Seventeen bound and core-excited states of ${\mathrm{Be}}^{+}$ are calculated using configuration-interaction wave functions. Relativistic and mass-polarization corrections are included. The relativistic corrections considered are correction to the kinetic energy, Darwin term, contact terms, and retardation effect. The fine structure is calculated by using spin-orbit and spin-other-orbit operators. The wavelengths computed for the transitions from the core-excited states improve the agreement between theory and experiment. The lifetimes for these states are also calculated. Our calculated transition wavelengths and fine structures for the bound states agree well in most cases with the experimental data tabulated by Bashkin and Stoner.

A semiclassical model of two-level atoms driven by a local field is developed. It is shown that this leads to optical bistability without the presence of an optical cavity. The quantitative and qualitative character of this mirrorless bistability is different from cases considered earlier.

Absolute transition probabilities for the 18 transitions of the $3s-4p$ transition array of neutral carbon have been studied in emission with a wall-stabilized arc. Values are given for ten individual lines and one pair of strongly blended lines (476.23 and 476.25 nm). An upper bound is set for the remaining six lines of the array which were too weak to be observed in this work. An important feature of this work is the use of digital least-squares-fitting techniques to separate overlapping lines and to provide accurate line-wing corrections. Problems associated with demixing effects have been avoided by normalizing relative transition probability measurements to an absolute scale set by atomic lifetimes.

A relaxed-orbital multiconfiguration Hartree-Fock calculation of the $L_1-L_{23}{M}_1$ Coster-Kronig transitions in Ar has been performed. The effects of exchange between the continuum electron and the bound-state electrons have been examined. With regard to transition energies, excellent agreement with experiment is attained. Calculated transition probabilities are slightly closer to measured rates than in previous theoretical work that does not include complete relaxation, but an important discrepancy still remains that apparently cannot be resolved within the independent-particle framework.

Photoionization of excited states of the xenon dimer (${\mathrm{Xe}}_2$) has been observed and absolute ionization cross sections have been measured for several laser wavelengths between 248 and 351 nm. Production of the excimers is accomplished by two-photon ionization of ground-state Xe atoms at 193 nm, followed by formation and the subsequent dissociative recombination of $\mathrm{Xe}_2^{}{}_{}{}^{+}$ $1{\left(\frac{1}{2}\right)}_u$ ions, collisional and radiative relaxation of the Xe $6p$ and $6s^{\prime }$ manifolds, and formation of low-lying excimer states by three-body collisions. Absolute photoionization cross sections are subsequently determined at 351.1, 337.1, 307.9, 277.0, and 248.4 nm by combining a second rare-gas—halide excimer (or ${\mathrm{N}}_2$) laser pulse with a microwave-absorption technique to monitor the absolute photoelectron density (in real time) as a function of the intensity of the second laser pulse. The use of microwave absorption allows for the detection of photoelectrons in the presence of a high-pressure background gas. Laser-induced fluorescence and spontaneous emission studies of the temporal behavior of the populations of all of the Xe $6p$ states as well as the $6s^{\prime }{\left(\frac{1}{2}\right)}_0$ and $6s{\left(\frac{3}{2}\right)}_1$ levels confirm that a molecule is being photoionized. The molecular states involved are $0_u^{+},1_g$, and $2_g$ which correlate with the $6s{\left(\frac{3}{2}\right)}_1$ excited level and a ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ (ground-state) atom. The optical transitions associated with each laser wavelength $\lambda$ studied appear to be ${\mathrm{Xe}}_2^{*}{0}_u^{+}\to {\mathrm{Xe}}_2^{+} 1{\left(\frac{3}{2}\right)}_g (\lambda =248.4\mathrm{} \mathrm{nm})$; $1_g (or 2_g)\to 1{\left(\frac{3}{2}\right)}_u (\lambda =277.0\mathrm{} \mathrm{nm})$; and $1_g (or 2_g)\to 1{\left(\frac{1}{2}\right)}_u$ for $\lambda =307.9,337.1, \mathrm{and} 351.1$ nm. The discrepancy between the measured cross sections and the values calculated previously (Lorents, Eckstrom, and Huestis, 1973) from a quantum-defect approach is roughly a factor of 2 at 308 nm but increases rapidly at shorter wavelengths. Also, in contrast to theoretical predictions for the $6s$ atomic Xe excited states in which the photoionization cross section $\sigma$ falls monotonically with photon energy, the measured $\sigma$ peaks at 7×${10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$ for $\lambda =308\mathrm{}$ nm ($\hslash \omega =4\mathrm{}$ eV). The profile of the photoionization cross-section spectrum that is reported here for $\mathrm{Xe}_2^{}{}_{}{}^{*}$ is, however, remarkably similar to that calculated by Rescigno et al. [J. Chem. Phys. 68, 5283 (1978)] for the ${}_{}{}^1{}_{}{}^{}\Sigma$ excited state of the ${\mathrm{Ar}}_2$ excimer ($\mathrm{Ar}_2^{}{}_{}{}^{*}$).

