Excitation energies, oscillator strengths, and transition probabilities for the $4s^2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}-4s4p{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$, $4s^2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}-4s5p{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$, and $4s^2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}-4s6p{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ resonance transitions of elements of the zinc isoelectronic sequence are calculated using the relativistic random-phase approximation. The elements considered range from Gaii to Ulxiii and include many of interest in current fusion research. A graphical analysis of the systematic trends of the oscillator strength as a function of the inverse nuclear charge provides a means of estimating the oscillator strengths for those elements whose values are not explicitly calculated.

Two frequency-stabilized cw dye lasers and an atomic beam were used to prepare sodium atoms in the aligned $F=2\mathrm{}$, $M_F=2\mathrm{}$ ground state, and to study power broadening in the transition from this ground state to the $3P_{\frac{3}{2}}$ $F=3\mathrm{}$, $M_F=3\mathrm{}$ excited state. This system is, to extremely good accuracy, a two-level atom. The line shape was determined as a function of the incident field strength and found to be accurately a Lorentzian over a large range of incident field strengths. The power broadening and saturation at resonance of the two-level system also agree with theory.

Theoretical investigations employing the recently devised Stieltjes-Tchebycheff procedure and variational calculations in Hilbert space are reported of the photoexcitation and ionization cross sections in atomic lithium. The calculations include orbital configurations corresponding to both valence and $K$-shell electron excitations, allowing for core polarization and for configuration interaction in both the ground and excited states. Hylleraas correlation factors are employed to aid the convergence of the configuration-interaction expansions. The resulting discrete and continuum dipole spectra, and related dipole spectral sums, are in excellent agreement with previously reported polarized-orbital and many-body calculations, with the results of semiempirical investigations based on one-electron model potentials, with recent measurements of the static dipole polarizability, and with the results of a recent analysis of the experimentally determined $f$ numbers. Discrepancies between the theoretical and experimental photoionization cross section in the higher-energy valence region are attributed to systematic errors in the measured values, in accordance with previous observations. Although the Stieltjes-Tchebycheff technique is particularly suitable for studies of photoionization in molecular systems, the present results indicate that highly reliable cross sections are also obtained from the approach in applications to many-electron atomic systems when appropriate square-integrable wave functions are employed.

The results of a nuclear-magnetic-resonance experiment are presented which directly demonstrate the spinor character of a spin-½ nucleus, ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$. The interferometric spectroscopic technique used and its potential applications are discussed.

Many-body perturbation theory is applied to calculate double-electron photoionization for neon and argon. Cross sections for the outer-shell $n{p}^2$ and $\mathrm{nsnp}$ pair excitations are included in both the dipole-length and dipole-velocity formulations. Results are in generally good agreement with recent experimental data.

Molecules irradiated by intense laser fields become "dressed molecules" that possess significantly different properties due to changes in the electronic energy structures and wave functions. These new branches of distorted electron-field potential surfaces support different or new vibrational spectra. In this sense, a class of molecules is created with diagonal and off-diagonal properties that can be controlled by varying the laser intensity, frequency, and polarization. An ab initio theory that analyzes the dressed molecule with the field and their interaction treated as one dynamic system (rather than perturbatively) is formulated and summarized. The theory is applied to the study of single/multiphoton dissociation of molecules by intense lasers. Numerical results for the rate of $\mathrm{LiH}(X{}_{}{}^1{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}, v=3)+4\mathrm{}\hslash \omega (\lambda =1.0648\mathrm{} \mu \mathrm{m}, \mathrm{YAlG}:{\mathrm{Nd}}^{3+})\to \mathrm{Li}\mathrm{}\left(2p\right)+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ via the repulsive state LiH(${\mathrm{B}}^1$II) are given. Subsequent fluorescence from $\mathrm{Li}\mathrm{}\left(2p\right)\mathrm{}$ can be detected experimentally.

Recently reported satellite transitions in nickel and iron are shown to be two-electron, one-photon transitions involving $s$ and $p$ electrons satisfying the Heisenberg two-electron selection rules. Relativistic Dirac-Fock transition energies agree with the experimental data, and theoretical transition energies are presented for other elements.

The development of the theory of the effect of a laser on electron-atom scattering is continued by the derivation of explicit relations between the observed electron-atom scattering cross sections in the presence of a laser and exact electron-atom scattering cross sections with no laser present. No approximation concerning the scattering interaction is made. The only approximations concerning the laser are that (1) the laser-atom interaction energy is small compared to atomic energies, (2) the Rabi frequency times the collision time is small, and (3) the laser intensity in appropriate units is small.

