The three-body attachment reaction in ${\mathrm{O}}_2$, $e+2\mathrm{}{\mathrm{O}}_2\to {{\mathrm{O}}_2}^{-}+{\mathrm{O}}_2$, is studied by electron-beam techniques. Whereas swarm experiments show a smooth variation of the attachment coefficient with energy, the present electron-beam experiment shows pronounced structure. The peaks of this structure occur at the positions of the vibrational levels of the ${\mathrm{O}}_2^{-}$ system, which serve as compound states and have been identified in a previous experiment. These compound states dominate the low-energy cross sections in ${\mathrm{O}}_2$. They can decay by autodetachment, thus accounting for the bulk of the vibrational cross sections in ${\mathrm{O}}_2$ at low energy; alternatively, they can be stabilized by a subsequent collision, thus leading to the formation of stable ${\mathrm{O}}_2^{-}$. Thus we establish clearly that three-body attachment in ${\mathrm{O}}_2$ is a two-stage process and that the intermediate is a vibrationally excited state of ${\mathrm{O}}_2^{-}$. We also obtain the temperature dependence of the three-body attachment coefficient and we discuss the anomalous behavior at higher pressures. The experimental observations are in excellent agreement with the theory of Chapman and Herzenberg.

Experimental results obtained by Hanle and Bitter-Brossel effects on the $N=1\mathrm{}$ and $N=2\mathrm{}$ ($v=0, 1, 2, \mathrm{and} 3$) levels of the $\mathrm{}\left(1s3p\right)\mathrm{}{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ state of the parahydrogen molecule excited by electron impact are presented. Resonances are found at the experimentally lowest possible frequencies (21-64 MHz) in a region where the N. S decoupling is nonexistent for the $N=2\mathrm{}$ level [the measured Landé $g$ factors are 0.77 ± 0.01 and 0.48 ± 0.02 corresponding to a pure Hund's-coupling case (b)] and just beginning for the $N=1\mathrm{}$ level (at 21 MHz the apparent measured $g$ is 1.235 ± 0.01). These results together with the calculations carried out in the case of complete N·S coupling lead to lifetimes $\tau =(3.10\mathrm{}\pm 0.3)\times {10}^{-8\mathrm{}}$ see ($N=1\mathrm{}$) and $\tau =(3.15\mathrm{}\pm 0.3)\times {10}^{-8\mathrm{}}$ sec ($N=2\mathrm{}$) and ${\mathrm{H}}_2$* - ${\mathrm{H}}_2$ cross sections $\tau =232\mathrm{}\pm 30$ ${\mathrm{\AA }}^2$ ($N=1\mathrm{}$) and $\sigma =240\mathrm{}\pm 30$ ${\mathrm{\AA }}^2$ ($N=2\mathrm{}$). The quantities $g$, $\tau$, and $\sigma$ were all found to be independent on the vibrational number. Risk of cascade was eliminated.

In the preceding paper some of our results on the magnetic-resonance experiments performed at 64 MHz indicated a beginning of N·S decoupling on the $N=1\mathrm{}$ $\mathrm{}\left(1s3p\right)\mathrm{}{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ state of ${\mathrm{H}}_2$ excited by electron impact. In the present paper we present further results on the resonance experiments performed at higher frequencies in order to determine the fine structure of this level. Our findings indicate that the energy separation between $J=1\mathrm{}$ and $J=2\mathrm{}$ levels is 160±5 MHz and between $J=1\mathrm{}$ and $J=0\mathrm{}$ levels it is 2100±600 MHz, and in addition the former exhibits a small dependence on the vibrational number. The relative order of these levels is $J=1, 2, 0$ instead of the theoretically predicted 2, 1, 0. The Landé $g$ factor is 1.249±0.010, which corresponds to a pure Hund's-coupling case (b).

The Glauber approximation has been applied to calculate the excitation cross section for the $2s-2p$ transition in lithium by electron impact using the frozen-core approximation. The integrated inelastic cross section has been compared with other theoretical calculations and with the experimental data. With this frozen-core, effectively one-electron formulation of electron-lithium excitation, it is found that the Glauber approximation provides better agreement with experimental data than the Born approximation.

