The moments of a spectral line are evaluated in a general way and compared with results which invoke standard assumptions of line-broadening theory. Cesium-rare-gas systems are analyzed for a variety of experimental conditions in the hope of extracting useful information about excited-state interactions. The computation uses atomic-beam results for the ground-state interaction and assumes that the excited-state potentials are represented to a first approximation by $V_f=\frac{G}{R^{12}}-\frac{D}{R^6}$. The calculation, which includes a comparison of line shapes, indicates that the following numbers (in cgs units) are reliable for the long-wavelength component of the resonance lines of cesium: with argon, $G=4.87\mathrm{}\times {10}^{-102\mathrm{}}$, $D=4.74\mathrm{}\times {10}^{-58\mathrm{}}$; with helium, $G=0.459\mathrm{}\times {10}^{-102\mathrm{}}$ and $D=-0.614\mathrm{}\times {10}^{-58\mathrm{}}$. Analysis of the cesium-xenon system yields results which illuminate the practical difficulties associated with an otherwise attractive technique.

A systematic convergent method of studying intermolecular forces in excited states is detailed. Extensive comparison between theory and experiment indicates that high-resolution line-shape experiments over a wide range of frequencies will permit the inference of parameters in realistic forms of the potential energy. The analysis focuses on the ${}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}-{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ resonance line of cesium pressurized by helium, argon, and xenon. When the model is used with ground-state potentials inferred from atomic-beam experiments, and when the excited state is described by $V=\frac{G}{R^{12}}-\frac{D}{R^6}$, the following reliable parameters were determined: helium, $G=0.459\mathrm{}\pm 0.060$ and $D=-0.614\mathrm{}\pm 0.061$; argon, $G=6.48\mathrm{}\pm 0.20$ and $D=5.23\mathrm{}\pm 0.05$; xenon, $G=53.6\mathrm{}\pm 5.8$ and $D=19.1\mathrm{}\pm 0.57$, where the units of $G$ are ${10}^{-102\mathrm{}}$ erg ${\mathrm{cm}}^{12}$ and of $D$ are ${10}^{-58\mathrm{}}$ erg ${\mathrm{cm}}^6$.

In the local-effective-potential approximation of the Kohn-Sham self-consistent scheme applied to an atomic system, it was reported that while the calculated exchange energies for various atoms were accurate to within 10%, the correlation energies of atoms were too large by a factor of 2. A model system is set up to study the reason why the exchange energy estimates are so much better than those of the correlation energy even though they were treated on the same footing. It was found that, in using expressions derived from an infinite electron gas system to study finite systems, the major source of error comes from the fact that the low-lying levels of a finite system are discrete and have finite spacings. The replacement of summation by integration in the perturbation diagrams results in an overestimate of correlation energy, and a small error in the exchange energy in a finite system like an atom.

Electronic structures of hypothetical molecules containing quarks, or fractionally charged particles, are treated. By regarding the quark charge $Q$ as a continuous variable, approximations satisfying a consistency condition at small-$Q$ values are formulated. Their validity is checked with the exact solutions of the one-electron two-center problem and applied to two-electron two-center problems of ${\mathrm{H}}^{-}$-quark and He-quark molecules.

We present a clarification of the often misunderstood concept of rearrangement that affects particle removal from finite fermion systems. A separation energy is defined which depends on the speed of removal as a result of physical rearrangement processes. It is shown how single-particle eigenvalues can be observed when a single-particle description applies to the many-body system. Calculations of atomic rearrangement energies are discussed, and a linear $Z$ dependence is derived. The photo-ionization spectrum for $1s$ electrons from Ne is used as a quantitative example to extract rearrangement energy and time. Possible application to nucleon-removal data analysis is discussed.