The results of semiclassical calculations on one-, two-, three-, and four-photon absorption in truncated models of the hydrogen atom are presented. The temporal behavior near "resonance" is confirmed to be Rabi-like, with a transition probability given by $P\left(t\right)=\left\{\frac{{\gamma }^2}{[{(\frac{{\omega }_0}{N}+\delta -\omega )}^2+{\gamma }^2]}\right\}{sin}^2\left\{\right(\frac{\mathrm{Nt}}{2}\left){[{(\frac{{\omega }_0}{N}+\delta -\omega )}^2+{\gamma }^2]}^{\frac{1}{2}}\right\},$ where the resonance shift $\delta$ is proportional to the intensity of the monochromatic driving field with frequency $\omega$ and the power broadening $\gamma$ is proportional to the $\frac{N}{2}$ power of intensity. $N$ is the number of photons involved and $\mathrm{h}{\omega }_0$ is the energy separation between initial and final states. Calculated values of $\delta$ and $\gamma$ are given for several models; also, for the two-photon $1s\to 2s$ absorption, $\delta$ and $\gamma$ are given which include the contributions of all bound $p$ states.

The photoionization cross section of the hydrogen negative ion is computed using a discrete-basis-set expansion to represent both the ground and continuum states of the system. This discrete-basis-set representation is used to construct an approximation to the dynamic polarizability, which in turn is used in an analytical continuation procedure for complex values of the frequency. This "discretization" of the continuum makes the method potentially applicable to larger systems, and a study of the basis-set dependence is made. The final results are in good agreement with more elaborate calculations and with experimental results. The dynamic polarizability in the normal dispersion region is also computed.

A generalization of Dirac's transformation of the off-resonance single-photon scattering amplitude that leads to the Kramers-Heisenberg dispersion formula is described. The amplitude is first calculated to order $e^2$ in perturbation theory with the minimal-coupling interaction Hamiltonian as perturbing energy, and is then transformed so that the effects of multipole transition moments of all orders and types (electric, magnetic, and diamagnetic) readily become manifest. No appeal is made to any multipolar expansions, however, as exact integral expressions are used for the summed series. It is shown that the same dispersion formula is obtained by using the multipolar Hamiltonian partitioned in the usual way, and this despite the fact that the unperturbed Hamiltonians are different in the two calculations.

Schemes for determining the multiplet ratios in ionization and electron-attachment processes are derived and several simple examples are discussed. The multiplet ratios depend only on geometrical factors and intial-state properties. The conditions for the applicability of the schemes are as follows: (a) The picture of ionizing (attaching an electron to) a shell must be valid; (b) the multiplet ratio is defined as the ratio of the total intensities corresponding to ionic states of distinct symmetries arising due to ionization of a given shell; and (c) the photon energy must be large enough so that the multiplet ratios do not depend on electric-dipole transition matrix elements.

The object of this paper is to study the influence of the characteristics of the excitation pulse on resonant multiphoton ionization. A classical description of the field is introduced in the exactly solvable model initially developed by Beers and Armstrong. A detailed solution is given for square pulses. The case corresponding to a highly excited resonant level is particularly studied both analytically for square pulses and numerically for different amplitude-varying shapes.

The Compton scattering of a photon from an unpolarized electron bound in a central field is treated relativistically. The distribution of the emitted electrons for a photon scattering in a given direction is obtained as a function of the radial components of the initial Dirac wave function. This expression, in the lowest power of the coupling constant, leads to the Klein-Nishina formula. The off-mass shell and binding corrections to the free Compton scattering formula, which are important near the ionization threshold, are found. Using exact hydrogenlike wave functions, various approximate formulas as functions of the atomic number $Z$ are discussed, and some possible limitations of the usual description of Compton profiles are considered.

The microwave cross section $\sigma$ for Debye-like spectra resulting from overlapping lines at high pressures is computed. The main idea is a modification of Anderson's model, by which the cross section is computed for an effective line instead of computing it for the single overlapping lines. This gives a natural explanation of the observed reduction of $\sigma$ compared to $\sigma$ for the isolated lines. Complete numerical calculations are carried out for the case of Debye spectra of symmetric-top molecules. Agreement with experiment is satisfactory.

Linewidths and shifts of the five prominent visible Si II multiplets are measured in a conventional shock tube. The Stark effect from impacting plasma electrons is the dominant broadening mechanism. Electron densities range widely [(4-15) × ${10}^{16}$ ${\mathrm{cm}}^{-3\mathrm{}}$], but temperatures (9500-12 500°K) do not. Optical depth and source inhomogeneity are rarely troublesome. Depending upon interference, blending, and signal-to-noise ratios, broadening-parameter accuracies are between 15-25% and shift uncertainties are 15-100%. Comparison data are examined.

