The generalized oscillator strengths $f\left(\overrightarrow{\mathrm{K}}\right)$ as a function of momentum transfer $\overrightarrow{\mathrm{K}}$ are calculated for the (i) $2s-2p$, $3s$, $3p$, $3d$, (ii) $2p-3s$, $3p$, $3d$, (iii) $3s-3p$, $3d$, and (iv) $3p-3d$ transitions of the lithium atom using the Hartree-Fock wave function of Weiss. Calculations are carried out using both the length and velocity formulations of the Born-approximation integrals. For these transitions of lithium, the $f\left(\overrightarrow{\mathrm{K}}\right)$ values were used to obtain integrated inelastic cross sections within the first Born approximation for electron impact. The results of the total cross section for $2p$, $3s$, and $3d$ from the ground state are compared with the available Born calculations and recent experimental data.

Charge transfer into a number of excited $s$ states of atomic hydrogen by proton impact on hydrogen molecule has been studied for both gerade and ungerade transitions of the molecular ion for the energy range 50 keV to 5 MeV. Using a contour integral representation of the hydrogenic wave function, the molecular Brinkman-Kramers amplitude has been expressed in a closed form, while the molecular Jackson-Schiff amplitude involving proton-proton interactions has been reduced to a one-dimensional integral over the real variables. Just as in the case of ground-state formation of hydrogen atoms, molecular effects play a significant role in the case of excited-state capture of an electron; and a hydrogen molecule cannot be regarded as a pair of independent hydrogen atoms at any energy in the considered range. The cross sections at a particular energy satisfy the inverse $n^3$ law approximately. The charge transfer involving the gerade transition of the molecular ion is the most important process; although, depending on the choice of the molecular wave function, there is a 10-28% chance of the charge-transfer process involving the ungerade transition.

New results of relatively high-precision measurements to study atomic pair production by photons in the threshold region together with some other previous measurements are presented for a critical evaluation of the new calculations with corrections of Coulomb effect and atomic-electron screening effect in the low-energy pair production. This evaluation reveals the degree in which the theory is in greater agreement with measurements in the threshold region and indicates the trend of cross sections as a function of atomic number and photon energy.

A theoretical method previously developed for the two-photon ionization of alkali-metal atoms is extended to the spin-orbit coupling scheme. We have obtained the Green's function of this problem in the framework of quantum-defect theory and so we have been able to perform the infinite summations related to perturbation theory. The generalized transition probability rates are calculated in the off-resonant and resonant regions, respectively, for polarized incident radiation. Destructive interference effects between the unperturbed atomic states in the infinite summations producing a finite deep minimum in the off-resonant region, are predicted by our theory, both for linearly and circularly polarized incident radiation. A detailed calculation of electron-spin polarization is given. Comparisons of values predicted by the present work with experiment and other theoretical calculations are made for the case of atomic cesium initially in the ground $6S$ state.

Photoelectron spectra resulting from the interaction of ${}_{}{}^{46}{}_{}{}^{}\mathrm{Sc}$ (energy 889.2 and 1120.4 keV) and ${}_{}{}^{60}{}_{}{}^{}\mathrm{Co}$ (energy 1173.2 and 1332.5 keV) gamma rays with tin, tantalum, gold, lead, and thorium targets have been measured by the coincidence method developed by Ranganath et al., for the direct estimation of $K$-shell cross sections in the case of radioisotopes emitting monoenergetic gamma rays. Since the two coincidence peaks (in both the cases) are not well resolved, $K$-shell photoionization cross sections are estimated by fitting a Gaussian to each peak. Good agreement is observed between the present cross sections and the theoretical cross sections.

Momentum exchange was observed between laser light and an electron beam using the inverse Čerenkov effect. This interaction was accomplished by introducing a gas with an index of refraction which reduced the phase velocity of the light wave to match the velocity of the electron. A 30-MW Nd: YAG 1.06-μm laser intersected 102-MeV electrons at an angle of 18 mrad in hydrogen gas. The beams overlapped in the interaction region for approximately ${10}^5$ optical wavelengths. The energy exchange by the inverse Čerenkov effect was verified in two ways: First, a change was observed in the electron energy distribution in the presence of the laser, and second, this change was observed to be a function of the index of refraction, as determined by the pressure of the gas. A ±13% variation about the pressure for optimum energy exchange reduced the interaction by one-half. The results of the experiment agree with the predictions of a Monte Carlo computer simulation of the interaction. Methane gas was also investigated as a phase-matching medium. Possible applications include laser-driven particle accelerators and stimulated Čerenkov devices, such as optical klystrons and traveling wave tubes.

