We compare the experimental curves of Skribanowitz et al., showing superradiance from pumped HF gas, with the "single-mode" time-evolution formula of Bonifacio and Lugiato. All parameters are varied freely except the length $L$ of the sample. It is found impossible to obtain even rough agreement. When ${\tau }_c$ is taken longer than $\frac{L}{c}$, no ringing is predicted; when shorter, the predicted ringing is many times faster than that observed.

A comparison between a mean-field theory of superfluoresence and a recent experiment can be made only with some caution regarding the preparation of the system and the value of the loss parameter. Quantitative agreement can be found provided the loss parameter is not taken literally to be $\frac{c}{2L}$ but rather is fixed by fitting the experimental data.

An earlier calculation of the asymptotic decay of the angular-velocity autocorrelation function is reexamined and extended to the case where the test particle is not a linear molecule or identical to the bath particles. The results of some recent molecular-dynamics calculations are discussed.

The charge-exchange formation of the ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2},\frac{1}{2}}^{}{}_{}{}^{}$ states of ${\mathrm{Ar}}^{-}$ formed by ${\mathrm{D}}^{-}$-on-Ar collisions is measured. The autodetached electrons ejected from the ${\mathrm{Ar}}^{-}$ states are observed at 125.3° from the beam direction. These results are compared with similar measurements made with an ${\mathrm{H}}^{-}$ ion beam. A dip in the cross section occurs at 1.5 keV beam energy for the ${\mathrm{H}}^{-}$ and at 3 keV for the ${\mathrm{D}}^{-}$. As a function of beam velocity the exchange cross sections are the same up to the velocity corresponding to 2-keV ${\mathrm{H}}^{-}$ (4-keV ${\mathrm{D}}^{-}$). At higher velocities the ${\mathrm{D}}^{-}$ results are greater.

The energies and widths of the $S$-wave resonances of ${\mathrm{H}}^{-}$ are calculated by using a continuum wave function in which the resonance effect is removed. This method improves our earlier results and brings the existing accurate theoretical results into excellent agreement.

Using the results of a previous paper, we study the evolution of a completely excited system of $N$ two-level atoms, distributed in a circular cylinder with dimensions much larger than the wavelength, interacting with all modes of radiation field. We emphasize the distinction between $r$-conserving ($r\mathrm{C}$) and $r$-nonconserving ($r\mathrm{NC}$) processes ($r$ is the so-called cooperation number). Considering the number of photons emitted as the discrete independent variable, this evolution is described by a partial difference equation. Numerical solutions of this equation show the transition from $r\mathrm{NC}$ dominance at the beginning to $r\mathrm{C}$ dominance later. This is also a transition from incoherent to coherent emission of radiation.

A variational method used recently in the theory of liquid metals and screened Coulomb systems is extended to treat the thermodynamic properties of a classical, uniform, one-component plasma. The Helmholtz free energy and corresponding thermodynamic derivatives can all be expressed in concise parametric form as functions of an equivalent hard-sphere packing function. The results are generally found to agree well with recent Monte Carlo calculations, especially at temperatures close to the observed crystallization temperature.

Cross sections for electron-${\mathrm{H}}_3$${\mathrm{O}}^{+}$ recombination have been measured over an electron energy range of 0.060-1.15 eV by using a trapped-ion technique to contain an ion sample at a temperature of ≃ 400 K. The cross section deduced from these measurements can be represented by $\sigma =4.6\mathrm{}\times {10}^{-18\mathrm{}}{E}^{-2.9\mathrm{}}$ ${\mathrm{cm}}^2$ for $0.038<E\le 0.110$ eV; $\sigma =4.8\mathrm{}\times {10}^{-16\mathrm{}}{E}^{-0.79\mathrm{}}$ ${\mathrm{cm}}^2$ for $0.110<E\le 0.420$ eV; and $\sigma =7.5\mathrm{}\times {10}^{-17\mathrm{}}{E}^{-2.9\mathrm{}}$ ${\mathrm{cm}}^2$ for $E>\mathrm{}0.420\mathrm{}$ eV. Uncertainties are estimated to be at the ± 50% level. Recombination-rate coefficients were calculated from the deduced cross sections, assuming a Maxwellian electron velocity distribution and trial forms for the cross section below 0.038 eV. Assuming the theoretical $E^{-1\mathrm{}}$ behavior for the cross section just above zero energy and comparing with the measured rate coefficient of Leu et al. at 540 K, we can deduce consistent cross sections below 0.038 eV to be $\sigma =6.0\mathrm{}\times {10}^{-15\mathrm{}}{E}^{-1\mathrm{}}$ ${\mathrm{cm}}^2$ for $0<E<\mathrm{}0.023\mathrm{}$ eV, and $\sigma =4.6\mathrm{}\times {10}^{-18\mathrm{}}{E}^{-2.9\mathrm{}}$ ${\mathrm{cm}}^2$ for $0.023<E<\mathrm{}0.038\mathrm{}$ eV. The calculated rate coefficients have temperature dependence $T_e^{-0.5\mathrm{}}$ at 50 K and $T_e^{-1.43\mathrm{}}$ at ${10}^5$ K, and values of the coefficient are in good agreement with all direct measurements.

