As part of a systematic study of approximations commonly made in solutions of the Boltzmann equation for electrons in molecular gases, we have investigated the effects of anisotropic scattering on electron transport coefficients in ${\mathrm{N}}_2$ and have extended our study of the multiterm expansion technique to higher E/n. A critical survey of published data yields a set of differential and integral cross sections for electron energies from 0.003 to ${10}^4$ eV. For electric-field–to–gas-density ratios E/n between 10 and 500 Td (1 Td${=10\mathrm{}}^{\mathrm{-}21}$ V ${\mathrm{m}}^2$), the changes in the commonly measured transport and reaction coefficients resulting from the introduction of anisotropic elastic and inelastic scattering, while keeping the elastic momentum-transfer cross section constant, are less than 1%.

These calculations were made with use of the multiterm spherical-harmonic expansion solution of the Boltzmann equation. For 500<E/n<1500 Td the changes in scattering anisotropy cause changes in transport and reaction coefficients which increase with E/n to about 10%. The errors in drift velocity, mean energy, and the reaction coefficients resulting from the use of the two-term spherical-harmonic expansion rather than a six-term expansion are less than 3% at 1500 Td.

However, the errors in the diffusion coefficients become large (>25%) at our highest E/n. The calculated transport coefficients are in generally good agreement with experiment for E/n less than 300 Td, but the differences increase at higher E/n. The importance of proper interpretation of ionization and excitation experiments at high E/n is illustrated by calculations which model either an exponential growth of density in time or an exponential growth with position. The calculated ionization coefficients are low compared to most experiments for E/n less than 200 Td. At E/n>600 Td the agreement is good for the spatial growth experiments, but the calculated values are below experiment from the temporal growth experiments. The calculated excitation coefficients are generally higher than experiment at low and high E/n but in agreement with experiment at E/n near 150 Td.

We report on the observation and absolute measurements of the population dynamics for several Sr i and Sr ii levels when the vapor is illuminated by a short laser pulse. When the laser beam excites the 5s5p ${}^1$$P_1$ resonance level, we show that a pool of metastable population is created, allowing an efficient heating of the medium by superelastic collisions with seed electrons, and a strong final ionization is achieved. When the laser source excites the 5s10s 7thinsp${;}^1$$S_0$ Rydberg level, superelastic collisions do not occur and a drastic change in the population behavior is observed. In both cases the dynamics of the energy transfer towards the plasma is detailed.

We have studied the long-range interaction potentials of the heteronuclear alkali-metal-atom dimers in the case when one of the atoms is in the first excited state ($n_A$P) and the other is in the ground state ($n_B$S). The presentation of the general expressions for the interaction energies in the Hund’s case (c) is followed by the calculation of the corresponding $C_6$ constants for all heteronuclear alkali-metal-atom pairs. In the case of heavier perturbers (Rb and Cs) the $C_6$ constants are found to be significantly influenced by the perturber’s fine structure. The van der Waals interaction in the K-Rb system is exceptionally strong resulting in $C_6$ constants considerably larger than in all other alkali-metal-atom heteronuclear systems. The intermediate-coupling region (ICR) is defined as the region of internuclear separation R where the interaction energy is of the order of the atomic spin-orbit splitting, while the exchange energy is still negligible. Analysis of the general form of the energy matrices in the ICR shows that the homonuclear alkali-metal-atom dimers can be treated as a special case. In the large-R limit, the ICR results reduce to those obtained in Hund’s case (c). As an example, we have calculated the ICR interaction potentials of the K-Rb system, taking into account only the leading dipole-dipole interaction. Finally we have discussed the construction of the absorption coefficient in the wings of the resonance lines, both in the impact and in the quasistatic approximation.

The imprisonment of the 2537-Å resonance radiation from mercury in the mercury-argon discharge of fluorescent lamps is treated by a Monte Carlo method. The effects of emission and absorption linewidths, hyperfine splitting, isotopic composition, collisional transfers of excitation, and quenching are explicitly incorporated in the calculations. The calculated spectra of emitted radiation are in good agreement with measured spectra for several combinations of lamp temperature and mercury composition. Also in agreement with experiments, the addition of ${}_{{\mathrm{}}^1{\mathrm{}}_{80}^{96}}{}^{}{}_{}{}^{}\mathrm{Hg}$ to natural mercury is found to increase lamp efficiency. The method is useful for a number of problems in radiation transfer.