The purpose of this paper is to show by a model calculation that the internal conversion theory may be used to obtain auto-ionization rates for $\Delta {\nu }_{\mathrm{if}}=1\mathrm{}$ vibrational transitions in ${\mathrm{H}}_2$, within the right order of magnitude. Thus, the present calculation remedies the apparent inability of the model to predict desirable rates as calculated by previous authors. The results obtained compare fairly well with the experimental estimates of Chupka and Berkowitz, but are closer to the alternative theoretical calculations of Berry and Nielsen for $\Delta {\nu }_{\mathrm{if}}=1\mathrm{}$. It explicitly shows the $\frac{1}{n^3}$ dependence of rates for increasing principal quantum numbers $n$, and follows the so-called "propensity rule" for vibrational transitions involved. Limitations and possible refinements of the present model are discussed, and the generalization for molecules other than ${\mathrm{H}}_2$ is indicated. Within the approximation of the model, it provides a simple formula from which rates may be easily estimated.

Electric quadrupole transition probabilities for the oxygen atom auroral line ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}-{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ ($\lambda =5577\mathrm{}$ λ) and the ${}_{}{}^2{}_{}{}^{}P-{}_{}{}^2{}_{}{}^{}D$,${}_{}{}^1{}_{}{}^{}S-{}_{}{}^1{}_{}{}^{}D$ lines in CI, NI, NII, OII, and OIII, which are of atmospheric and astrophysical interest, are calculated. The nonclosed-shell many-electron theory (NCMET) of atomic structure developed by Sinanoğlu and co-workers, which treats electron correlation accurately in both ground and excited states, predicts novel correlation effects which are included in the wave functions used to calculate the transition probabilities. These are many-body calculations on "forbidden" lines, the first of their kind. We explicitly examine the effect of electron correlation on the quadrupole line strengths. It is found that the Hartree-Fock values are reduced by 13-17% when all the important correlation effects are included in the wave functions. In view of the accuracy of the wave functions and of the method of calculation, the results obtained are expected to be accurate with a less than 5% uncertainty. For the much discussed O I ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}-{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ (5577 Å) transition we find $A_Q=1.183\mathrm{}$ ${\sec }^{-1\mathrm{}}$. Comparison is made with previous experimental and theoretical work.

The linked-cluster many-body perturbation theory has been applied in a calculation of the correlation energy of the neon atom in the ground state (${}_{}{}^1{}_{}{}^{}S$). The pair-correlation energy, obtained by summing the correlation energy between all pairs of states in the atom, is found to be - 0.413 26 a.u. About 5% of the pair-correlation energy comes from excitations to $g$, $h$, and $i$ states. Pair-pair interactions are found to be important and contribute 0.022 44 a.u. to the correlation energy. Correlation diagrams involving simultaneous excitations of three and more particles are found to be relatively unimportant and lead to a net contribution of only about 0.003 a.u. Our final value for the correlation energy is - 0.389 14 a.u., which is in excellent agreement with the nonrelativistic experimental correlation energy of - 0.389 a.u. A detailed comparison is made with the available configuration interaction calculations both with respect to numerical results as well as to the relative importance of various physical effects which contribute to the correlation energy.

Total elastic scattering cross sections have been computed for the scattering of electrons by neutral neon and argon in the energy range 0-1 Ry. These results were obtained by the polarized-orbital method wherein a polarization potential accounts for the distortion of the atomic electron distribution by the scattering electron. The polarization potentials are determined using perturbed orbitals obtained by the Sternheimer and Hartree-Fock-Slater (HFS) approximations. Dipole polarizabilities are also calculated. The results are used to evaluate total scattering cross sections by the two approximations and evaluate their capabilities by comparison with experimental data. The HFS-based approximation works very well for neon giving substantially improved cross sections over earlier Sternheimer-based calculations by Thompson. However, little improvement is obtained in either case for argon.