The interaction of a damped cavity with a two-level atom is examined. The treatment is fully quantum mechanical. Expressions are obtained for the effect of damping and fluctuations in the walls of the cavity on the atom-cavity interaction, at zero temperature and in the limit of small damping. The physical situation can be realized with Rydberg atoms and a cavity.

The two emission lines resulting from the two-electron transitions $1s^{-2\mathrm{}}\to 2s^{-1\mathrm{}}2p_{\frac{3}{2}}^{-1\mathrm{}}$, $1s^{-2\mathrm{}}\to 2s^{-1\mathrm{}}2p_{\frac{1}{2}}^{-1\mathrm{}}$ were resolved for the transition elements Cr, Fe, Co, and Cu. Their energies were determined and were found to agree well with calculations. The relative intensities of the two transitions were measured and found to be $\frac{I\left(K{\alpha }_1{\alpha }_3^h\right)}{I\left(K{\alpha }_2{\alpha }_3^h\right)}\simeq \frac{3}{4}$. For the same initial state, the intensity of the emission lines resulting from the simultaneous transitions of two electrons was found to be comparable to the emission intensity from the uncorrelated single-electron transitions. This is some 3 orders of magnitude greater than what has been previously reported, both theoretically and experimentally.

We describe the photoexcitation spectra from bound Ba Rydberg states $6snl$ to the analogous autoionizing $6pnl$ states. The spectra are obtained with high laser power bringing out weak spectral features corresponding to changes in $n$ of the outer $\mathrm{nl}$ electron. These spectra are explained using a quantum-defect-theory approach which shows that the optical cross section is a product of the spectral density of the autoionizing states and the overlap integral from the initial bound state. When a saturation effect is taken into account, synthetic spectra calculated in this way accurately reproduce the observed spectra. Experimental spectra of unperturbed autoionizing series are presented together with the two-channel quantum-defect theory relevant to this case. In addition, the new features which arise in the case of interacting series are shown as well as a model three-channel quantum-defect-theory treatment.

We report observations of inelastic collisions of atoms excited by a weak monochromatic laser field whose frequency is close to the resonance frequency of the transition from the ground state to an excited state. Our experiments use sodium atoms in a gas cell with the laser frequency detuning from resonance ($\left|\Delta \right|<\mathrm{}6\mathrm{}$ GHz) much smaller than the inverse of a collision duration. In this frequency region, our results may be interpreted in terms of inelastic collisions involving virtually excited atoms. The inelastic collision rate is determined by measuring the ratio of fluorescence from the collisionally populated level to emission from the laser populated level. By studying this emission ratio as a function of perturber pressure we show that the inelastic collision rate constant for virtually excited atoms is the same as the thermally averaged rate constant for level-to-level population transfer. Measurements of the emission ratio as a function of the laser detuning from resonance explicitly show how the correlation of collision rates with excitation frequency due to the Doppler effect is lost as the laser is tuned more than several Doppler widths from line center. The collisions of virtually excited atoms fundamentally limit experiments utilizing the Doppler effect to obtain velocity-dependent excited-state collision rates.

Single-particle trajectories in a free-electron-laser device consisting of a linear periodic wiggler superimposed on a strong uniform axial guide field are examined by a formalism suitable for perturbation analysis and adaptable to wigglers of arbitrary geometry. For motion locked on to a single resonance (between the gyromotion and the periodicity induced in the axial velocity by the wiggler) and for sufficiently weak wiggler fields, bounded oscillations of the gyroradius and of axial velocity are possible for a limited region of parameter and phase space. Optimal parameters for which the largest fraction of particles entering the drift chamber experience limited excursions in gyroradius and in axial velocity are determined. The mean drift of the guiding center off axis is used to determine the allowable length of the wiggler and of the drift tube for beam propagation. With increasing wiggler field bounded motion is eliminated, leading to transition between resonances, chaotic motion, and significant spread in the axial velocities of electrons. Comparison with experimental results is presented.