Two of the most fundamental aspects of the sodium-neon resonantly photopumped x-ray laser system are examined: the functional dependencies of the sodium-plasma pumping-line power output and the atomic-level kinetics in the neon which determine gain. For sodium, the growth of pumping power with size, temperature, and density of the plasma is quantified with numerical and analytic calculations. In the neon an analytic model of the gain kinetics is developed which allows quantitative assessments of the effects of each important rate and process on the gain. Both analytic models should be applicable to similar resonantly pumped systems by using the appropriate rates for those systems. In addition, a novel way of depleting the lower lasing state in an optically thick laser medium is presented.

Asymmetric resonance profiles observed in H atoms in a strong electric field are derived analytically. The most significant deviations from a Lorentzian line shape, $H^F$=γ/(${\mathrm{scre}}^2$+${\gamma }^2$), occur for resonances near the top of a potential barrier. Parametrization as a Fano profile is inappropriate. The line-shape formula, a Lorentzian with energy-dependent reduced width ${\gamma }_Q$(scre) =ln[1+Q(1-Q${)}^{\mathrm{-}1\mathrm{-}\mathrm{scre}}$]/ln[( 1-Q${)}^{\mathrm{-}1}$], depends on a single asymmetry parameter Q (0

A multiconfiguration version of the Tamm-Dancoff approximation (MCTD) is developed to study photoexcitation of atoms in cases where the simultaneous excitation of two atomic electrons is important. Starting from a multiconfiguration Dirac-Fock description of the ground state, the variational principle is applied to give equations for a final-state wave function consisting of both singly excited and doubly excited configurations. To illustrate the method, the MCTD equations are applied to determine the 2pns and 2pnd autoionizing resonances in the low-energy photoionization cross section of Be and the corresponding 3pns and 3pnd resonances in Mg. The predicted cross sections are found to be in good agreement with previous theoretical results as well as with the available experimental data.

We consider pulses of coherent electromagnetic radiation impinging upon an autoionizing atom. Analytic solutions in the cases of hyperbolic-secant- and exponential-pulse envelopes are given for the ground-state atomic population and for the photoelectron spectrum. The sensitivity of these quantities to the pulse area and to the interference between the autoionizing state and the continuum is studied.

A critical theoretical study of the electron momentum distributions obtained for ${\mathrm{H}}_2$${(\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathrm{g}}^{+}$) by the (e,2e) reaction technique for transitions to the ground and the n=2 and 3 excited states is presented. Two very highly electron correlated ground-state wave functions for ${\mathrm{H}}_2$${(\mathrm{}}^1$${\mathrm{\Sigma }}_{\mathrm{g}}^{+}$), each of which yields more than 96% of the ‘‘exact’’ binding energy and the exact Born-Oppenheimer wave function of ${\mathrm{H}}_2$${\mathrm{}}^{+}$ in the ground and various excited states, were employed in the computations within the context of the plane-wave impulse approximation (PWIA). For the ground-state transition, the theoretical values computed from both correlated wave functions and a self-consistent-field wave function are all in relatively good agreement with experiments for recoil momenta in the range (0.11≤q≤1.0 a.u.). In order to discriminate among the various theoretical values reported here it is highly desirable to have experimental data for q smaller than 0.05 a.u. The experimental data for the transitions to the n=2 excited states (2s${\sigma }_g$, 2p${\pi }_u$, and 2p${\sigma }_u$) are surprisingly not in as good agreement with the theoretical values reported here. The failure to describe the transition to excited states with a molecular angular momentum quantum number other than zero may be due to (i) the inadequacy of the ground-state wave function, (ii) the failure of the Franck-Condon principle in the transition, (iii) the need to go beyond the PWIA, and/or (iv) the need for improved and extended experimental data.

We have measured the orientation of the Ba 6p ${\mathrm{}}^1$P level produced by collision-induced excitation from the ground state by circularly polarized light. The detuning dependence of the far-wing excited-state orientation can be interpreted in terms of reorientation of molecular orbitals which occur during the collision. Effects due to rotational coupling are seen to occur at large blue-wing detunings. We have also determined the collisional rate for destruction of orientation by measuring the pressure dependence of the excited-state orientation.

