Highly excited principal quantum states of ${\mathrm{H}}_3$ molecules formed by electron-capture collisions of ${\mathrm{H}}_3^{+}$ in ${\mathrm{H}}_2$ gas have been observed. An intense electric field was used to strip the orbital electron from the excited ${\mathrm{H}}_3$. Comparisons with data obtained with excited ${\mathrm{H}}_2$ indicates that the fraction of ${\mathrm{H}}_3$ ionized was proportional to the $\frac{3}{4}$ power of the electrostatic-stripping field.

$1s-1s$ elastic and $1s-2s$ inelastic total cross sections for $e$-H collision have been calculated with and without exchange effects using the Faddeev formalism as developed by Sloan and Moore. We have considered the effect of coupling to $1s$ and $2s$ intermediate states. Our theoretical results have been compared with the existing experimental findings and other theoretical calculations. In the intermediate-energy region, our results for the inelastic process are found to be in close agreement with the experimental observations. Our results for both systems indicate that coupling to states other than the initial and final ones causes a reduction in the cross sections, and even up to 500 eV the effect of exchange is not negligible.

18- to 46-MeV ${}_{53}{}^{}{}_{}{}^{}\mathrm{I}$ ions were scattered by thin ${}_{52}{}^{}{}_{}{}^{}\mathrm{Te}$ targets. The $L$ x rays produced in the nearly identical particles ${}_{53}{}^{}{}_{}{}^{}\mathrm{I}$ and ${}_{52}{}^{}{}_{}{}^{}\mathrm{Te}$ were measured in coincidence with the scattered I ions. The differential cross section for $L$ x-ray emission shows a maximum at impact parameters comparable to the $L$-shell radii. For the ion energies $E$ investigated, the total cross section for $L$ x-ray emission in I and Te was found to be proportional to $E^{0.8}$. The results are discussed and compared with theoretical models for inner-shell excitation.

We present classical calculations of ion-atom elastic differential cross sections for energies between 4 and 627 keV and for a variety of projectile-target combinations. These calculations are based on two new interaction potentials. The first is an extension of Smith's shell potential, and the second is obtained from the unperturbed interaction of the Hartree-Fock-Slater electron densities of the target and projectile. Calculations of cross sections and distances of closest approach for these potentials are compared with predictions of the screened-Coulomb potential and the available experimental data. For collisions between light particles at energies of a few keV the static potential appears to be more accurate than the extended-shell and screened-Coulomb potentials. For collisions between heavier particles both of the new potentials are usually more accurate than the screened-Coulomb potential.

The incoherent-scattering function, or Compton scattering factor, has been calculated for the neutral carbon atom with a Hartree-Fock wave function and with configuration-interaction wave functions containing up to 40 terms. Values obtained with the correlated wave functions differ from the Hartree-Fock value by as much as 22%.

An impact-parameter method using Coulomb trajectories has been used to calculate cross sections for the following two electron-detachment collision processes: (i) $e^{-}+{\mathrm{H}}^{-}\to \mathrm{H}\mathrm{}\left(1S\right)+2\mathrm{}{e}^{-}$; (ii) $e^{-}+{\mathrm{H}}^{-}\to \mathrm{H}\mathrm{}\left(2S\right)+2\mathrm{}{e}^{-}$. The cross section for process (ii) is found to be approximately two orders of magnitude smaller than that for (i). The results of process (i) are compared with the available experimental data. The plane- and Coulomb-wave cross sections in dipole approximations are calculated both at high and low energies and are compared with the semiclassical results. The asymptotic behavior of the cross sections at high energies is investigated in detail. Energy distributions of ejected electrons at three different incident energies are also calculated.

The unitarity relation of quantum-scattering theory is studied for the general case of scattering by an arbitrary noncentral force and it is shown how it can be utilized to determine the phase of the scattering amplitude from the measured differential cross section. It is found that the unitarity relation leads to a pair of nonlinear integral equations for the phase of the scattering amplitude if the cross section is known. It is shown that from these equations one can obtain, without introducing approximations, a system of linear algebraic equations for a certain set of scalars from the values of which one can readily calculate the phase. In general, the above system of linear equations may admit also redundant nonphysical solutions for the phase. However, when the magnitude of the cross-section data satisfies certain conditions the solution of the equations is unique and must equal the correct physical value of the phase. Unlike previous methods for phase determination, the present approach is based on a form of the unitarity equation which is not simplified by any of the assumptions of parity, rotational, or time-reversal invariance for the underlying scattering interaction. Therefore, it can be applied to the determination of the phase also in cases such as particle scattering by, or in the presence of, external fields which do not possess the above-mentioned symmetries. A generalization of this method to many-channel scattering is also provided. Similar results hold also for the determination of phases in the theory of electromagnetic-wave scattering by an obstacle of arbitrary shape.