A single pass of an intense cw light beam through a strongly absorbing medium can be characterized by two parameters, the input on-axis intensity normalized to the saturation value $I_{0,0}$, and the Fresnel number $F$ for an absorption length ${\alpha }^{-1\mathrm{}}$. For both large $I_{0,0}$ and $F$, propagation can be divided in two parts: At the very beginning, the transverse profile of the beam experiences an encoding. For a beam tuned exactly on resonance, encoding reduces to a stripping of the profile from the wings to the center, progressively, as the light beam goes further into the cell. For $F>>1\mathrm{}$ and $I_{0,0}>>1\mathrm{}$, and both of the same order of magnitude, this stripping can be modeled by a circular aperture placed at the end of the encoding region. Afterwards, the beam is assumed to propagate in free space, its profile exhibits Fresnel interferences and on-axis enhancement. Using a perturbative treatment, the width and the location of the aperture are analytically estimated, and the model is successfully compared with numerical predictions of on-resonance self-focusing. For $I_{0,0}\lesssim F$, the stripping and free-space propagation cannot be separated because near-axis stripping coexists with large diffraction effects on the wings. This case, the best for observing cw on-resonance enhancement, would gain in a more sophisticated model, taking into account diffraction by successive apertures.

Multiphoton ionization of cesium atoms by intense (5×${10}^{11}$ W ${\mathrm{cm}}^{-2\mathrm{}}$), short (54 ps) laser pulses at the neodymium-doped yttrium aluminum garnet laser frequency is studied. Experimentally, the energy spectrum and angular distribution of the photoelectrons are recorded using a time-of-flight spectrometer. Strong-field effects are clearly demonstrated by evidence of simultaneous four- and five-photon ionization (above-threshold ionization) and by intensity-dependent angular distributions. Theoretically, differential generalized cross sections for four- and five-photon ionization are computed and are shown to be strongly affected by light shifts and high-order coupling of nonresonant bound states. Comparison between theory and experiment includes effective order of nonlinearity, intensity dependence of four- and five-photon electron signal around the saturation intensity, relative values of angular-distribution coefficients, and the ratio of five- to four-photon signals. Intensity effects are generally well predicted both for angular distributions and for saturation. Some discrepancy remains between experimental and theoretical angular-distribution coefficients. The ratio of the total number of electrons emitted in the five- and four-photon processes is measured to be (2.9±0.5)×${10}^{-2\mathrm{}}$, at 6×${10}^{11}$ W ${\mathrm{cm}}^{-2\mathrm{}}$, encompassing the theoretical value of 3.3×${10}^{-2\mathrm{}}$.

In this paper, we consider the mean-field equations for the laser with a saturable absorber (LSA) and concentrate on the low-intensity solutions. We show that the LSA equations may admit two successive bifurcations. The first bifurcation corresponds to the transition from the zero-intensity state to time-periodic intensities and is a Hopf bifurcation. The second bifurcation corresponds to the transition from these time-periodic intensities to quasiperiodic intensities which are characterized by two incommensurable frequencies. In order to describe these transitions, we investigate a particular limit of the parameters and propose a new perturbation method for solving the LSA equations. We give analytical conditions for the existence of both the primary and secondary bifurcations.

The problem of coherent four-wave mixing is treated quantum theoretically in the dressed-atom picture using a set of "angular-momentum-like" operators. The phases of the radiation fields are considered by including a space-dependent phase factor in the raising (lowering) field operators. All possible transition pathways are considered, and their contributions to the total transition probability are added coherently. It is shown that interferences between the different pathways play an essential role and that the phases of the radiation fields should be properly handled. The result of this calculation is a directional, time-dependent transition probability that automatically expresses the phase-matching requirements of a coherent four-wave mixing process.

Single crystals of KCl containing $\mathrm{O}_2^{}{}_{}{}^{-}$ centers (8×${10}^{16}$-7×${10}^{17}$ ${\mathrm{cm}}^{-3\mathrm{}}$) were excited at low temperatures ($T<\mathrm{}30\mathrm{}$ K) using frequency-quadrupled single pulses of a mode-locked Nd-doped yttrium aluminum garnet laser. At excitation intensities above 20 GW/${\mathrm{cm}}^2$ a spontaneous emission of coherent light was observed which could be identified as Dicke superfluorescence. This superfluorescence was observed on two of the zero-phonon lines in the vibrational progression of the $\mathrm{O}_2^{}{}_{}{}^{-}$ fluorescence spectrum (0-10 and 0-11 at 592.8 and 629.1 nm, respectively). We have studied the time dependence, the statistics of the delay times, and the intensities. The observed delay times vary between 0.5 and 10 ns, the observed pulse widths between 0.5 and 6 ns, and the coherence time was found to be longer than 100 ps. The observed linewidths of the superfluorescence ($0.016\mathrm{nm}\cong 14\mathrm{GHz}$) is a factor of 2.5 smaller than that of the spontaneous fluorescence (0.042 nm at 4.2 K). The superfluorescence is observed only below a critical temperature which depends on the $\mathrm{O}_2^{}{}_{}{}^{-}$ concentration (8 to 28 K for concentrations between 8×${10}^{16}$ and 7×${10}^{17}$ ${\mathrm{cm}}^{-3\mathrm{}}$).

