Following low-energy electron-impact excitation of molecular nitrogen, the method of delayed coincidence is used to separate the prompt and delayed radiation of the $C{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}\to B{}_{}{}^3{}_{}{}^{}\Pi _g^{}{}_{}{}^{}$ transition. The emission function of the prompt radiation, due to direct $C$-state excitation, is seen to increase smoothly above threshold. The emission function of the delayed emission, due to collisional deactivation of metastable states, is composed of two sharp peaks at 12.0 and 12.7 eV as well as a broader peak at about 22 eV. The first of these peaks is recognized as the direct resonant excitation of the metastable $E{}_{}{}^3{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ state. Evidence is found indicating that the other peaks, which may be associated with the excitation of the $a^{\prime \prime }{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ state, lead to indirect excitation of the $E$ state.

Cross sections for inner-shell ionization by slow heavy charged particles, if compared to predictions given in the plane-wave Born approximation, are reduced strongly by the Coulomb deflection of the particle in the field of the target nucleus, and by the increase in binding energy of the target electrons induced by the presence of the particle. We use the framework of the perturbed-stationary-state approximation to incorporate these effects ab initio into the theory of inner-shell ionization and derive the binding effect given by Brandt, Laubert, and Sellin. Our result formally unifies the Coulomb deflection of the particle trajectory with the perturbation of the atomic states in their effect on the ionization cross section and suggests systematic ways for further improvements.

Photoelectron angular distributions should show pronounced variations with energy across autoionization resonances. This prediction applies quite generally to both atomic and molecular autoionization. Examples illustrate both the magnitude of the spectral variation and the inability of the Cooper-Zare model to account for the phenomenon. Calculations are reported for autoionization in xenon between the fine-structure levels $5p^5 {}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{\circ }{}_{}{}^{}$ and $5p^5 {}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{\circ }{}_{}{}^{}$ of the ion ground-state doublet. An analysis is given of the recent measurements by Niehaus and Ruf on autoionizing levels of the mercury Rydberg series $5d^{9}6s^2\left({}_{}{}^2{}_{}{}^{}D\right)np$ and $5d^{9}6s^2\left({}_{}{}^2{}_{}{}^{}D\right)n^{\prime }f$ below the ${\mathrm{Hg}}^{+}$ $5d^{9}6s^2 {}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}$ threshold.

Elastic total and spin-exchange cross sections are computed for electron scattering by Li, Na, and K, for energies below the first excitation threshold. The method used is the variational form of solution of continuum Bethe-Goldstone equations. Results are in substantial agreement with close-coupling calculations and with recent experimental data.

The coincidence technique of Kessel and Everhart has been used to study the ${\mathrm{Ar}}^{+}+\mathrm{Kr}\to {\mathrm{Ar}}^{+m}+{\mathrm{Kr}}^{+n}+(m+n-1\mathrm{})e$ reaction at incident ion energies from 15 to 230 keV, and scattering angles from 10° to 40°, corresponding to distances of closest approach ranging from 0.38 to 0.06 Å. $\overline{Q}$ values varied from less than 100 eV to greater than 3 keV, and the average numbers of ejected electrons varied from ½ to $\frac{7}{2}$ for argon and from $\frac{5}{2}$ to 8 for krypton. Unresolved $Q$ structure is probably present at 0.2 to 0.3 Å. As with all previous data which the authors have handled where the $Q_{\mathrm{mn}}$ profiles are not multiply peaked, the ${\mathrm{Ar}}^{+}$-Kr $\overline{Q}$ values were found to be fit by the empirical relation ${\overline{Q}}_{\mathrm{mn}}=A+B{U^{\prime }}_m+C{U^{\prime \prime }}_n$ where the $U\text{'}\mathrm{s}$ are spectroscopic energy deficits, with rms errors averaging about 2.5%. Several indirect means show that the krypton is responsible for some 65% of the energy loss, possibly decreasing to about 55% at the highest ${\overline{Q}}_{\mathrm{mn}}$ values studied. The intrinsic ionization probabilities from the present study reproduce fairly well the probabilities from previous ${\mathrm{Ar}}^{+}$-Ar and ${\mathrm{Kr}}^{+}$-Kr studies.