A quantum-mechanical unified theory of foreign-gas pressure broadening of atomic lines which includes the impact and statistical theories and duration-of-collision effects is developed. The model consists of an absorber atom with two internal states $u$ (upper) and $l$ (lower) interacting with a structureless perturber gas via two spherical pairwise additive potentials $V_u\left(\mathcal{r}\right)$ and $V_l\left(\mathcal{r}\right)$, e.g., a simple model of an alkali-atom line perturbed by a rare gas. The dipolemoment correlation function is analyzed in the time domain using Liouville (tetradic) techniques. The correlation function reduces exactly to a two-body form $\phi \mathrm{}\left(t\right)\mathrm{}$ containing the proper thermal weight factors. Detailed balance is obeyed and no $\left|\frac{\hslash (\omega -{\omega }_0)}{\mathrm{kT}}\right|<\mathrm{}1\mathrm{}$ restriction is required. The impact theory follows from a long-time analysis of $\phi \mathrm{}\left(t\right)\mathrm{}$. Sum rules or spectral moments are used to study short-time behavior revealing conventional statistical-theory effects (including satellite bands) and the important duration-of-collision effects which link the statistical and impact regimes. The sum rules are expressed as quadratures involving potential functions and the quantum-mechanical radial distribution function. Unified methods for calculating the total line shapes are suggested: (1) Padé approximants (ratios of polynomials) can be used to interpolate from the known short-time behavior to the known long-time beahvior; this requires the least computational effort; (2) exact results for this model may be obtained numerically from the overlap integrals of radial wave functions (Franck-Condon factors) for the two potentials $V_u$ and $V_l$; (3) classical phase (trajectory) expressions are given which are reasonable approximations in both the impact and statistical limits. A number of related topics are discussed including diabatic effects, collision-induced absorption, non-Lorentzian wings of molecular vibration-rotation bands, and the Condon approximation for the dipole-moment transition strength vs $\mathcal{r}$. The use of line shapes to probe atomic interactions, especially in excited states, is emphasized and the suggestion made that experiments be done over as wide a temperature range as possible with the measured line shapes in computer-readable form. The entire line-shape problem is described as the study of the spectrum of an atom-perturber "quasimolecule" (with primarily unbound states).

Methods have been developed for depositing electrons on the surface of liquid helium, either from the gas side or from the liquid side. In a suitable applied electric field they escape from the surface into the gas and the rate of escape has been measured. Electrons inside the surface escape by a thermally activated process. Those outside the surface escape much more rapidly by what appears to be a tunneling process. Analysis of the equilibrium between bound and free electrons identifies important features of the binding which have not previously been considered.

Surface modes in a homogeneous system with a sharp boundary are discussed using the collisionless Boltzmann equation for the Wigner distribution function. In a one-component system of fermions interacting via a Yukawa potential, we show that there is an acoustic surface mode. In the limit of long wavelengths, it becomes indistinguishable from the analogous bulk zero-sound mode. For a system of electrons and ions, we find a low-frequency in-phase surface mode, in addition to a high-frequency out-of-phase optical surface mode. For long wavelengths, the low-frequency mode is phononlike with a speed identical to that given by the Bohm-Staver expression.

The normalization of the electron density associated with approximate variational solutions of the Thomas-Fermi (TF) equation for neutral atoms is discussed, and the applicability of a procedure of Anderson, Arthurs, and Robinson for obtaining the closest approximation is investigated. It is concluded that using single-parameter trial functions, the normalization requirement for the electron density cannot be strictly satisfied when the numerical value of the parameter is determined from the minimization of the difference between the complementary upper and lower bounds to the exact TF energy of a neutral atom. It is also concluded that, using multiple-parameter trial functions, this procedure is applicable since the numerical values of all but one of the parameters can be found from the minimum between the complementary bounds without violating the normalization requirement.