Total cross sections for $K$-shell ionization of the ground state of multielectron targets by electron impact have been computed using the single-particle Glauber approximation. Various hydrogenic product wave functions are used to describe both the bound and continuum electron. Projectile-target electron exchange effects are simply approximated by limiting the region of integration over ejected electron momenta so as to avoid double counting. Using this exchange approximation and choosing reasonable effective charges initially and finally for the target, agreement is obtained with existing helium data at projectile energies above 100 eV. The effects of changing various parameters are shown and discussed, and comparisons are made with Born approximations. For $Z>\mathrm{}3\mathrm{}$ differences between our Glauber and Born total cross sections are small.

An analysis is given of multiphoton transitions between discrete quasimolecular states during the near-adiabatic collision of atoms and/or molecules. The variation of level spacing with changing internuclear separation can permit resonance absorption of one or more photons. Sufficiently intense laser beams can also significantly distort the molecular structure to modify potential surfaces, change activation energies, and so on. Through these two mechanisms specific chemical reactions in gases can be made to occur with rates that depend on laser power.

We have measured relative intensities of emission from the $2p$, $3s$, $3p$, $3d$, $4s$, $4d$, $5s$, and $5d$ states of ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ produced in 444-eV (relative energy) collisions (2-keV ions on thermal molecules) of ${}_{}{}^7{}_{}{}^{}\mathrm{Li}_{}^{+}{}_{}{}^{}$ with ${\mathrm{H}}_2$. From these, relative values of the direct charge-transfer cross sections ${\sigma }_c$ were obtained. It was found that ${\sigma }_c$ decreases rapidly and smoothly (approximately as ${10}^{-(n-3\mathrm{})\mathrm{}}$), with increasing principal quantum number $n$ (for $n=3,4,5$) while the variation in ${\sigma }_c$ with angular momentum quantum number is not regular; ${\sigma }_c\left(3\mathrm{}s\right)\sim {\sigma }_c\left(3\mathrm{}p\right)$ but ${\sigma }_c\mathrm{}\left(\mathrm{nd}\right)\mathrm{}\sim 10{\sigma }_c\mathrm{}\left(\mathrm{ns}\right)\mathrm{}$, in sharp contrast to the behavior of capture cross sections at high energies.

Relative subshell photoionization cross sections for the elements have been derived from published data on the relative strength of lines observed in a photoelectron spectrometer and the results converted to an absolute scale based on a value for the $\mathrm{Na}\mathrm{}\left(1s\right)\mathrm{}$ cross section. Values obtained have been found to be in substantial agreement with the predictions of a recent theoretical study for the stronger transitions in elements with $Z<\mathrm{}56\mathrm{}$. Final-state effects have been demonstrated to be particularly significant in the photoionization of the $3d$ and $4d$ subshells in the lanthanides and actinides. The data derived in the present study strongly suggest that electron attenuation in inorganic (nonmetallic) compounds follows a functional dependence on kinetic energy which does not vary by more than 15% from compound to compound.

