The theory of intermolecular nuclear spin relaxation by translational self-diffusion in liquid crystals is developed. Torrey's treatment of simple liquids is extended and modified for the liquid-crystalline phases by taking into account the anisotropy of the molecular motion, the elongated molecular shape, and the spin distribution on a molecule. Results, obtained for the frequency and angular dependence of $T_1$ in the nematic phase, are presented graphically for a variety of parameters and are compared with Torrey's results for classical liquids. A brief comparison with the available experimental data is presented.

We have studied the bound states of the potential $V\left(r\right)=-\frac{Z}{(r+\beta )}$. The $S$-wave energy level $E\left(\beta \right)$, as a function of the parameter $\beta$, has a logarithmic singularity at the origin. The imaginary part of $E\left(\beta \right)$ for $\beta \to 0$ goes as $Z^{4+2l}{\beta }^{2+2l}$, where $l$ is the angular momentum.

A microscopic theory for the dynamics of simple classical liquids is formulated with the longitudinal and transverse current-fluctuation spectra expressed in terms of relaxation kernels. The kernels are approximated by two-mode decay integrals coupling longitudinal and transverse excitations that result in a closed set of nonlinear equations which can be solved numerically. The only input required is the pair potential and the static two- and three-particle correlation functions. The theory gives correctly the zeroth, second, and fourth moments for the dynamical structure factor, the zeroth and second moments of the longitudinal and transverse current correlation functions, the free-particle limit, a proper hydrodynamical limit, and reflects the long-time anomalies of the dynamical transport coefficients.

The mode-coupling theory for the dynamics of classical liquids formulated by the present authors has been applied to calculate the fluctuation spectra of the transverse and longitudinal currents, as well as the dynamical transport coefficients for liquid argon near its triple point. The results are compared with the neutron scattering data and with the molecular-dynamics calculations.

A dynamical theory is presented for the enhanced fluctuations that occur in a time-dependent Ginzburg-Landau model system with the order parameter not conserved which is quenched from a thermodynamically stable to an unstable state. In a certain weak-coupling, long-time, and long-distance limit, diffusion and saturation effects can be treated separately. As a result explicit expressions are found for the probability distribution functional, the two-point reduced distribution function, and the pair correlation function of the fluctuations, which evolve from an arbitrary initial probability distribution functional. The behavior of the latter two functions is also displayed graphically. A central role is played by the time-independent nonlinear transformation of the order parameter which takes care of the saturation effects. The nature of such a transformation is discussed in a general context. If the problem is viewed as a nonequilibrium critical phenomenon, the theory corresponds to the Landau mean-field theory. An expansion in $\epsilon =4-d$ is suggested to improve our treatment, where $d$ is the dimensionality of space.

The kinetic-energy distribution of H-H fragment pairs arising from dissociative charge-exchange collisions of 5-keV ${\mathrm{H}}_2^{+}$ ions was measured using a flight-time-difference method. The spectrum exhibits 13 discrete kinetic energies between 7 and 10.5 eV in the center-of-mass frame of the projectile. Predissociation of the $c{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ state by the repulsive $b{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ state explains most of the structure observed. In addition, evidence is found for predissociation of the $e{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ state.

We comment on the work of Kimble and Mandel with respect to Markovian approximations and the Lamb shift. The importance of the quantum properties of the free electromagnetic field in spontaneous-emission calculations is discussed.

The coefficient for emission of the Balmer $\beta$ line from backscattered H atoms has been measured for 2-200-keV hydrogen ion impact on polycrystalline targets of Mo, Cu, and stainless steel. The dependence on primary energy is successfully modeled using a modification of a formulation used previously at low (2-30-keV) impact energies.

The role of structural correlations in single-particle motion and self-diffusion in a dense Lennard-Jones fluid is studied via renormalized kinetic theory.

A generalized off-shell unitarity relation for the two-body scattering $T$ matrix in a many-body medium at finite temperature is derived, through a consistent real-time perturbation expansion by means of Feynman diagrams. We comment on perturbation schemes at finite temperature in connection with an erroneous formulation of the Dyson equation in a paper recently published.

In this work, a theory of laser nonlinear spectroscopy and its application to the study of atomic collisions is developed. A three-level system (TLS) is considered in low-pressure gases. The effect of weak velocity-changing collisions (vcc) upon atomic coherences is introduced into the TLS equations established by Hänsch and Toschek. It appears that a TLS is suitable for the observation of the effect of vcc upon optical coherences.

Absolute cross sections for electron capture into the $3s$ state of atomic hydrogen have been measured for 10-150-keV proton impact on Kr and Xe. The experimental procedure involved the quantitative measurement of the Balmer-alpha radiation emitted by the spontaneous decay of fast hydrogen atoms in flight. The $3s$-state radiation was identified by its characteristic lifetime. The cross sections for both target gases reach a maximum in the projectile energy range under consideration. The Xe cross sections are approximately 40% higher than those for Kr near 25 keV but are similar above 80 keV. These values are consistent with existing $3s$ cross-section measurements and with an $n^{-3\mathrm{}}$ scaling of existing total electron-capture cross sections in accordance with Born-approximation predictions.