The Faddeev-Watson multiple-scattering (FWMS) expansion is investigated in the eikonal approximation. For the case with the classical trajectories taken to lie along straight lines, the second-order FWMS expansion reduces to the well-known Glauber-eikonal approximation. Application of the second-order FWMS expansion in the eikonal approximation is carried out for elastic and inelastic ($e$, H) scattering with the classical trajectories taken as intersecting two straight-line segments. The result suggests that there is a substantial cancellation between the first-order and second-order terms in the FWMS expansion for pair Coulomb interactions.

This paper reports an investigation of parametric frequency conversion in a vapor of ${\mathrm{Rb}}^{87}$ atoms in which nearly resonant optical waves are coupled with microwaves at the ground-state hyperfine-structure (hfs) frequency of ${\mathrm{Rb}}^{87}$ by the nonlinear susceptibilities of ${\mathrm{Rb}}^{87}$ vapor. These nonlinear susceptibilities are greatly enhanced by optical pumping of the ground-state hfs levels of ${\mathrm{Rb}}^{87}$ and by using nearly resonant light. The frequency-conversion process generates optical sideband waves which are separated in frequency from the carrier light waves by the ground-state hfs frequency of ${\mathrm{Rb}}^{87}$ (6.835 GHz). These sidebands have been directly observed in the spectral profiles of ${\mathrm{Rb}}^{85}$ resonance light which had passed through ${\mathrm{Rb}}^{87}$ vapor. The conversion efficiency of power from the carrier waves to the sideband waves in a 45-cm length of vapor was greater than 1%. The observed behavior of the sidebands is in excellent qualitative agreement with the predictions of a semiclassical theory.

The crossed-beam technique has been used to measure absolute emission cross sections for the excitation of electric dipole transitions in the ${\mathrm{Ba}}^{+}$ ion by electron impact at energies near and below threshold. The basic experimental method involves intersecting modulated ion and electron beams at right angles in a well-defined collision volume. A portion of the photon flux radiated from the collision volume by excited ions is detected by an optical system viewing the collision volume along the axis perpendicular to both beams. The total emission is calculated from the portion detected using the experimentally determined response of the detection system to isotropic radiation and a correction for anisotropy, obtained from the polarization of detected emission. The emission cross section is then calculated from the total emission, the two beam currents and their spatial distributions, and the energies. The cross sections measured are absolute in the strict sense that the optical detection system was calibrated with a light standard by a technique which takes into account all spatial and spectral variations. A stable point source of light has been devised to determine the variation of the detection-system response with the position in the collision volume where the photons are produced. Another small light source has been developed for transferring to the detection system the calibration of a tungsten-ribbon standard of spectral radiance traceable to blackbody standards. Techniques of careful spectral comparison of the sources are used for this purpose. An electron source has been developed with the energy resolution and current necessary for crossed-beam measurements in the 3- to 20-eV range. This tool made possible the examination of the range of impact energies near and below the excitation threshold.

The cross sections for $M$-shell electron ionization by direct Coulomb excitation of heavy target atoms by incident heavy charged particles are evaluated. Incident particles are described in the plane-wave Born approximation, and screened hydrogenic wave functions are used for the atomic electrons. Numerical results are given for Au, U, and No, and the theory is compared with experimental data for Ho as an illustration. Explicit expressions for the absolute values of the $M$-subshell form factors of bound-free transitions are presented as functions of momentum and energy transfers. The results are discussed.