The transition probabilities and the shifts of the crossing and anticrossing points of a two-level system (spin-1/2 atom) under the simultaneous influence of a static magnetic field and three orthogonal oscillating rf fields are calculated by using the resolvent formalism in which the rf fields are quantized. A new interference effect, which can be called "crossing of the third kind" in the rf transition, is predicted, and can be interpreted as the interference between different-order transition processes such as single- and two-photon processes, single- and three-photon processes, and so on. Furthermore, for coexistence of the single- and two-photon processes and of the single- and three-photon processes, we can obtain expressions of the transition probabilities (or effective dipole-coupling coefficients) similar to the results obtained in our previous paper, where the interference between single- and two-photon processes were treated by using the time-dependent Schrödinger equation.

We consider optical second-harmonic generation for a pump beam of arbitrary transverse profile. The analysis is carried out in the parametric approximation and the phase-matching condition is assumed to be satisfied along a principal axis of the nonlinear crystal. The diffraction effects associated with propagation of the pump beam and the second-harmonic beam are fully incorporated. An explicit expression for the harmonic field is obtained and it requires a twofold surface integration over the pump-beam cross section. The general formalism is shown to be readily extended to incorporate the case of partially coherent pump beams.

We have observed a collapse of the Na hyperfine doublet into a single peak due to laser-induced optical pumping when the product of laser power and buffer gas pressure exceeds ∼0.1 mW Torr. The complex line shapes observed under these conditions have been quantitatively explained by a model which describes the laser-induced change in the population of the ground-state hyperfine levels and also includes pressure broadening and diffusion of atoms out of the laser beam. The line-shape distortion can occur at laser intensities ${10}^3$ below that required for radiative saturation, and must be considered in experiments involving the line shape or the population of the hyperfine levels.

We study inhomogeneously broadened three-level atoms ($\Lambda$ configuration). Two energy levels are strongly coupled by an intense standing wave. A weak laser field at an adjacent transition is used as a probe. The probe response is calculated by Green's functions involving continued fractions. The general solution is extendable to other three-level configurations as well to other types of multimode saturators. The connection of various approximate solutions to the exact one is discussed. We concentrate on the Doppler-free case where both transitions have nearly equal frequencies. For this we derive a reasonably accurate closed-form solution, the parameter dependencies of which are investigated in detail. In addition to its average changes the dynamics of the saturated transition plays an important role in the steady-state probe response. The spectra show sharp resonances which cannot be explained in terms of traveling wave superposition models. The width of the velocity distribution has a strong effect on the shape of the spectrum—some resonances are smeared away because of incomplete Doppler dephasing. The relaxation processes influence differently the resonances, which facilitates their interpretation.

The effects of cooperative atomic interactions on photon statistics in a single mode as well as two-mode two-photon lasers are studied using the equation of motion for the reduced-density operator for the field. The steady-state solution of this equation of motion is used to determine the photon number distribution. The importance of the cooperative effects is discussed.

The electronic energy loss and straggling of swift charged particles in weakly interacting plasmas are described in a quantum-mechanical formalism that includes thermal effects. It applies to plasmas over wide ranges of densities and temperatures reaching from degenerate to nondegenerate systems, as they are found in solids, stars, and in dense and dilute fusion plasmas. Using approximations for the dielectric function, we calculate the stopping power $S$ and the straggling $\Omega$ for slow particles in plasmas of varying degree of degeneracy, and discuss the dependence of the results on particle velocity and plasma temperature $T$. For nondegenerate plasmas, one obtains the relation ${\Omega }^2=2\mathrm{kTS}$ between these quantities.

We study through computer simulation the physical processes of a linearly polarized electromagnetic pulse of highly relativistic amplitude ($\frac{\mathrm{eE}}{m\omega c}\gg 1$) in an underdense plasma accelerating particles to very high energies. We consider first an electron-positron plasma. The maximum momenta achieved scale as the square of the wave amplitude. This acceleration stops when the bulk of the wave energy is converted to particle energy. The pulse leaves behind as a wake a vacuum region whose length scales as the amplitude of the wave. The results can be explained in terms of a snow plow or pistonlike action of the radiation on the plasma. When a mass ratio other than unity is chosen and electrostatic effects begin to play a role, first the ion energy increases faster than the electron energy and then the electron energy catches up later, eventually reaching the same value.

The equilibrium pair-correlation function and static dielectric response function are calculated for the one-component two-dimensional plasma in the convolution (Totsuji-Ichimaru) approximation. The long-wavelength ($k\to 0$) compressibility sum rule is exactly satisfied for arbitrary values of the plasma parameter $\gamma$. For $\gamma <2\mathrm{}$ the approximation scheme accurately describes the short-range ($r\to 0$) behavior of the pair-correlation function $g\left(r\right)\mathrm{}$ while for $\gamma \ge 2$, it does not. As $\gamma \to 4$ the isothermal compressibility tends to zero as it should. The correlation energy is also calculated for this model and compared with the results for other approximation schemes and the Monte Carlo results.