We present (i) a new method for deriving natural widths of kinetic-energy-loss ($Q$) distributions, and (ii) a set of natural widths derived by this method from new experimental data for ${\mathrm{O}}^{+}$-Ne and ${\mathrm{O}}^{+}$-Ar scattering at 50, 100, and 200 keV. The $Q$ distributions measured by the usual delayed-coincidence techniques are broadened by experimental factors that include the thermal motion of the target gas, the finite slit widths of the scattered-particle collimators, and the energy spread in the incident beam. The present method takes explicit account of these experimental factors in obtaining natural widths from broadened experimentally measured $Q$ distributions. At a given beam energy $T_0$ and scattering angle, the natural widths are nearly independent of the final charge states of the colliding particles. For ${\mathrm{O}}^{+}$-Ar collisions, the natural widths are also independent of ${\mathcal{r}}_0$, the distance of closest approach of the colliding particles, but they increase with increasing $T_0$. For ${\mathrm{O}}^{+}$-Ne collisions, they increase with decreasing ${\mathcal{r}}_0$ and with increasing $T_0$.

The analytic properties of the Jost function or Fredholm determinant for single- and many-channel scattering problems suggest that they may often be less rapidly varying functions of the energy than the $S$ matrix or cross sections. This idea is combined with a pointwise rational-fraction interpolation to give a rapidly convergent and highly accurate method of interpolating scattering information over a continuous range of energies. Narrow resonances are easily found by examination of the zeros of the real part of the Fredholm determinant.

Experimental differential scattering cross sections for excitation of helium by electron impact from its ground state to its $2{}_{}{}^1{}_{}{}^{}S$ state are presented at four incident electron energies in the range 26-55.5 eV for scattering angles between 10° and 70° and at 81.6 eV for scattering angles between 10° and 80°. These differential cross sections are normalized by using previously determined $2{}_{}{}^1{}_{}{}^{}P$ cross sections and measured $\frac{2{}_{}{}^1{}_{}{}^{}S}{2{}_{}{}^1{}_{}{}^{}P}$ cross-section ratios. These experimental cross sections and cross-section ratios are compared with results predicted by the Born approximation, the polarized Born approximation, and several other first-order approximations in which direct excitation is calculated in the Born approximation and exchange scattering in various Ochkur-like approximations. Calculations based on these approximations are also compared to the data of other experimenters at energies up to 600 eV. The effect on the small-angle scattering of several nonadiabatic dipole-polarization potentials is examined. For the 34-81. 6-eV energy range, it is shown that the inclusion of polarization is necessary for accurate predictions of the angle dependence of the $2{}_{}{}^1{}_{}{}^{}S$ cross sections at small angles. Cross sections resulting from the use of analytic self-consistent-field wave functions for both the ground and excited states are presented. They agree well with those obtained from more accurate correlated wave functions.

The single-particle quantum states for ${\mathrm{He}}^3$ and ${\mathrm{He}}^4$ atoms adsorbed on rare-gas-plated graphite are analyzed in detail and compared to the corresponding states for adsorption on graphite and on argon-plated copper. The nature of the adsorption states depends primarily on the type of preplating gas and little on the type of underlying base. The adatoms on these substrates have high surface mobility, but the periodic surface potential does produce strong band-structure effects. The mass difference between ${\mathrm{He}}^3$ and ${\mathrm{He}}^4$ is found to be more important than the difference in statistics. The specific heat, which is calculated neglecting helium-helium interactions, is used to further compare the nature of adsorption on the various substrates.

It is shown how Rabi's treatment of the response of a two-level quantum-mechanical system to a monochromatic external driving field may be rigorously placed within the framework of the time-dependent quantum mechanics of a general system by using unitary transformations to separate out slowly varying contributions in closed form. The method is extended to include a certain class of nonmonochromatic fields and the concept of a linearly time-dependent (induced) transition probability is discussed.