The results of detailed multichannel close-coupling calculations of the autoionizing states converging on the ${}_{}{}^1{}_{}{}^{}D$ and ${}_{}{}^1{}_{}{}^{}S$ terms of the ground-state configuration of the nitrogen ion are described. The effect of these states on the photoionization of the ground-state terms of the nitrogen atom is also discussed. Photoionization cross sections are given for the processes $h\nu +\mathrm{N}({}_{}{}^4{}_{}{}^{}S,{}_{}{}^2{}_{}{}^{}P,{}_{}{}^2{}_{}{}^{}D)\to {\mathrm{N}}^{+}({}_{}{}^3{}_{}{}^{}P,{}_{}{}^1{}_{}{}^{}D,{}_{}{}^1{}_{}{}^{}S)+\epsilon l$ and the results are analyzed in detail in detail in terms of the level assignments, positions, widths, resonance-shape parameters, and quantum defects of the identified autoionizing series. The self-consistency of the calculations is demonstrated by comparison with other theoretical results and the one experimental measurement available. Some suggestions for possible experimental work are also made.

Detailed studies of the time dependence of the number density of ions have been made during the decay period of plasmas produced in He containing various concentrations of nitrogen molecules. Various reaction-rate constants were obtained: $\mathrm{He}\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S\right)+{\mathrm{N}}_2\to \mathrm{N}_2^{}{}_{}{}^{+}+\mathrm{He}+e\left[\right(6.3\mathrm{}\pm 1.0)\times {10}^{-11\mathrm{}} {\mathrm{cm}}^{3}invsec]$; ${\mathrm{N}}_2^{+}$ + ${\mathrm{N}}_2$ + He → ${\mathrm{N}}_4^{+}$ + He [(5.3 ± 0.3) × ${10}^{-30\mathrm{}}$ ${\mathrm{cm}}^6$ ${\sec }^{-1\mathrm{}}$] and ${\mathrm{N}}^{+}$ + ${\mathrm{N}}_2$ + He → ${\mathrm{N}}_3^{+}$ + He [(4.6 ± 0.4) × ${10}^{-29\mathrm{}}$ ${\mathrm{cm}}^6$ ${\sec }^{-1\mathrm{}}$]. Evidence for the charge-transfer process ${\mathrm{N}}_2^{+}$ + N → ${\mathrm{N}}^{+}$ + ${\mathrm{N}}_2$ was obtained. The values of the ambipolar-diffusion coefficients of nitrogen ions in He were found to be $D_a{p}_0\left({\mathrm{N}}^{+}\right)=970\mathrm{}\pm 50$; $D_a{p}_0\left(\mathrm{N}_2^{}{}_{}{}^{+}\right)=920\mathrm{}\pm 40$, and $D_a{p}_0\left(\mathrm{N}_3^{}{}_{}{}^{+}\right)=840\mathrm{}\pm 70$ ${\mathrm{cm}}^2$ ${\sec }^{-1\mathrm{}}$ Torr, while the diffusion coefficient of $\mathrm{He}\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}S\right)$ was $D_m{p}_0=480\mathrm{}\pm 30$ ${\mathrm{cm}}^2$ ${\sec }^{-1\mathrm{}}$ Torr.

Cross sections for electron capture into the $2s$ and $2p$ states of atomic hydrogen have been measured for proton impact on He, Ne, Ar, ${\mathrm{N}}_2$, and ${\mathrm{O}}_2$. In addition, capture into the $2s$ state has been measured for proton impact on ${\mathrm{H}}_2$. Generally, these measurements have been carried out in the energy range from 20 to 130 keV. Absolute calibration of the helium-filled iodine Lyman-alpha counter was obtained by a normalization procedure involving previous $2p$ capture measurements for impact on He, Ne, and Ar, after an investigation of the detector response for electron impact on ${\mathrm{H}}_2$. Calibration for the $2s$ capture was established by determining the $2s$ cross section relative to the $2p$ cross section for 20- and 30-keV impact on Ne. The polarization effect in the Stark-quenched $2s$ radiation was minimized by observing the Stark-induced radiation at 54.7° to the electric field direction. The $2s$ cross sections relative to the previously measured $3s$ cross section show a remarkable (about 10%) agreement with the $n^{-3\mathrm{}}$ law (predicted at high energies) above 20 keV for all gases, excluding He. It appears that the $n^{-3\mathrm{}}$ behavior sets in at about 100 keV for He. In general the $2s$ cross section tends to be somewhat higher than predicted by the $n^{-3\mathrm{}}$ law for impact on He in the range from 25 to 100 keV. It appears that the $2s$ cross sections will agree with the coupled-state calculation of Sin Fai Lam for impact on He above 100 keV. The $2p$ cross sections are lower than those predicted by theory for impact on He in this energy range. The $2p$ cross sections relative to the previously measured $3p$ cross sections appear to roughly follow an $n^{-3\mathrm{}}$ behavior at the higher energies, again with the possible exception of helium. Comparisons are made with the results of other experimental investigations.