The formation of a dense adsorbed film on a smooth substrate is studied via Monte Carlo simulations of a lattice gas with nearest-neighbor interactions. The existence of the wetting transition which is predicted by a simple meanfield approximation is verified. We also find the sequence of first-order transitions which appear in the mean-field approximation. In contrast to the predictions of the mean-field approximation, the critical temperatures of these transitions appear to approach a limiting value well below the critical temperature of the bulk three-dimensional lattice gas as the thickness of the adsorbed film increases. This behavior, which was first predicted on physical grounds by de Oliveira and Griffiths, is presumably closely related to the roughening transition of the interface between the dense and tenuous bulk phases.

The absorption and velocity of ultrasound and the critical opalescence have been measured for a critical-composition mixture of nitrobenzene and 2,2,4-trimethylpentane along the critical isochore in the homogeneous phase of the system. The measurements cover the relatively wide range of temperature interval of 30 K to 7 mK from the critical value. The nearness of approach to the critical point was affirmed by the critical-opalescence measurements. The measurements of acoustic absorption covered the range of 1 to 91 MHz, and the strong frequency dependence observed can be satisfactorily described by the Fixman-Kawasaki theory with the adjustment of three parameters. Singular behavior for the sound absorption, consistent with critical slowing down, was observed when the mixture was more than about 3 K away from the critical point. When within about 0.3 K of the critical temperature the sound absorption was observed to become constant. The absence of any effects on the critical sound absorption, while the mixture was under a large electric field, is also reported.

The energy dependence of trajectories in the neighborhood of hyperbolic points is studied for a variety of two-degree-of-freedom conservative classical Hamiltonian systems displaying a "stochastic transition." In all cases studied the energy onset of substantial irregularity (defining a critical energy $E_c$) is shown to occur when local entropies, defined in terms of generalized characteristic multipliers, equal unity. Similar results are obtained for the standard map. The results suggest a unifying quantity for describing the onset of substantial irregularity in two-degree-of-freedom systems.

A quantum kinetic theory of time-correlation functions is described in terms of a formally exact closure of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy. The theory closely parallels existing treatments of the corresponding classical problem, so that direct comparisons between approximations for classical and quantum systems may be made. As an illustration, the formalism is applied to conditions of low density, but arbitrary degeneracy, and the resulting kinetic equation is shown to reduce to the linearized form of the Uehling-Uhlenbeck equation with the cross section appropriately modified to account for degeneracy. Also, classical approximations suitable for strongly coupled fluids are generalized to the quantum case. The results are applied to evaluation of the electrical conductivity for a two-component plasma in the following paper.

A recently developed quantum kinetic theory for time-correlation functions is applied to the calculation of the electrical conductivity in dense, strongly coupled plasmas. In the weak-collision limit the theory generalizes the Ziman expression to finite temperatures while, for strong collisions, it generalizes the result of Gould and of Williams and DeWitt to include strong ion coupling. Numerical results which compare the effects that strong ion coupling, bound (core) electrons, and strong collisions have upon the collision frequency are also presented.

The motion of a particle rigidly bounded to a surface is discussed, considering the Schrödinger equation of a free particle constrained to move, by the action of an external potential, in an infinitely thin sheet of the ordinary three-dimensional space. Contrary to what seems to be the general belief expressed in the literature, this limiting process gives a perfectly well-defined result, provided that we take some simple precautions in the definition of the potentials and wave functions. It can then be shown that the wave function splits into two parts: the normal part, which contains the infinite energies required by the uncertainty principle, and a tangent part which contains "surface potentials" depending both on the Gaussian and mean curvatures. An immediate consequence of these results is the existence of different quantum mechanical properties for two isometric surfaces, as can be seen from the bound state which appears along the edge of a folded (but not stretched) plane. The fact that this surface potential is not a bending invariant (cannot be expressed as a function of the components of the metric tensor and their derivatives) is also interesting from the more general point of view of the quantum mechanics in curved spaces, since it can never be obtained from the classical Lagrangian of an a priori constrained particle without substantial modifications in the usual quantization procedures. Similar calculations are also presented for the case of a particle bounded to a curve. The properties of the constraining spatial potential, necessary to a meaningful limiting process, are discussed in some detail, and, as expected, the resulting Schrödinger equation contains a "linear potential" which is a function of the curvature.