A theoretical study of amplitude (AM) and frequency (FM) modulation components of an optical wave interacting resonantly with a homogeneously broadened two-level system is presented. It is shown that the AM component is usually less attenuated than the FM component; however, under conditions which depend on the modulation frequency, relaxation times, and the saturation parameter, the reverse may occur. In strongly saturated media the AM component can be amplified, a process limited by the depletion of the carrier intensity as the wave propagates in the absorber. The two- and three-wave cases of unidirectional saturation spectroscopy are considered and the effects of depletion are discussed. In the two-wave (single-probe) case a third wave is generated which substantially modifies the absorption profile for the probe. An analysis is included of the sideband evolution in a laser with an intracavity saturable absorber. By analyzing the problem in the frequency domain, some new insights concerning the role of the saturable absorber in passively mode-locked lasers are presented.

A semiclassical theoretical model is described under the plane-wave and mean-field approximations on the transmission characteristics of a system of two-level atoms with large permanent dipole moments contained in a Fabry-Perot cavity and driven by two coherent two-photon resonant fields. In the steady-state situation, the coupled field equations are solved by eliminating one of the field variables to obtain the state equation. This state equation is numerically analyzed in detail, thus providing the regions on two-dimensional maps corresponding to one, three, and five stationary states of the system. The linear stability analysis is also carried out for the case when the length of the cavity is such that the medium-relaxation times are much shorter than the cavity-photon life times for both the waves. The simple stability criterion that the negative-slope regions of the transmission curves are unstable holds, but only the lowest positive-slope branches show stability in all of the cases we tested numerically.

The pair-correlation function $g\left(r\right)\mathrm{}$ of the Kr-type model fluid with only pair interactions was calculated using the Rosenfeld-Ashcroft modification of the hypernetted-chain (HNC) equation which includes bridge diagrams, and gave results in excellent agreement with Monte Carlo $g\left(r\right)\mathrm{}$ data. These bridge functions and the known pair potential were used to analyze the neutron-diffraction structure-factor data of Teitsma and Egelstaff, to determine the effective strength of the three-body potential as a function of the density assuming it to be of the Axilrod-Teller (AT) form. The strength of the effective three-body contribution $s=\frac{\nu }{{\nu }_{\mathrm{theor}}}$, where ${\nu }_{\mathrm{theor}}$ is the theoretical value, decreases for higher densities, suggesting that the many-body terms (beyond the Axilrod-Teller form) screen the AT interaction as the density increases. The results are very sensitive to the uncertainties in the structure factor $S\left(k\right)\mathrm{}$ for small $k$ if parameter optimization is used to determine the effective pair potential. However, prediction of the compressibility using $s=1\mathrm{}$ allows us to conclude that ${\nu }_{\mathrm{theor}}$ is consistent with the experimental data for low densities, to within the uncertainties in the presently available pair potentials and in the structure-factor data.

A new technique which provides an absolute measurement of the smectic elastic constant $B$ is presented. This technique measures second sound on samples whose top surface is an air—liquid-crystal interface. The free surface of the sample is electrically driven and the resulting surface displacements are measured with an optical heterodyne technique. The smectic elastic constant is obtained from the spectrum of the scattered light which is determined by the bulk second-sound modes. Two bilayer and two monolayer smectic-$A$ liquid crystals were studied. Near the smectic-$A$—to—nematic phase transition the data can be described by a simple power law $B=B_1{(T-T_{\mathrm{NA}})}^{\phi }$. However, the resulting critical exponents $\phi$ are not universal. In addition, the $B_1$ values for the bilayer smectics are considerably smaller than the values for the monolayer smectics.

The motion of a random walker on a Sierpiński gasket is studied in $d$ dimensions using a renormalization-group approach. The relation $\tilde{\delta }=\overline{d}-2+\omega$ is established from the behavior of recursion relations and is verified in numerical studies (here $\overline{d}$ is the fractal dimension, $\omega$ describes coupling-constant scaling, and $\tilde{\delta }$ describes the distance-time relationship of a random walk). When this relation is combined with $\tilde{t}=d-2+\tilde{\zeta }$, an Einstein relation is derived.