Electron-capture and electron-loss cross sections for various gaseous (${\mathrm{N}}^{+}$, ${\mathrm{O}}^{+}$, ${\mathrm{Ar}}^{+}$, ${\mathrm{Kr}}^{+}$, and ${\mathrm{Xe}}^{+}$) and metallic (${\mathrm{Al}}^{+}$, ${\mathrm{K}}^{+}$, ${\mathrm{Fe}}^{+}$, ${\mathrm{Ba}}^{+}$, and ${\mathrm{Ba}}^{++}$) ions in collisions with atomic oxygen have been measured in the energy range 30 keV to 2 MeV. Beam-in-static-gas techniques were employed. Ions formed by an electron-impact ion source were mass selected by a rf quadrupole mass filter and were accelerated by a Van de Graaff accelerator into a fast well-collimated ion beam. This ion beam was then steered through an atomic-oxygen target chamber development to provide a collision region containing thermally dissociated oxygen atoms in the ground state. The charge states of the emerging fast-ion beam were measured and this information along with knowledge of the atomic-oxygen-target thickness within the target chamber was used to deduce the electron-capture and electron-loss cross sections of the particular fast heavy ion on neutral atomic oxygen. Comparison with theoretical calculations and other experimental data were made where possible.

In the calculation of excited-state cross sections for electron impact on hydrogen atoms, the hypothesis $A={\overrightarrow{\nabla }}_1\ln {\phi }_j\left({\overrightarrow{\mathrm{r}}}_1\right)·({\overrightarrow{\nabla }}_R\ln g_j^{\pm }-{\overrightarrow{\nabla }}_{\rho }\ln g_j^{\pm })=0\mathrm{}$ is used to solve the Schrödinger equation of the system. The purpose of this work is to take into account this term assuming that ${\overrightarrow{\nabla }}_1\ln {\phi }_j\left({\overrightarrow{\mathrm{r}}}_1\right)$ is equal to a constant vector ${\overrightarrow{C}}_j$ dependent on the atomic state under consideration. Taking into account the justification and the consequences of this hypothesis, the equation of the system is solved when one puts the term $A$ into this form. The transition amplitudes $T_{0n}$ are calculated by "prior" and "post" approximations and compared, and the cross sections are obtained and discussed for four transitions. These various results show that the introduction of the term $A$ favors the prior approximation because it is expressed by a constant modification of the incident electron energy, which is not the case for the post approximation.