This paper presents a new method for the simulation of electrical-breakdown phenomena, and plasma phenomena where both binary electron-neutral-gas-molecule collisions and collective interactions among charged particles are important. Elastic, exciting, and ionizing electron-neutral-gas-molecule collisions are included using a Monte Carlo technique. Electron-ion pairs are released in ionizing collisions. The simulation also includes the release of electron-ion pairs by photoionization. Collective interactions (space-charge effects) are included using a one-dimensional-plasma model which regards the charged particles as charge sheets. Poisson's equation is solved in one dimension based on the positions of the charge sheets to find the accelerating forces on the sheets. The method is used to simulate the growth of electron avalanches and anode- and cathode-directed streamers in nitrogen-filled parallel-plane gaps. Avalanche-simulation results are used to calculate values for the drift velocity and the ionization coefficient in nitrogen. The calculated values for these quantities agree with experimental values over a wide range of $\frac{E}{p}$, the applied electric field divided by the pressure. Velocities for anode- and cathode-directed streamers are calculated based on the streamer-simulation results. The calculated streamer velocities agree with available experimentally measured streamer velocities. The streamer-simulation results also show that photoionization is the essential mechanism for streamer formation and growth.

Previous studies of the commutator-type Green's functions are extended to the anticommutator type. The existence of an $\omega =0\mathrm{}$ pole in the latter but not former case is demonstrated. Its residue is simply related to the long-time behavior of the corresponding correlation function.

The variational ground-state energy of a charged-boson gas, obtained previously for an intermediate density range using a Bijl-Dingle-Jastrow (BDJ) type of correlated trial wave function, is improved in two steps: (i) application of the paired-phonon analysis for optimization of the variational description of the ground state in the BDJ function space, using the hypernetted-chain equation for the correlation function, and (ii) use of the improved liquid-structure function to evaluate the second-order perturbation correction generated by three-phonon components. The paired-phonon analysis yields quite small corrections to the ground-state properties including the energy and the liquid-structure function, and the perturbation corrections to the energy are also found to be very small. It is demonstrated that in the high-density limit the procedure yields the ground-state energy exact through second order in the density expansion.

An atomic deuterium maser operating on hyperfine transitions was used to measure the ground-state hyperfine separation in deuterium. The result was ${\nu }_0\left(\mathrm{D}\right)=327\mathrm{} 384 352.5222\left(17\right)\mathrm{}$ Hz where the hydrogen hyperfine frequency is assumed to be exactly 1420 405 751. 768 Hz. The construction of the device is discussed and a theory of the deuterium maser is presented with special attention given to frequency shifts occurring in the output frequency. In addition, a possible shift of the deuteron Larmor frequency because of the earth's gravitational field was also investigated and found to be <${10}^{-4\mathrm{}}$ Hz.

Experimental studies are reported of spontaneous-emission profiles observed in the axial and radial directions from high-current arc discharges of the type used in cw argon-ion lasers. The greatly increased sensitivity from a new computer-oriented method of line-profile analysis has permitted observation of linewidth parameters over a wide range of discharge current and pressure. These studies have shown the existence of several interesting new effects and have required a substantial modification of previously held concepts regarding the nature of line broadening in these discharges. A new theory for line-profile analysis in the radial direction is presented which incorporates the Tonks-Langmuir potentials and provides a correction for an arbitrary number of charge-exchange collisions in the radial acceleration of ions to the wall. A modification of the earlier theory of Kagan and Perel is suggested which brings that method of transverse line-profile analysis into reasonably close agreement with the present (more complex) method of analysis. Values for the mean radial velocity and electron temperature are obtained from profile analysis in the transverse direction. Studies of ion and neutral temperatures based on Voigt profile analysis in the axial direction are presented, along with the determination of the average electron density based on Stark broadening of the neutral and ionic lines. Precise values of the natural widths on the major argon-ion laser transitions are determined through extrapolations of the axially observed Lorentz-width data taken at low pressures to zero discharge current.

The Gross-Pitaevskii equation for the order parameter of a superfluid boson system is derived in a form which is applicable to a system in which the two-body potential has a strong repulsive core, as is the case for liquid helium. The equation of motion for the order parameter, defined as the matrix element of the field annihilation operator between the states of an ($N-1\mathrm{}$)-particle and an $N$-particle system, is obtained. The term describing the average potential due to the other particles is expanded in a perturbation series, in which the coherentstate representation is used. The resulting expansion is the same as using the Bogoliubov approximation and Wick's theorem, and shows that the Bogoliubov expansion is exact in the limit of an infinite number of particles. The perturbation expansion is partially resummed to give a Hartree field in which the potential has been replaced by the $T$ matrix, which gives a finite average effective field.