Exact formulas are derived for the factorial cumulants of the photoelectric counting distribution of partially polarized Gaussian and Gaussian-plus-coherent light for arbitrary detector areas. The results make it possible to follow the transition from Bose-Einstein statistics in the small-area limit to Poisson statistics in the large-area limit. Numerical results are presented for a circular geometry. These methods, which enable experimentally measured photocount statistics to be extrapolated to zero detector area, are expected to be useful in measurements of small departures from Gaussian statistics. Other theoretical results make it possible to express the statistics of the sum of photocounts from different photocathodes, or the multiaperture, single-cathode (MASC) photocount statistics of light of arbitrary coherence properties, in terms of the multicathode (MC) counting statistics. Explicit expressions are derived for the MASC photocount cumulants for the special case of partially polarized Gaussian light.

The ratio ${\mu }_N$ of the cross section for circularly polarized light to that for linearly polarized is numerically investigated for $N$-photon ionization of atomic hydrogen. For $N<\mathrm{}4\mathrm{}$, it appears that the gain factor is greater than unity. For $N\ge 4$, the ratio ${\mu }_N$ is generally smaller than unity and decreases when the multiphoton order $N$ increases.

The linearized hydrodynamic equations for superfluid ${\mathrm{He}}^4$ are derived starting from the kinetic equations of Khalatnikov. Only the lowest-order dissipative terms are considered. The Boltzmann equation for the phonons and rotons is solved formally by expanding the distribution function in terms of the eigenfunctions of the linearized collision operator. The resulting hydrodynamic equations contain dissipative terms of the form proposed by Landau and Khalatnikov. Formal expressions are given for the viscosities and the thermal kinetic coefficient. Finally, relations which may hold between the dissipative coefficients when the collision operator has special properties are discussed.

The impact-parameter formalism for Stark broadening of partially degenerate neutral lines emitted by an atom immersed in a dense plasma is extended to include the quadrupole term of the electron-atom interaction, considered in the second order of the Dyson expansion. The corresponding nondiagonal broadening functions and their impact-parameter averages are derived and their properties are studied in detail. The nondiagonal quadrupole shift function is shown to be negligible with respect to the dipole term, for most situations of physical interest. These new functions are also useful in the collision theory of electrons with atoms and molecules.

By making a systematic analysis of correlation functions in terms of irreducible and reducible parts, Ma and others have developed a dielectric formulation of the dynamics of a condensed Bose system which fully includes the background (or excited) atoms. We show that this formulation quite generally leads to the density and single-particle-correlation functions both having two resonances ${\tilde{\omega }}_1$ and ${\tilde{\omega }}_2$ although with different weights. If the condensate $n_0=0\mathrm{}$, the ${\omega }_2$ mode only appears in the single-particle spectrum while ${\omega }_1$ only appears in the density-fluctuation spectrum. For finite values of $n_0$, these modes are coupled and renormalized to ${\tilde{\omega }}_1$ and ${\tilde{\omega }}_2$. As a specific illustration, we use the shielded-potential approximation (SPA) for the reducible self-energies. In this model, we find the free-particle excitations (${\omega }_2$) are coupled to the zero-sound density fluctuations (${\omega }_1$) through the action of the condensate. In the SPA, the reducible self-energies have a pole at ${\omega }_1$. The usual Bogoliubov, Hartree-Fock, and ordinary $t$-matrix approximations involve nonsingular self-energies and hence do not exhibit the ${\tilde{\omega }}_1$ mode. Experimentally, it appears that the high-frequency ${\tilde{\omega }}_2$ mode has never been detected, but this is probably owing to the fact that it is strongly damped as a result of its coupling to the zero-sound mode. Using the two-fluid hydrodynamic equations, one can argue that at low frequencies the ${\tilde{\omega }}_1$ excitation corresponds to first sound and the ${\tilde{\omega }}_2$ excitation corresponds to second sound. Finally, we briefly discuss the possibility of singularities in the irreducible self-energies at high frequencies and the resulting two-roton bound states.