Electron-impact energy-loss spectra of ${\mathrm{O}}_2$ have been analyzed for incident electron energies from 4 to 45 eV, scattering angles from 10° to 90°, and energy losses from 0 to 5 eV. The inelastic processes observed were the excitation of the $a{}_{}{}^1{}_{}{}^{}\Delta _g^{}{}_{}{}^{}$ and $b{}_{}{}^1{}_{}{}^{}\Sigma _g^{}{}_{}{}^{+}$ electronic states and vibrational excitation in some cases to $v^{\prime \prime }=13\mathrm{}$. The excitation cross sections at each energy were made absolute by normalizing the sum of the integral cross sections (all inelastic, ionization, and elastic) to measured electron-${\mathrm{O}}_2$ total cross sections. The differential cross sections for the $a{}_{}{}^1{}_{}{}^{}\Delta _g^{}{}_{}{}^{}$ and $b{}_{}{}^1{}_{}{}^{}\Sigma _g^{}{}_{}{}^{+}$ states show nearly isotropic behavior, as expected for optically spin-for-bidden transitions. The elastic differential cross sections are strongly forward peaked at higher energies, but become only slightly forward peaked at the lower energies. The integral cross sections for the excitation of the $a{}_{}{}^1{}_{}{}^{}\Delta _g^{}{}_{}{}^{}$ and $b{}_{}{}^1{}_{}{}^{}\Sigma _g^{}{}_{}{}^{+}$ states reach their maxima near 7 eV and are more than an order of magnitude larger than previous estimates. The integral elastic cross section reaches its maximum at around 10 eV.

An eikonal theory of elastic electron-atom scattering in the region of intermediate energies is proposed. In addition to the effects of the static and polarization potentials, we also take into account the leading absorption corrections, using the equivalent-potential method. Detailed calculations are performed for elastic electron-helium scattering in the energy range 100-500 eV. Our results are in good agreement with the recent experimental data.

Semiclassical approximations are applied to atomic collisions with complex potentials. The effects of damping due to the imaginary parts of the complex potentials are investigated in the JWKB and eikonal approximations. Numerical illustrations are given for a model (${\mathrm{H}}^{-}$, H) system constructed in Paper I of this series. The calculated results for such a model are compared with available experimental measurements for electron-transfer and collisional-detachment processes in the (${\mathrm{H}}^{-}$, H) collision system at high energies. Important differences, which come primarily from the inadequacy of the model potentials and the non-adiabatic effects, are found between the theoretical and experimental results.

A set of coupled equations with a self-consistent optical potential which is explicitly expressed in terms of a set of functions constructed to account for the polarization, correlations, and short-range interactions is derived for scattering and rearrangement collisions. Applications of the self-consistent coupled equations to several atomic collision problems are considered. Numerical illustrations are given for the investigation of the resonance structures in elastic $e,H$ scatterings.

The behavior of a general quantum-mechanical system under the influence of an intense monochromatic driving field is discussed. The resonance representation is introduced to derive the analog to the Rabi formula for the case where the driving field is at a resonance of the system. The first approximation result contains the slowly varying perturbation contribution to all orders and is shown to be valid for both coherent and incoherent monochromatic driving fields.

The dynamics of the liquid state of two organic free-radical solutions has been studied by means of EPR, NMR, and DNP (dynamic nuclear polarization). In our spectrometer these effects can be measured simultaneously and over a wide range of temperatures. The aim was to study the gradual transition from the ordinary liquid state to a greatly supercooled liquid state, and in particular the change from the Overhauser-type DNP to the solid-type DNP. The samples were a 0.02-mole/liter solution of tanone in isopropanol and a 0.03-mole/liter solution of tetrachlorosemiquinone in tetraethyleneglyco. The EPR can be explained in terms of random rotational modulation of the anisotropic $g$ factor of the radical, with a correlation time which is an exponential function of reciprocal temperature. At the temperatures of interest, $T_{1e}$ and $T_{2e}$ differ by at least one order of magnitude. The NMR follows from the Torrey model, the protons relaxing through dipole interaction with the electron spin while their molecule is temporarily adsorbed in the solvation layer of a radical. The data can be fitted by a model with a dipole-dipole correlation function based on a rather broad distribution of correlation times, the mean value and temperature dependence being similar as in EPR. The DNP shows a typical gradual transition from the (even) Overhauser effect to the (odd) solid effect as the temperature is lowered. This happens when the correlation time and $T_{2e}$ cross. A theoretical analysis of the DNP on the basis of the liquid structure as revealed by EPR and NMR is given in the following paper.