Total cross sections have been calculated for electron transfer into all states of ${\mathrm{He}}^{+}$ during collisions of ${\mathrm{He}}^{++}$ ions with H atoms at ${}_{}{}^4{}_{}{}^{}\mathrm{He}_{}^{++}{}_{}{}^{}$ energies from 0.1 to 20.0 keV. The coupled molecular-state approximation that is used incorporates in the basis up to 20 states $1s\sigma , 2s\sigma , \dots , 4f\varphi$ of the frozen He${\mathrm{H}}^{++}$ molecule. Convergence of cross sections with respect to the size of the bound-state basis is studied; at 8 keV, the eight states $1s\sigma$, $2p\sigma$, $3d\sigma$, $4f\sigma$, $2p\pi$, $3d\pi$, $4f\pi$, and $3p\sigma$ of the 20 states considered have been found sufficient to determine the 20-state cross section to within a few percent. The nuclei are assumed to follow classical paths, some estimate being made of the effect of nonrectilinear motion at the lower energies. A comparison is made with experimental results, and agreement with most of the recent experimental results is found to be excellent down to about 8 keV; at lower energies, the theoretical cross section falls off rapidly with decreasing energy, in contrast to the single early low-energy measurement.

Spectroscopic analysis of optical emissions resulting from collisions between diatomic molecules (${\mathrm{N}}_2$, CO, ${\mathrm{O}}_2$) and hydrogen or helium atoms has been performed over the kinetic energy range ∼150-2400 eV. The data yield product vibronic-state distributions from collision-induced excitation, impact ionization, and excitation transfer processes. For most of the processes observed spin is conserved. It was found that vibrational-state distributions of excited electronic product molecular ions were not in accord with those predicted from a simple vertical transition model. Excited neutral molecules, on the other hand, exhibited state distributions that could be characterized by this model.

A search was made to observe a difference in the x-ray yield from equal velocity ${\mathrm{H}}^{+}$ and ${\mathrm{H}}_2^{+}$ projectiles of 300-1200 keV/amu incident on thin metallic-film targets. Two different experimental techniques are described in which we observed x-rays arising from ionization of electrons with binding energies from 73 to 778 eV. To within the experimental uncertainty of approximately 1% no difference in yield could be detected.

Alternative formulations of atomic problems are connected in terms of the Green's function for the radial motion of a single electron in an effective potential field. The quantum-defect theory (QDT) represents an electron outside an ion by a Coulomb function with a phase shift contributed by the additional interactions that prevail inside the ion core. We interpret the phase-shifted portion of this radial function as arising from the application of a Green's function propagator to the short-range operator that represents the coupling to other channels of the electron + ion system. The alternative representation of the same radial function, as a superposition of zero-order functions for configurations with different energies, differs only by having the same Green's function expanded in a set of zero-order eigenfunctions. This analysis of configuration mixing leads to a reformulation of reaction matrices which extends the initial QDT treatment of bound states.

The technique of spin-exchange optical pumping was used to measure the ratio $\frac{g_J\left({}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}\right)}{g_J\left({}_{}{}^{23}{}_{}{}^{}\mathrm{Na}\right)}$ for the alkali metals in their ${}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ ground states. Zeeman hyperfine splittings were produced in a magnetic field of 43 G, the $\Delta F=0\mathrm{}$ transition frequencies measured, and the $g_J$ and $\frac{g_I}{g_J}$ ratios evaluated by means of a best fit to the Breit-Rabi expression for the alkali-metal energy levels. The resonance lines were collected and displayed by a minicomputer programmed for repetitive-scan signal averaging. Possible systematic effects of pumping light, buffer pressure, etc., were considered in obtaining the final results $\frac{g_J\left({}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}\right)}{g_J\left({}_{}{}^{23}{}_{}{}^{}\mathrm{Na}\right)}=1.000\mathrm{}01771\left(7\right)\mathrm{}$ and $g_J\left({}_{}{}^{23}{}_{}{}^{}\mathrm{Na}\right)=2.002\mathrm{}29563\left(16\right)\mathrm{}$. The measured value for $\frac{g_I}{g_J}\left({}_{}{}^{23}{}_{}{}^{}\mathrm{Na}\right)$ is in good agreement with results from atomic-beam experiments.

A complex scale transformation of the time-independent Schrödinger equation leads to a symmetric eigenvalue problem containing both bound states and resonance (complex) eigenvalues as solutions. An extended virial theorem is stated, and its necessary fulfillment is pointed out. The latter, in conjunction with a symmetric stationary principle, allows for determination of resonance (complex) eigenvalues by means of elementary matrix manipulations. Application to the Stark effect in the hydrogen atom shows agreement with previous calculations based on numerical integration.