In an attempt to help resolve previously observed discrepancies between the theory for ultrasonic attenuation and the data at the vapor pressure, we have extended our measurements to higher pressures. We report data on the temperature dependence of the attenuation from 0.1 to 1.0 K at frequencies of 15, 45, 105, and 256 MHz for pressures between 0 and 24.7 atm. At low pressures or temperatures, the data resemble the theoretical predictions, but the measured attenuation is about twice that predicted by most theories. At higher pressures and for temperatures above about 0.3 K, the attenuation shows a sharp reduction below the value extrapolated from low temperatures according to previous theories. It has recently been suggested that this unexpected behavior is due to a restriction on the number of thermal phonons that are able to play a part in the attenuation process at higher temperatures and pressures.

The pair distribution for normal He atoms in the vicinity of a metastable $2{}_{}{}^3{}_{}{}^{}S$ He atom is calculated in the zero-temperature limit, from first principles, using a variational Jastrow wave function and the Percus-Yevick integral equations for fluid mixtures. From this pair function, the "bubble radius," coordination number, and energy per metastable atom are calculated.

The rate of absorption of energy from a weak signal field by an atom driven by a strong pump field is evaluated. The pump field and the signal field are assumed to induce transitions between the same pair of states, and their frequencies are both assumed to lie near the atomic resonance frequency for the transition in question. We find that the signal-field absorption line-shape function takes on negative values, representing stimulated emission rather than absorption, even though population inversion does not occur. This amplification of the signal field, which is most pronounced at high pump intensities, is shown to occur primarily at the expense of the pump field, which suffers an increased rate of attenuation. The results are discussed in the context of a theorem which expresses the absorption line-shape function for general atomic systems in terms of a suitable atomic correlation function.

For liquids, the part of the effective pair potential due mainly to the highly liquid-structure-dependent three-body interactions is calculated. Molecular solvation structures around two interacting molecules are generated on the computer by averaging over various ways of packing the liquid molecules. The results are used to check the analytical expressions which were derived by Sinanoğlu for a solvation-structure-dependent potential for liquids on the basis of various physical approximations. The general features of the structure-dependent analytical potential are found to be reproduced by machine computations on the model. Computer calculations also test a generalization of the three-body potential to include finite cores of sizeable molecules like benzene, C${\mathrm{Cl}}_4$, and similar ordinary solvents.

Computations incorporating the three-phonon interaction process are presented of phonon spectral functions, yielding frequency and lifetime dispersion curves, for the bcc solid phase of both ${\mathrm{He}}^3$ and ${\mathrm{He}}^4$. Comparison of the compressibilities obtained from ground-state energy and elastic constants as functions of molar volume quantify the effects of certain analytical approximations. A model calculation shows the sensitivity of elastic anisotropy and long-wavelength dispersions to the precise form of the three-phonon vertex.

Numerical calculations of the dynamic scattering function $S(\overrightarrow{\mathrm{k}}, \omega )$, the intermediate scattering function, and the van Hove distribution function $\mathrm{G}(\overrightarrow{\mathcal{r}}, t)$, based on an approximate expression for $S(\overrightarrow{\mathrm{k}}, \omega )$ proposed in an earlier paper, are presented. The liquid structure factor $S\left(\overrightarrow{\mathrm{k}}\right)$ and first two even moments of $S(\overrightarrow{\mathrm{k}}, \omega )$, which are needed as input, are obtained by means of the Percus-Yevick equation with a Lennard-Jones potential, making the calculation entirely self-contained. The calculation is applied to the liquid-argon case studied through molecular dynamics by Rahman; comparisons with these results and those of experiment show good qualitative agreement. A brief description of the numerical procedure is included.

The coherent states of two-dimensional harmonic oscillators are introduced to describe the elementary excitations of liquid helium. It allows a simple derivation of the liquid-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ density matrix at low temperatures, first obtained by Penrose.

The long-time behavior of space- and time-dependent correlation functions is obtained including the ring contributions or correlated two-body effects. The latter give rise to anomalous hydrodynamic effects and persistent correlations in the nonhydrodynamic part.

Perturbation-theoretic calculations are carried out for the lowest five states of the helium atom using a Hamiltonian which is not symmetric in the particle indices such that the zerothorder spatial functions can be written as simple products of hydrogenic orbitals. The perturbation expansions are reasonably convergent except for the fifth state which is divergent as expected. By 19th order in the expansion the energies of the first two excited states are accurate to 2 × ${10}^{-4\mathrm{}}$ and the expectation values of $\frac{1}{2}(1\mathrm{}\pm P)$ are accurate to 1 × ${10}^{-4\mathrm{}}$.