The autoionization widths of the lower ${}_{}{}^2{}_{}{}^{}\mathrm{S}$, ${}^2$$P^o$, and ${}_{}{}^2{}_{}{}^{}\mathrm{D}$ Feshbach resonances in Li i, Be ii, and B iii are calculated with the saddle-point complex-rotation method. For Be ii and B iii the radiation widths are also computed. Relativistic and mass polarization corrections to the resonance energy are included. The width results for the [1s(2s2p)${}^3$P]${}^2$$P^o$ and (1s2p2p)${}^2$D states are compared with other theoretical results and with the recently published experimental results for Li i and Be ii. Transition wavelengths involving these autoionizing states are also calculated and compared with theory and experiment. Due to the substantial difference between theory and experiment on the Li[1s(2s2p)${}^3$P]${}^2$$P^o$ width, a detailed study is made on the convergence of this width with respect to the closed channel, open-channel target state and out-going electron wave function to access the stability and reliability of the theoretical result.

Double photoionization (DPI) of ${\mathrm{CH}}_4$ has been studied in the photon-energy range 35–52 eV by the photoion-photoion coincidence (PIPICO) method. Throughout this energy range the measured DPI cross section is found to be much smaller than that of the corresponding process in the isoelectronic neon atom. Unlike the case of rare-gas atoms, where the ratio of the double- to single-photoionization cross section attains a constant value at higher energies, this ratio for methane passes through a maximum at about 47 eV. Comparison of experimental with calculated energies of ${\mathrm{CH}}_4$${\mathrm{}}^{2+}$ electronic states gives evidence that both triplet ${(}^3$${\mathrm{T}}_1$) and singlet ${(}^1$E) states are populated by ejection of two electrons from the 1$t_2$ orbital of ${\mathrm{CH}}_4$. In agreement with the calculations of Siegbahn, our results show that the Franck-Condon factors for excitation of the ${}_{}{}^3{}_{}{}^{}\mathrm{T}_1^{}{}_{}{}^{}$ state are spread over a wide energy range (≃2 eV). ${\mathrm{CH}}_4$${\mathrm{}}^{2+}$ in its ${}_{}{}^3{}_{}{}^{}\mathrm{T}_1^{}{}_{}{}^{}$ state rapidly dissociates (via an indirect process) into ${\mathrm{CH}}_3$${\mathrm{}}^{+}$(X̃${\mathrm{}}^1$${\mathrm{A}}_1^{\mathcal{’}}$)+H ${}_{}{}^{+}{}_{}{}^{}$(${\mathrm{}}^1$S), which is the most favorable dissociation pathway, both energetically and dynamically. At higher excitation energies, ${\mathrm{CH}}_4$${\mathrm{}}^{2+}$ in its ${}_{}{}^1{}_{}{}^{}\mathrm{E}$ state dissociates into the three products ${\mathrm{CH}}_2$${\mathrm{}}^{+}$(X̃ ${}_{}{}^2{}_{}{}^{}\mathrm{A}_1^{}{}_{}{}^{}$)+${\mathrm{H}}^{+}$(${\mathrm{}}^1$S)+H (${}^2$S) with a 5-eV kinetic-energy release. Comparison of experimental PIPICO curves with simulated curves derived on the basis of various fragmentation models leads us to conclude that the ionic fragments ${\mathrm{CH}}_2$${\mathrm{}}^{+}$ and ${\mathrm{H}}^{+}$ are ejected at 180° from each other and that they take almost all the available kinetic energy. This would indicate that the Coulomb repulsion between positive charges plays a dominant role in the process of dissociation into these three fragments.

A systematic investigation was conducted on the effects of the effective and magnetic interactions on the energy-level schemes of the 3$d^N$ configurations (N=2,3,...,8) in the fifth spectra of the iron group. The interactions considered were the effective electrostatic interaction described by α, β, T, and $T_x$, the mutual magnetic spin-other-orbit and spin-spin interactions parametrized by $M^0$ and $M^2$, and the effective electrostatic–spin-orbit (effective EL-SO) interaction represented by $Q^2$ and $Q^4$. The values of the various radial integrals were determined by using both ab initio and semi- empirical methods. The introduction of all above-mentioned ‘‘weak’’ interactions greatly improved the fit between theory and experiment, concerning both the term values and the multiplet splittings. Close agreement prevails between corresponding parameter values obtained in the semiempirical and in the ab initio methods. All parameters vary with N (along the row) in a smooth and regular manner; in particular, the variations of the spin-dependent parameters agree with their theoretical dependence on the effective nuclear charge. All the above results crucially depend on the simultaneous introduction of all parameters representing perturbations of the same type and order, that is, all effective electrostatic parameters should simultaneously be introduced in one stage and all the spin-dependent weak interactions should simultaneously be introduced in a subsequent stage.

