of $\mathrm{Ne}\left({}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$ atoms to the $\mathrm{Ne}\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$ state is 5.5 × ${10}^4$ ${\sec }^{-1\mathrm{}}$/Torr. Atoms in the $\mathrm{Ne}\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$ level undergo two-and three-body collisions with neon ground-state atoms. The deexcitation rate for the transition $\mathrm{Ne}\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$ to $\mathrm{Ne}\left({}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}\right)$ is 1.80 × ${10}^3$ ${\sec }^{-1\mathrm{}}$/Torr. The three-body collision coefficient for $\mathrm{Ne}\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$ is 5.0 ${\sec }^{-1\mathrm{}}$/${\mathrm{Torr}}^2$. Metastable $\mathrm{Ne}\left({}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}\right)$ atoms are collisionally excited to the $\mathrm{Ne}\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$ state at the rate 160 ${\sec }^{-1\mathrm{}}$/Torr, and they are destroyed in three-body collisions with rate coefficient 0.60 ${\sec }^{-1\mathrm{}}$/${\mathrm{Torr}}^2$. The two-body deexcitation frequency for $\mathrm{Ne}\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$ and two- and three-body collision coefficients for $\mathrm{Ne}\left({}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}\right)$ are in agreement with the results of Phelps. Studies of the emissions from He-Ne mixtures were performed at relatively high helium pressures of 200 and 400 Torr, respectively. At each helium pressure controlled amounts of neon impurity were added. Time-resolved measurements were made at the wavelengths of the $\mathrm{He}\left(2\mathrm{}{}_{}{}^1{}_{}{}^{}S\right)$ metastable, the helium continuum emissions, and at the wavelengths of $\mathrm{Ne}\left({}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$ and $\mathrm{Ne}\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$. The decay constants for $\mathrm{He}\left(2\mathrm{}{}_{}{}^1{}_{}{}^{}S\right)$ and $\mathrm{Ne}\left({}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$ are shown to be consistent with resonant excitation transfer from $\mathrm{He}\left(2\mathrm{}{}_{}{}^1{}_{}{}^{}S\right)$ to the $\mathrm{Ne}\left(3\mathrm{}{s}_2\right)$ laser level (Paschen notation). The pressure dependence of the emissions from $\mathrm{Ne}\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$ in helium is governed primarily by collisional deexcitation to the metastable $\mathrm{Ne}\left({}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}\right)$ state. The two-body collision coefficient for the destruction of $\mathrm{Ne}\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$ atoms by helium is 8.3 × ${10}^3$ ${\sec }^{-1\mathrm{}}$/Torr.

Two-photon resonantly enhanced parametric generation processes have generally been described using time-dependent perturbation theory. In this paper we show that a theory of two-photon coherent effects can be used to derive and explain these nonlinear mixing processes. Our technique makes use of the adiabatic following (AF) approximation to obtain solutions to a vector model describing the two-photon resonance. We show that the usual results for the nonlinear susceptibilities correspond to the $\overrightarrow{\mathrm{r}}$ vector of Feynman, Vernon, and Hellwarth adiabatically following the $\overrightarrow{\mathrm{\gamma }}$ vector in the small-angle limit. Consequently, the theory allows a natural extension to large angles, and power-dependent nonlinear susceptibilities are obtained. We then use these AF results for the polarization to study the propagation of pulses nearly resonant with a two-photon transition, and we demonstrate that the pulse reshaping is due to the two related effects of a nonlinear pulse velocity and self-phase modulation.

The buildup of radiation from noise is considered in the case of the small-signal regime of a swept-gain amplifier with small Doppler width, of the sort indicated in recent schemes for an x-ray laser. The treatment uses the fully quantized electromagnetic field in order to take into account the spontaneous emission. The pulse is seen to grow nonexponentially with a rate that vanishes in the limit of large distances. The gain is generally much smaller than would be expected on the basis of the usual development. Many of the features normally associated with the small-signal regime of an amplifier, such as threshold conditions and spectral narrowing, are not seen. Instead we find spectral broadening, saturation, and the formation of steady states.

