A close relationship between the angular distributions of secondary electrons produced by photoionization and by impact of fast charged particles is pointed out. The dipole-interaction term in the charged-particle impact cross section [which has $\frac{\left(\ln T\right)}{T}$ dependence, $T$ being proportional to the incident energy] has essentially the same angular dependence as the photoelectrons ejected by unpolarized light. An analysis of recent electron-impact data on He and ${\mathrm{N}}_2$ indicates consistency with the present theory.

The three-body electron-attachment coefficient for ${\mathrm{O}}_2$ has been determined by microwavecavity techniques to be 2.1 × ${10}^{-30\mathrm{}}$ ${\mathrm{cm}}^6$/sec±10% at 300 °K, 1.5 × ${10}^{-30\mathrm{}}$ ${\mathrm{cm}}^6$/sec±15% at 200 °K, and 7.2 × ${10}^{-31\mathrm{}}$ ${\mathrm{cm}}^6$/sec±20% at 113 °K. Initial electron densities were produced by singlepulse photoionization of small amounts of NO in the ${\mathrm{O}}_2$. For a given ${\mathrm{O}}_2$ pressure the electron density decay rates were found to be independent of the NO concentration used in this study. Mass analysis of ions in the afterglow shows that N${\mathrm{O}}^{+}$ is the predominant initial positive ion. Although ${\mathrm{O}}_2^{-}$ is the initially predominant negative ion observed at 300 °K, it reacts rapidly at low temperature to form ${\mathrm{O}}_4^{-}$ and N${\mathrm{O}}_3^{-}$.

The vibrational cross section by electron impact on ${\mathrm{N}}_2$ exhibits a broad maximum near 22 eV. This maximum can be observed in the first three vibrational states, at all angles of observation. The angular distribution of the electrons having excited nitrogen to the vibrational states $v=1, 2, 3$ is measured. The shape of the angular distribution changes as the incident energy is varied from 20 to 28 eV. We interpret our observations in terms of the possible existence of a number of overlapping compound states above 20 eV.

Variational functionals are constructed for solving Feshbach equations for multichannel scattering and rearrangement collisions. The open-channel and closed-channel components of the state function are varied separately. This separation disentangles the violent fluctuation in the open-channel component from the closed-channel component and speeds up the convergence in the resonance energy region. Numerical illustrations are given for the elastic ($e$, H) scattering.

We have measured the energy-independent ratio of the proton apparent-excitation cross sections between corresponding triplet and singlet states of helium for the $n=3\mathrm{}$ level. In the Russell-Saunders description of the states of helium, proton excitation of triplet states is forbidden; i. e., $\Delta S=1\mathrm{}$ transitions are not allowed (Wigner spin rule). However, the spin-orbit interaction for the two electrons in helium mixes the spin states. Thus, there is a small singlet component in the triplet-state wave function. The square of the small singlet-triplet mixing parameter $\gamma \left(3\mathrm{}{}_{}{}^3{}_{}{}^{}X\right)$ is equal to the ratio of the proton excitation cross sections to corresponding triplet and singlet states, i. e., ${\gamma }^2\left(3\mathrm{}{}_{}{}^3{}_{}{}^{}X\right)=\frac{{\sigma }_{\mathrm{p}}\left(3\mathrm{}{}_{}{}^3{}_{}{}^{}X\right)}{{\sigma }_{\mathrm{p}}\left(3\mathrm{}{}_{}{}^1{}_{}{}^{}X\right)}$. The symbol $X$ refers to the orbital angular momentum states $S$, $P$, or $D$. If we designate the ratio of the proton apparent-excitation cross sections $\frac{Q_{\mathrm{p}}\left(3\mathrm{}{}_{}{}^3{}_{}{}^{}X\right)}{Q_{\mathrm{p}}\left(3\mathrm{}{}_{}{}^1{}_{}{}^{}X\right)}$ by ${\beta }^2\left(3\mathrm{}{}_{}{}^3{}_{}{}^{}X\right)$, then ${\beta }^2\left(3\mathrm{}{}_{}{}^3{}_{}{}^{}X\right)={\gamma }^2\left(3\mathrm{}{}_{}{}^3{}_{}{}^{}X\right)+(\mathrm{cascade}\mathrm{contributions}$. Our results for ${\beta }^2\left(3\mathrm{}{}_{}{}^3{}_{}{}^{}X\right)$ for the $n=3\mathrm{}$ states of helium are as follows: ${\beta }^2\left(3\mathrm{}{}_{}{}^3{}_{}{}^{}S\right)=0\mathrm{}\pm 0.0002$, ${\beta }^2\left(3\mathrm{}{}_{}{}^3{}_{}{}^{}P\right)=0.0028\mathrm{}\pm 0.0007$, and ${\beta }^2\left(3\mathrm{}{}_{}{}^3{}_{}{}^{}D\right)=0.06\mathrm{}\pm 0.014$.