Angular distributions of energy-resolved photoelectrons and branching ratios for formation of the 6s and 5d configurations of ${\mathrm{Ba}}^{+}$ are reported for resonance-enhanced multiphoton ionization of barium. Three excited states of barium were prepared and photoionized: (5d6p${)\mathrm{}}^3$$P_1^o$, (5d6p${)\mathrm{}}^3$$D_1^o$, and (6s6p${)\mathrm{}}^1$$P_1^o$. For the (5d6p${)}^3$$P_1^o$ and (5d6p${)\mathrm{}}^3$$D_1^o$ states, photoelectrons corresponding to the fine-structure levels of the 5d ion core were resolved. For the (6s6p${)\mathrm{}}^1$$P_1^o$ state the photoelectron angular distributions have been measured as functions of the independently variable angle between the polarization vectors of the exciting and ionizing laser radiation pulses. Approximate theoretical expressions based on direct photoionization of the dominant electron configuration of each excited state are generally successful in accounting for the data, but specific discrepancies are noted. Significant intermediate-state interactions are required to account for details of the observations, and some final-state interactions are also implied.

This paper introduces a new formalism for analyzing two-photon devices (e.g., parametric amplifiers and phase-conjugate mirrors), in which photons in the output modes are created or destroyed two at a time. The key property of a two-photon device is that it excites pairs of output modes independently. Thus our new formalism deals with two modes at a time; a continuum multimode description can be built by integrating over independently excited pairs of modes. For a pair of modes at frequencies Ω±ε, we define (i) quadrature-phase amplitudes, which are complex-amplitude operators for modulation at frequency ε of waves ‘‘cos[Ω(t-x/c)]’’ and ‘‘sin[Ω(t-x/c)]’’ and (ii) two-mode squeezed states, which are the output states of an ideal two-photon device. The quadrature-phase amplitudes and the two-mode squeezed states serve as the building blocks for our formalism; their properties and their physical interpretation are extensively investigated.

This paper provides the mathematical foundation for the two-mode formalism introduced in the preceding paper. A vector notation is introduced; it allows two-mode properties to be written as compactly as the comparable properties for a single mode. The fundamental unitary operators of the formalism are described and their properties are examined; particular attention is paid to the two-mode squeeze operator. Special quantum states associated with the formalism are considered, with emphasis on the two-mode squeezed states.

We present a theory that describes how one strong classical wave and one or two weak quantum-mechanical waves interact in a nonlinear two-level medium. The analysis is applicable to several popular problems with and without cavities. In particular, the theory treats laser and optical bistability instabilities, predicting when the instabilities grow from spontaneous emission. The theory is a multimode extension of Scully-Lamb theory that derives the equations that describe population pulsations, combination tones, mode locking, resonance fluorescence, Rayleigh scattering, and phase conjugation with quantum-mechanical fields. Hence the theory both presents new results on instabilities and phase conjugation, and also unifies the treatment of a variety of phenomena in the context of Lamb theory. The present paper (first of the series) presents the basic formalism, leaving most applications to subsequent papers in this series. The following paper presents equivalent derivations based on a purely operator formalism.

This paper treats the interaction of one strong classical field mode and one or two weak quantal modes with two-level systems. The analysis is carried out in a purely operator formalism that complements the method presented in the preceding paper and produces the same results. The present approach automatically collects all contributions to second order in the weak-field interactions, and can be easier to extend to more complicated cases. The analysis allows one to treat problems such as predicting the growth of sidemodes in laser- and optical-bistability instabilities, the resonance fluorescence spectrum, Rayleigh scattering, and quantum noise in small-signal phase conjugation.

Stimulated Raman process is used to selectively pump a highly excited vibrational state in a molecular beam. Theoretical evaluation shows that continuous lasers with power of less than 1 W can efficiently pump a single rotational-vibrational level of many simple molecules. The characteristics of the selectively pumped molecular beam and operational conditions are discussed theoretically. The experiment on a ${\mathrm{Na}}_2$ beam is found to agree with theoretical predictions. The flux of 4×${10}^7$ ${\mathrm{s}}^{\mathrm{-}1}$ in the v=31, J=5 excited level has been obtained with use of two cw dye lasers with powers of 80 and 300 mW.

Boundary-value problems for the reduced wave equation that give rise to Gaussian and generalized Gaussian beams in paraxial regions are studied via complex ray geometrical optics. Expressions for the field valid both within and outside the paraxial region are obtained, and the results are compared with those given by paraxial wave optics and evanescent-wave theory.