The fractional pressure shifts (fps) of the ground-state hyperfine frequency of ${}_{}{}^{133}{}_{}{}^{}\mathrm{Cs}$ were remeasured for a number of buffer gases and found to be (in units of ${10}^{-9\mathrm{}}$/Torr): for He, 123.5 ± 1.0; ${\mathrm{H}}_2$, 118.0 ± 0.5; Ne, 63.5 ± 0.5; ${\mathrm{N}}_2$, 90.0 ± 1.0; Ar, -21.5 ± 1.0; ${\mathrm{CH}}_4$, -104.0 ± 0.5; ${\mathrm{CD}}_3$H, -92.5 ± 0.5; ${\mathrm{C}}_2$${\mathrm{H}}_6$, -118.5 ± 2.5; ${\mathrm{C}}_3$${\mathrm{H}}_8$, -291.5 ± 1.5; ${\mathrm{C}}_4$${\mathrm{H}}_{10}$, -390.5 ± 2.5; and ${\mathrm{C}}_2$${\mathrm{H}}_4$, -269.0 ± 2.5. In addition, the fps for the buffers ${\mathrm{D}}_2$, 188.0 ± 0.5; ${\mathrm{CF}}_4$, -21.5 ± 1.0; and ${\mathrm{CD}}_2$${\mathrm{H}}_2$, -95.5 ± 0.5 were measured for the first time. Trends in the observed fractional shifts are discussed qualitatively in terms of the effects of anisotropic intermolecular interactions on the long-and short-range contributions to the fps.

Using close-coupling theory, multichannel expressions are derived for the angular distributions of photoelectrons from atomic oxygen. These expressions are used to calculate angular distributions for photoelectron ejection from either the outer $2p$ subshell or the inner $2s$ subshell. Comparison with other theoretical work is made.

The atomic angular-factor calculation methods given in a previous work are simplified and extended to include a treatment of spin-orbit operators and multiple shell configuration ${\left(l{l}^{\prime }\cdots \right)}^n$. A tableau formula is given for the matrix between Slater states and states of definite total spin.

The ground-state momentum density $\rho \left(\overrightarrow{\mathrm{p}}\right)$ and Compton profile $S(\overrightarrow{\mathrm{k}},\omega )$ of ${\mathrm{TiCl}}_4$ have been calculated. Molecular-orbital (MO) wave functions were obtained in the Hartree-Fock-Slatter (HFS) model by use of the discrete variational method. Results for MO wave functions are compared with atomic superposition models based on Hartree-Fock and HFS atomic eigenfunctions. Shifts in spherical average momentum density and Compton profile owing to chemical bonding are examined; the symmetry and magnitude of the anisotropy is studied. Following the spherical-harmonic analysis of Mijnarends, we discuss practical methods for obtaining ($\mathrm{lm}$) components of $S$; simple expressions for certain moments of the anisotropic density are given.

The effect of mixing two high-power ruby-laser beams in several gases has been investigated by means of light scattering. Coherently scattered light has been observed with intensities of up to three orders of magnitude, exceeding that of incoherent Rayleigh scattered light. The dependence of the effect on laser power, gas density, and refractive index is described. It is shown that for higher pressures (∼ 100 Torr) a threshold power exists for the effect, and that saturation is observed with increasing pressure as well as increasing mixing beam power.

We outline a complete theory of the nonlinear susceptibility of cesium around 1.06 μm, and present the first measurements of the negative nonlinear refractive index $n_2$ primarily responsible for the self-defocusing that is observed. For linearly polarized light, our measured value of $n_2$ is $-(1.4\mathrm{}\pm 0.2)\times {10}^{-30\mathrm{}}N$ esu, where $N$ is the atomic density. This is in reasonable agreement with our calculated value of $-2.62\mathrm{}\times {10}^{-30\mathrm{}}N$. The main portion of $n_2$ comes from a two-photon resonance between the $6s$ and $7s$ levels, and an additional negative term arises from induced population changes between $6s$ and $6p$. For circular polarization, $n_2$ arises mainly from the induced population changes, giving the measured and calculated values of $-(0.26\mathrm{}\pm 0.03)\times {10}^{-30\mathrm{}}N$ and $-0.525\mathrm{}\times {10}^{-30\mathrm{}}N$, respectively. In our experiments where the 35-psec pulses were shorter than the $6s-6p$ inverse linewidth, the nonlinear susceptibility depends mainly on the instantaneous intensity; however, for longer pulses, one would obtain additional contributions proportional to time integrals over the intensity. Since the useful output power from large Nd laser systems is limited by self-focusing due to the laser glass, our results suggest the possibility of increasing this power by using Cs vapor for compensation.