A method is described whereby it is possible to make accurate empirical estimates of ionization potentials that are missing in Moore's "atomic energy levels," and so obtain empirical total atomic binding energies $B_Z$ with estimated uncertainties less than 0.005%, for all $Z<~18$. These $B_Z$ values are used to compute values of $\frac{\partial B_Z}{\partial Z}$, with quite small a signed uncertainties (∼0.15% for $Z>~12$). The relativistic Dirac-Hartree-Fock calculations of Mann reproduce these empirical values to within amounts a few times the uncertainties.

This series of papers is concerned with the derivation of the equations of the classical picture of atomic collisions, $i\hslash \frac{d}{\mathrm{dt}}{d}_i\mathrm{}\left(t\right)=\Sigma \stackrel{}{j}{h}_{\mathrm{ij}}\mathrm{}\left(t\right)\mathrm{}{d}_j\mathrm{}\left(t\right)\mathrm{},$ which describe the "time" dependence of electronic-quantum-state amplitudes as the nuclei move along a classical trajectory. These equations are derived in two ways. In the first formulation, which coincides with the intuitive classical picture of the collision, the nuclear part of the wave function is treated as a superposition of narrow wave packets, each traveling along a classical trajectory. In the second formulation, a semiclassical approach is used. The validity and meaning of the two formulations are discussed and compared.

The time-dependent equations of the classical picture of inelastic collisions (classical-trajectory equations) are derived using the momentum-space semiclassical approximation. Thereby it is shown that the classical-trajectory equations remain valid in the vicinity of classical turning points provided that (a) the momentum-space semiclassical approximation is valid, (b) the trajectories for elastic scattering in the various internal states differ only slightly, and (c) the slopes of the elastic scattering potentials have the same sign. A brief review of the existing derivations of the classical-trajectory equations is given, and the general conditions for their validity are discussed.

A unified formal treatment of the two-state potential-curve-crossing problem in atomic collision theory is presented, and the case of close crossings analyzed in detail. A complete solution for this case, including necessary computations, is given using a suitable generalization of the linear model originally suggested by Landau, Zener, and Stueckelberg. Our solution is based upon a hierarchy of approximations concerned with (i) choice of a discrete basis set for electronic coordinates, (ii) semiclassical treatment of the nuclear motion, (iii) an appropriate model for the two-state electronic Hamiltonian, and (iv) a complete solution to that model.