In a previous paper we showed how time-dependent projection operators may be employed to enable the Nakajima-Zwanzig projection-operator technique for deriving exact master equations to deal efficiently with two or more coupled classical or quantum systems, neither of which is reservoir like. We considered in detail the case where the relevant part of the classical-system probability-density function (PDF) or quantumsystem density operator (DO) is a product of the PDF's or DO's for the separate subsystems, and we applied the techniques developed to problems in quantum optics and in the kinetic theory of dilute nonideal gases. In this paper we make the time-dependent projection-operator approach useful for a greater variety of systems by allowing the relevant part of the PDF or DO to include correlations between two of the interacting subsystems. This extension allows us to describe well the dynamics of strongly interacting systems in a low degree of approximation while avoiding the use of infinite resummations. We derive exact generalized master equations in this manner for the same two cases as in our earlier work, namely a classical gas of $N$ molecules interacting via a two-body potential and a quantum-optical system of $N$ two-level atoms interacting with an electromagnetic field. In the former case, the relevant part of the PDF contains two-body correlations, and we obtain two exact coupled master equations for the singlet and doublet PDF's $F_1\mathrm{}\left(t\right)\mathrm{}$ and $F_2\mathrm{}\left(t\right)\mathrm{}$. In the latter case, the relevant part of the DO contains atom-field correlations, and the result is three exact coupled equations for the single-atom DO ${\rho }_1\mathrm{}\left(t\right)\mathrm{}$, the field DO $R\left(t\right)\mathrm{}$, and the DO for one atom plus the field $\chi \mathrm{}\left(t\right)\mathrm{}$. From the exact equations we derive approximate equations by making simplifying assumptions. In the case of the gas we carry out a straightforward density expansion of the ${\dot{F}}_2$ master equation and obtain a set of kinetic equations for dense gases, which have been derived previously by Frieman, Goldman, and Dorfman and which describe well effects due to the finite mean free path. In the quantum-optical case we derive kinetic equations for a single-mode laser by treating the $\dot{\chi }$ equation in the Born-Markoff approximation. The equations describe gain saturation and other effects on the field dynamics which are of infinite order in the atom-field coupling constant. It is shown that these equations reduce to previously derived laser master equations if atom-atom correlations can be neglected. Finally, we mention possible generalizations of the time-dependent projection-operator approach used in this paper and briefly discuss its application to other problems, including the kinetics of liquids, collisional line broadening, superradiance, and amplified spontaneous emission.

Light pulses created by stimulated Raman scattering have been found to exhibit a complex time dependence which resembles relaxation oscillations. A focused laser pulse generated both forward and backward Raman emissions which appeared as a series of pulses with durations much shorter than the incident laser pulse. Time dependence of the Raman emission was observed directly by use of a streak camera. The number of observed pulses increased with the intensity of the incident pulse, while separation of the pulses in time depended on the length of the focal region. Beam focusing was incorporated in the coupled wave equations for stimulated Raman scattering. These rate equations were then solved numerically, and the results are in good qualitative agreement with the experimental observations. The short Raman pulses are created by a process associated with depletion of the incident laser pulse. This process occurs under a broad range of conditions.

We discuss the propagation of an electromagnetic pulse through an active medium prepared in a state of inversion between two levels of the same parity. Since no electric dipole transition is possible between the chosen atomic levels, we investigate the possibility of amplification of an injected signal having a carrier frequency equal to one-half the atomic-transition frequency. We show that under suitable conditions a nonlinear atomic polarization can be generated which oscillates at the same frequency as the incident electromagnetic pulse. The coupled atom-field evolution is described by the usual self-consistent approach. When atomic relaxation effects are negligible, we derive an equation describing the spatial evolution of the energy of the propagating pulse. From this equation we characterize the threshold condition for power amplification and classify the multiple steady-state solutions of the propagation problem. The evolution of the pulse envelope through the amplifier is analyzed with the help of a hybrid computer simulation. Pulse-envelope modulation and multiple-pulse formation even in the asymptotic limit of long amplifiers are displayed.

A general method is presented for describing self-focusing phenomena in various media by means of a geometrical-optics approach. The general formalism applies to a wide class of media: inhomogeneous, anisotropic, dispersive, and time varying. In contradistinction to previous methods, which derive pertinent wave equations and analyze them by assuming intensity-dependent wave speeds, here the appropriate Hamilton equations are derived, from which self-focusing phenomena evolve directly. Simple examples illustrate the feasibility of the method to deal with spatial and temporal effects in various media.