We develop a systematic method of operator perturbation theory in the Heisenberg picture, which is the formal analog of time-independent stationary-state perturbation theory in the Schrödinger picture. However, we use the eigenoperators and operator eigenfrequencies to calculate the time evolution of the dynamical variables of interest. The spectrum of the unperturbed Hamiltonian is assumed to be discrete. The method is especially well-suited for treating systems where the unperturbed Hamiltonian represents noninteracting fermions and/or bosons, and therefore, we illustrate the method using the exactly solvable model of Jaynes and Cummings: a single two-level atom interacting with a single quantized field mode. The time evolution of these operator solutions is shown to be unitary order by order in powers of the interaction strength. We find that the time evolution of exact operator solutions is well approximated for significantly longer times by the time evolution of this method's operator solutions than by the time evolution of the same operator solutions calculated using the Dyson expansion. We also demonstrate that time-dependent operator solutions are very convenient for computing quantities such as correlation functions.

The steady-state behavior of amplifiers in which the excitation is swept at the speed of light is discussed in the semiclassical approximation. In the present work we examine the case where the decay time of the population is comparable to that of the polarization. Pulse propagation is shown to obey a generalized sine-Gordon equation which contains the effects of atomic relaxations. The analytical expression of the steady-state pulses (SSP) gives two threshold conditions. In the region of limited gain the SSP is a broad pulse with small area which can be obtained by small signal theory. In the second region of high gain the SSP is the superradiant $\pi$ pulse. Its pulse power is not limited as in usual superradiant theory because, as we show, for a swept excitation the cooperation-length limit does not exist.

The response of a two-level atom to a smoothly varying near-resonant driving pulse can be described by the usual adiabatic-following approximation if the conditions $\frac{T_1^{-1\mathrm{}},T_2^{-1\mathrm{}}\ll t_p^{-1\mathrm{}}\ll \Omega \mathrm{}\left(t\right)\mathrm{}}{2\pi }$ are satisfied throughout the pulse. Here, $\Omega \mathrm{}\left(t\right)={\left[{\Delta }^2\mathrm{}\right(t)+\frac{p^2{\mathcal{E}}^2\mathrm{}\left(t\right)\mathrm{}}{{\hslash }^2}]}^{\frac{1}{2}}$ is the atomic precession frequency, $\Delta \mathrm{}\left(t\right)\mathrm{}$ the detuning, $\mathcal{E}\mathrm{}\left(t\right)\mathrm{}$ the field envelope, $t_p$ the effective pulse width, and $T_1$ and $T_2$ the atomic level and phase relaxation times, respectively. From Bloch's equations, we have developed a generalized version of this approximation applicable to cases where $T_1$ and $T_2$ can be comparable to or less than $t_p$. It allows the condition $T_1^{-1\mathrm{}}, T_2^{-1\mathrm{}}\ll t_p^{-1\mathrm{}}$ to be replaced by the weaker requirement $T_1^{-1\mathrm{}}$,$\frac{T_2^{-1\mathrm{}}{p}^2{\mathcal{E}}^2\mathrm{}\left(t\right)\mathrm{}}{{\hslash }^2{\Omega }^2\mathrm{}\left(t\right)\mathrm{}\ll \Omega \mathrm{}\left(t\right)\mathrm{}}$. If $T_1\gg t_p$, the atomic Bloch vector remains aligned nearly parallel to the effective driving field $\mathcal{E}\mathrm{}\left(t\right)\mathrm{}$, 0, $\frac{\hslash \Delta \mathrm{}\left(t\right)\mathrm{}}{p}$) in the rotating reference frame (as in the pure adiabatic following case); however, it decays in length if $T_2$ is comparable to $t_p$. The approximation bridges the gap between pure adiabatic following behavior for $t_p^{-1\mathrm{}}\gg T_1^{-1\mathrm{}}, T_2^{-1\mathrm{}}$ and rate-equation behavior for $t_p^{-1\mathrm{}}\ll T_2^{-1\mathrm{}}\approx \Omega \mathrm{}\left(t\right)\mathrm{}$, thereby allowing a more complete description of phenomena such as adiabatic inversion and resonantly enhanced self-focusing and defocusing.