We have studied a near-resonant charge-exchange process between incident protons and a cesium vapor target. The cross section ${\sigma }_{+0\mathrm{}}$ for the production of all the neutral states of hydrogen decreases slightly with increasing energy. It varies from (10±3) × ${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$ at 0.5 keV to (6.4±1.6) × ${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$ at 2.5 keV. The cross section ${\sigma }_{+m}$ for the production of the $2S_{\frac{1}{2}}$ metastable state of hydrogen is (1.7±0.6) × ${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$ at 2.4 keV. The percentage of metastable atoms in the outgoing neutral beam is found to be 0.27±0.08 for cesium target thickness less than ${10}^{13}$ atoms/${\mathrm{cm}}^2$. The outgoing fraction of $\mathrm{H}\left(2\mathrm{}{S}_{\frac{1}{2}}\right)$ atoms reaches a maximum equal to 0.13 for a cesium thickness of 1.2×${10}^{14}$ atoms/${\mathrm{cm}}^2$. The collisional quenching processes studied are the electron loss of $\mathrm{H}\left(2\mathrm{}{S}_{\frac{1}{2}}\right)$ on the noble gases ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, and HI at 2.5 keV and the electron attachment of $\mathrm{H}\left(2\mathrm{}{S}_{\frac{1}{2}}\right)$ on ${\mathrm{N}}_2$ at the same energy. The electron-loss cross sections ${\sigma }_{m+}$, in units of ${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$, and known with a 35% uncertainty, are 4.1 for He, 2.7 for Ne, 2.9 for Ar, 2.7 for Kr, 6 for Xe, 3.4 for ${\mathrm{H}}_2$, and 5 for ${\mathrm{N}}_2$. The cross section ${\sigma }_{m+}$ is always greater than ${\sigma }_{g+}$, the electron-loss cross section for the ground state of hydrogen. The maximum ratio 9.7 of these two cross sections is obtained with the halogen compound target HI, which is an interesting gas to selectively ionize $\mathrm{H}\left(2\mathrm{}{S}_{\frac{1}{2}}\right)$ in a beam containing the two species $\mathrm{H}\left(2\mathrm{}{S}_{\frac{1}{2}}\right)$ and $\mathrm{H}\left(1\mathrm{}{S}_{\frac{1}{2}}\right)$. A comparison of the data is made with theoretical predictions using an impulse approximation. Attachment cross sections of $\mathrm{H}\left(2\mathrm{}{S}_{\frac{1}{2}}\right)$ and $\mathrm{H}\left(1\mathrm{}{S}_{\frac{1}{2}}\right)$ have been measured on ${\mathrm{N}}_2$ at 2.5 keV. We obtain ${\sigma }_{m-}=(1.2\mathrm{}\pm 0.4)\times {10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ and ${\sigma }_{g-}=(9.7\mathrm{}\pm 2)\times {10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$.

Results are reported on an experiment to measure the ion temperature in a 100-kJ $\theta$-pinch deuterium plasma. A ruby laser was used for scattering observations at 5° and 90° using multichannel spectrum analyzers and gave $n=1.05\mathrm{}\times {10}^{17}$ ${\mathrm{cm}}^{-3\mathrm{}}$ and $T_i=300\mathrm{}$ eV. An independent measurement of the density was made by means of Rayleigh scattering. The neutron yield from the plasma was measured to be 8×${10}^8$ ${\sec }^{-1\mathrm{}}$. The observed neutron emission was compared with that expected from a plasma with an ion temperature of 300 eV and was found to be of thermonuclear origin.

The detection of ∼ 100-keV x radiation and of directly back-scattered light is described for neodymium-glass-laser light pulses focused on a polyethylene target. These observations can be explained in terms of the nonlinear excitation of plasma waves by the laser light.

A new general expression for the electrical resistivity of a substance is obtained with the help of projection techniques with the Liouville equation as the point of departure. No many-body detail is sacrificed and the "${\lambda }^{2}t$ limit" is not invoked. The first-order result in a perturbation expansion in orders of the scattering is presented in explicit form and shown to have a simple and physical appearance. It is also shown to reduce to the well-known Boltzmann expressions for simple cases.

The long-time behavior of velocity-correlation functions ${\rho }^{\mathrm{}\left(d\right)\mathrm{}}\mathrm{}\left(t\right)\mathrm{}$ characteristic for self-diffusion, viscosity, and heat conductivity is calculated for a gas of hard disks or hard spheres on the basis of the kinetic theory of dense gases. In $d$ dimensions one finds that ${\rho }^{\mathrm{}\left(d\right)\mathrm{}}\mathrm{}\left(t\right)\mathrm{}$, after an initial exponential decay for a few mean free times $t_0$, exhibits for times up to at least $\sim 40t_0$ a decay $\sim {\alpha }^{\mathrm{}\left(d\right)\mathrm{}}\left(\rho \right){\left(\frac{t_0}{t}\right)}^{\frac{d}{2}}$, where ${\alpha }^{\mathrm{}\left(d\right)\mathrm{}}$ is of the order of ${\rho }^{d-1\mathrm{}}$, $\rho =n{a}^d$ with $n$ the number density, and $a$ the hard-disk or hard-sphere diameter. The ${\alpha }^{\mathrm{}\left(d\right)\mathrm{}}\left(\rho \right)$ are determined by the same dynamical events that are responsible for the divergences in the virial expansion of the transport coefficients. In this paper the ${\alpha }^{\mathrm{}\left(d\right)\mathrm{}}\left(\rho \right)$ are calculated to lowest order in $\rho$. In this order, they are identical to the low-density limit of the ${\alpha }^{\mathrm{}\left(d\right)\mathrm{}}\left(\rho \right)$ that have been obtained by other authors on the basis of hydrodynamical considerations.