A method used by Hemmer and Jancovici to calculate quantum corrections to the equation of state for a hard-sphere gas is extended to cover the case of a more general intermolecular potential. The basis of the method is an expansion of the partition function about its classical limit, the terms in the expansion being integrals over products of classical correlation functions and certain "modified" quantum Ursell functions. Conditions are discussed under which this series can be truncated to give the quantum corrections to a specified order in $h$ (Planck's constant). A calculation of the first quantum correction is carried out for the square-well-plus-hard-core potential.

A theory for calculating low-frequency component electric microfield distributions for a plasma containing more than a single ion species is developed. Calculations at a charged point are made for a plasma containing $N^{+}$ singly charged ions and $N^{++}$ doubly charged ions together with a charge neutralizing number of electrons, $N_e(N_e=N^{+}+2\mathrm{}{N}^{++})$. Three different ion ratios ($R\equiv \frac{N^{++}}{N^{+}}$) are treated: $R=0.0, 1.0, \infty$. It is shown that the calculations allow for all ion-ion correlations to a high degree of accuracy. Numerical results are shown both graphically and in tabulated form.

The effect of transmission of radiation through one mirror of a laser is investigated. For a laser oscillator the result is to change the effective resonance frequency and $Q$ of the cavity. Using the same model for the cavity, a signal is injected into the active medium through the transmitting window, and its effect on the system studied. When the external signal is strong enough and sufficiently close to the natural frequency of the laser oscillator, the laser locks its frequency to the input signal. The equations describing the system are solved over the range of input frequencies where the laser is locked, and the resulting gain found. In the high-intensity limit the medium saturates, and the gain tends to that of a lossy cavity. As the input intensity vanishes, the gain approaches infinity and the system tends to a laser oscillator.

A transmitting window is used to weakly couple two resonant optical cavities. When active medium is placed in one cavity, the system describes a laser coupled to a resonant cavity, while active medium in both cavities describes two coupled lasers. Equations of motion for the fields in the two cavities are found. These equations are solved in the steady state when the cavities are sufficiently closely tuned that the lasers in the two cavities oscillate with the same frequency. In the locked situation, the second cavity tends to stabilize the frequency of operation against changes in length of the first cavity. When there is no active medium in the second cavity, and that cavity becomes very long, the laser acts as if it were looking into free space.

Previous theoretical results on the influence of a laser on the line shape of a coupled transition-laser-induced line narrowing-have been restricted to the case where the laser is detuned from the center of its atomic gain profile or is in the form of a traveling wave. This paper extends those results to include the case where the laser is an intense standing-wave field tunable to the center of its atomic gain profile (conditions for Lamb dip). The effect may be observed either in transmission, by probing the coupled transition with a weak traveling-wave field coaxial with the laser field, or else in spontaneous emission from the coupled transition viewed along the axis of the laser field. It is now well known that for a laser detuned from the center of its atomic gain profile, two narrow Lorentzian resonances of different widths appear superimposed upon the broad background signal at frequencies symmetrically located about the corresponding line center. When the laser is tuned to the center of its gain profile, however, additional fine structure develops. This structure, which is particularly significant when the laser field is intense, may have important applications in highresolution spectroscopy and laser-frequency stabilization. In this paper the laser frequency may be smaller or larger than the frequency of the coupled transition. In the latter case an intense laser introduces additional splitting effects, even when the laser is detuned. Splitting effects due to weakly saturating laser fields are also discussed. The problem is formulated by expanding elements of the ensemble-averaged density matrix in an infinite series of spatial Fourier components. A perturbation technique is employed, valid for a weak probe field and a standing-wave field of arbitrary intensity. One obtains an expression for emission induced by the probe field due to atoms moving with one velocity, written in terms of continued fractions in the general case and with Bessel functions in an important special case. This expression is integrated over the atomic velocity distribution by means of a computer to obtain the total emission due to atoms moving with all velocities. In some cases the integrated expressions may be written in closed algebraic form. A detailed discussions of line shapes and of the physical processes involved is included.