Short pulses of narrow-line low-intensity dye-laser light nearly resonant with the Zeeman-split ${}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ resonance line (7948 Å) of rubidium were observed to propagate through dilute rubidium vapor as slowly as $\left(\frac{1}{14}\right)c$. These slow pulse velocities showed that most of the energy in the propagating wave was contained by the vapor as coherent atomic excitation. The observed pulse velocities $v_p$ are in good agreement with the equation $v_p=\frac{d\omega }{\mathrm{dk}}$ for the group velocity obtained from linear-dispersion theory. Also, the experimental results are quantitatively explained by adiabatic following, in which the pseudomoments of the atoms remain aligned along the effective field of the laser light. The adiabatic-following model allows for a direct comparison of our results with the work on self-induced transparency. For high-intensity light, adiabatic following predicts a nonlinear pulse velocity and the possibility of observing self-steepening.

The cascade time of $K^{-}$ mesons has been measured in liquid deuterium using a deuterium-filled bubble chamber as the particle detector and absorber. The experimental result of $T_{\mathrm{cascade}{\mathrm{D}}_2}=6_{-6\mathrm{}}^{+7\mathrm{}}\times {10}^{-12\mathrm{}}$ sec is consistent with results for liquid hydrogen and with the prediction that "Stark-effect mixing" allows rapid capture from $s$ states of high principal quantum number $n$.

The Stark-pulse technique of Brewer and Shoemaker allows one to observe phenomena such as optical free-induction decay, optical nutation, and two-photon superradiance. In this paper, we develop a theoretical treatment of these phenomena under the appropriate experimental conditions. The calculations of the free-induction decay and the corresponding optical nutation are shown to be in excellent agreement with experiment. We also discuss the two-photon superradiance phenomenon of Brewer and Shoemaker as a Raman effect appearing in first-order perturbation theory. The analysis illustrates the essential features of the experimental observation.

The escape of electrons from their bubble state in liquid helium through the free liquid surface into the vapor phase is investigated. The measured escape rates are calculated in terms of a tunneling model which predicts a unique temperature and electric field dependence in excellent agreement with the experimental data. A fit of this model to the data yields the binding energy and the radius of the electronic bubble. The binding energy is found to be 0.70 eV in pure ${\mathrm{He}}^4$ and 0.56 eV in pure ${\mathrm{He}}^3$. The bubble radii are found to scale according to the bubble model; however, their absolute values appear to be too large. The results obtained from two different ${\mathrm{He}}^3$-${\mathrm{He}}^4$ mixtures are anomalous and not yet understood.

The theory of the distribution of the time average of the time-dependent microfield in a quantum plasma taken over a finite time interval is introduced and developed. The short- and long-time limits are derived. The Wigner phase-space representation is employed to derive the correct distribution for a classical plasma and to establish a formalism which can be used for low-order quantum corrections. Numerical results are presented for a classical gas of charged noninteracting particles. It is found that for time-averaging intervals, which are larger than the time it takes a particle traveling with the average thermal velocity to cross the ion-sphere radius, the distribution deviates from the corresponding Holtsmark distribution for the quasistatic model.

The structure factor $S\left(Q\right)\mathrm{}$ for liquid argon at 85 °K has been determined in a neutron scattering experiment to an accuracy of ∼0.01. The problem of obtaining $S\left(Q\right)\mathrm{}$ from the results of neutron scattering measurements, made as a function of scattering angle using a detector with an energy-dependent efficiency, is considered in detail. Smooth curves for $S\left(Q\right)\mathrm{}$ and its Fourier transform, the radial distribution function $g\left(r\right)\mathrm{}$, were obtained from the experimental data by an iterative procedure suggested by Verlet and carried out by Schiff, and are tabulated for convenience. The experimental results are in excellent agreement with the predictions of computer simulations based on either the Lennard-Jones two-body interaction, or on the Barker, Fisher, and Watts potential with corrections for three-body and quantum effects included.