The transport coefficients in high electric fields are obtained for electrons bound in image-potential-induced surface states on a dielectric liquid surface. A two-dimensional Boltzmann equation is solved in the diffusion approximation, assuming the principle electron scatterers are gas atoms and surface waves. At high temperatures, where gas-atom scattering dominates both energy and momentum relaxation, the transport coefficients are field independent even though the average electron energy is much higher than the product of Boltzmann's constant and the liquid temperature. At low temperatures, where surface-wave scattering dominates the momentum relaxation, the conductivity and Hall mobility increase rapidly with increasing electric field. For ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ this non-Ohmic transport should occur below 1 K at fields below 0.1 V/cm.

Density correlation between two microscopic volumes in argon fluid is given in terms of x-ray intensity data. Results show that the size of a region with maximum molecular correlation is approximately 40 Å for every thermodynamic point studied here. For points nearer the critical point, the maximum has a larger and broader shoulder, indicating that equally large correlations exist for different-sized cells. This result agrees with a view on the use of arbitrary cell size in the scaling-law theory.

We have detected the appearance of individual quantized vortex lines in liquid He II in narrow-diameter (∼1 mm) rotating cylindrical vessels which were slowly accelerated from rest. The angular velocities where the lines appear are qualitatively consistent with theory based upon minimization of the free energy. However, we find that the detailed behavior of the He II is quite history dependent and cannot be uniquely determined from existing theory. Our detection technique involves charging the vortex lines for a fixed length of time. A subsequent measurement of the amount of charge trapped provides an indication of the number of vortex lines present. In order to detect the small amount of charge trapped on a single line, we have extracted the trapped electrons through the meniscus and have developed a proportional counter to detect them in the vapor.

The line shapes of absorption spectra of trapped electrons in metal-ammonia solutions, water, and alcohols are compared in detail with photodetachment spectra of spherical potentials, which have been applied extensively in liquid helium. A qualitative discussion is presented to point out some uncertainty in the role of the bound-bound transition $1s\to 2p$, which is predominant in the dielectric continuum model. Apart from the uncertainty related to the effective mass of the polaron, the coherence of the $2p$ state in the more realistic fluctuation potential is likely to be small. A molecular model for the trapped electrons is briefly described.

An approximation method is developed which yields very simple and general analytical results for electromagnetic bound-bound or bound-free transitions for any arbitrarily high order of interaction with the electromagnetic field. The approximation is perturbative in the sense that transition probabilities are proportional to the field intensity raised to the power $N$, where $N$ is the order of the interaction. Limiting values of electromagnetic field strength are given within which the approximation is valid. These limits depend upon the binding potential which produces the bound states. A feature of the results is that they show the onset of high-order dominance effects which can occur at high-field intensities.

We analyze the phase modulation, or chirping, of coherent lossless light pulses propagating without distortion through resonant absorbers. In order to do this, we generalize the pioneering work of McCall and Hahn in two different directions. In the first place, of course, we abandon their assumption that the phase of the pulses has no temporal dependence. We prove that for slowly varying single pulses, chirping is not possible. However, we describe many multiple-pulse trains which are necessarily chirped, even under the slowly varying envelope restriction, and also describe the envelope modulations which produce large chirps. We show that certain zero-$\pi$ chirped pulse trains are contained as special cases of our general results. Our second generalization of the McCall-Hahn work concerns the background material in which the two-level resonant atoms are suspended. We allow the host medium to possess significant nonresonant nonlinearities. We find that undistorted lossless single pulses are possible in such a medium and that they are necessarily chirped.