From narrow-band and broadband spectra of barium hollow-cathode discharges obtained with the aid of a Fourier-transform spectrometer, we have determined the branching fractions of five moderately excited levels and the branching ratios between the infrared lines originating in the resonance level 6s6p ${}_{}{}^1{}_{}{}^{}°_1^{}{}_{}{}^{}$ of the neutral barium atom. By combining our emission measurements with lifetime and absorption data taken from the literature we were able to derive transition probabilities for 13 visible and 16 infrared transitions as well as upper limits for the A values of 15 additional infrared lines. The resulting transition probabilities cover five decades.

The absolute two-photon excitation cross section for the ${\mathrm{H}}_2$ E,F ${}_{}{}^1{}_{}{}^{}\Sigma _g^{}{}_{}{}^{}$ (v’=6)←${\mathrm{X}}^1$${\mathrm{\Sigma }}_{\mathit{g}}$ (v’’=0) Q(1) transition at 193 nm has been measured by observing the E,F ${}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ (v’=6)->B ${}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ (v’’=0) fluorescence at ∼750 nm. The measured integrated two-photon excitation cross section, (2.0±0.9)×${10}^{\mathrm{-}36}$ ${\mathrm{cm}}^4$, is in good agreement with the theoretical value of 2.8×${10}^{\mathrm{-}36}$ ${\mathrm{cm}}^4$, which is obtained from previously published calculations [Huo and Jaffe, Chem. Phys. Lett. 101, 463 (1983)]. The absolute cross section for photoabsorption by the E,F state at 355 and 193 nm was also measured by monitoring the depletion of the 750-nm fluorescence caused by a second laser. The measured cross sections for photoabsorption by the E,F (v=6) state are (9.7±2.4)×${10}^{\mathrm{-}18}$ ${\mathrm{cm}}^2$ at 355 nm and (6.4±1.3)×${10}^{\mathrm{-}18}$ ${\mathrm{cm}}^2$ at 193 nm. Comparison with theoretical estimates [Cohn, J. Chem. Phys. 57, 2456 (1972)] of the direct photoionization cross section of this state (8.5×${10}^{\mathrm{-}18}$ ${\mathrm{cm}}^2$ at 355 nm and 3.2×${10}^{\mathrm{-}18}$ ${\mathrm{cm}}^2$ at 193 nm) suggests that other processes may contribute to the photoabsorption.

Photoexcitation of the dissociating ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{}{}_{}{}^{}$ autoionizing state is found to be important. Cross sections for this additional channel, which may lead to dissociation (${\mathrm{H}}^{\mathrm{*}}$+H or ${\mathrm{H}}^{+}$+${\mathrm{H}}^{\mathrm{-}}$) or autoionization (${\mathrm{H}}_2^{+}$+${\mathrm{e}}^{\mathrm{-}}$), are calculated to be 3.6×${10}^{\mathrm{-}18}$ ${\mathrm{cm}}^2$ at 355 nm and 7.6×${10}^{\mathrm{-}18}$ ${\mathrm{cm}}^2$ at 193 nm. The calculated branching ratio strongly favors dissociation at 355 nm and autoionization at 193 nm.

The saddle-point complex-rotation method in the intermediate LSJ-coupling scheme is used with the Breit-Pauli spin-dependent perturbation operators to compute the spin-induced autoionization rates of the lithiumlike 1s2s2p ${}_{}{}^4{}_{}{}^{}P_J^o{}_{}{}^{}$ states from Z=3 to 18. The radiative transition rates of the J=(1/2 and (3/2 levels are also calculated in the intermediate LSJ-coupling scheme. The combined result yields lifetimes for these levels which are compared with the existing experimental and theoretical data in the literature.

Nonrelativistic intermediate-coupling Hartree-Fock calculations of fully split x-ray Kα satellite spectra of atoms with 10≤Z≤32 were carried out. The average energy shift of the satellite with respect to the Kα line was calculated from a weighted average of the individual lines using known LS-coupling relative intensities. The results are found to be in excellent agreement with an extensive set of measured energy shifts and with recent self-consistent-field calculations based on an electrostatically induced level-shift model for the 2p spectator vacancy. The measured data are also used to calculate the effective screening parameter of the 2p spectator vacancy. A value of ∼0.6 is found for our Z range, in close agreement with the published value for the 1s spectator vacancy. The weak linear decrease in this value with increasing Z is attributed to the presence of additional high-level vacancies as well as preemission electronic level rearrangement.

The screened hydrogenic radial integral both for discrete-discrete and discrete-continuum transitions is expressed in forms suitable for obtaining closed-form expressions for specific transitions. Two effective charge parameters $Z_i$ and $Z_f$, respectively, for the initial state and for the final state are retained in these formulas. As examples, explicit expressions for a few transitions are derived and a method for obtaining a series for a discrete-discrete radial integral, suitable for large final-state principal quantum numbers, is indicated.

The Li i 1s2${\mathit{p}}^2$${\mathrm{}}^4$P–2${\mathit{p}}^3$${\mathrm{}}^4$${\mathit{S}}^{\mathrm{o}}$ transition has been studied in the spectrum of foil-excited lithium ions; its wavelength has been determined to be λ=145.016±0.006 Å, in good agreement with previous experimental results. The lifetime of the triply excited 2$p^3$ ${}_{}{}^4{}_{}{}^{}S_{}^o{}_{}{}^{}$ level has been derived from decay curves as τ=13.5±1.5 ps. Both values agree with very recent theoretical predictions.

Lifetimes of each hyperfine level of the 6p ${}_{}{}^4{}_{}{}^{}P_{5/2}^{}{}_{}{}^{}$ state of singly charged ${}_{}{}^{129}{}_{}{}^{}\mathrm{Xe}$ and ${}_{}{}^{131}{}_{}{}^{}\mathrm{Xe}$ have been measured using laser excitation of a fast-ion beam. The collinear laser- and ion-beam arrangement was used to achieve high spectral resolution, and transitions to each hyperfine level were locally Doppler tuned into resonance between a pair of post-accelerating electrodes. Decay to the 6$s^4$$P_{5/2}$ state was observed through a monochromator immediately after the post-acceleration field, and cascade-free lifetimes were then determined by mechanically varying the distance between the excitation and observation points. Depletion of close-lying hyperfine levels prior to the excitation region was necessary in ${}_{}{}^{131}{}_{}{}^{}\mathrm{Xe}$ to sufficiently isolate transitions for these measurements. These results form the first set of lifetime measurements for each hyperfine level within a particular J state of an atomic ion. Although no variation in lifetime with F quantum number was detected outside of the determined error bars, application to studies of hyperfine-induced mixing is discussed.

We report a study of the autoionizing np Rydberg states near the lowest ionization threshold of ${\mathrm{H}}_2$. Using resonant two-photon excitation, intermediate states in specific rotovibrational levels in the double well, E,F ${}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ states are prepared. Then, a second, tunable laser is used to photoionize via excitation of the np Rydberg states. Because of the stepwise laser excitation scheme employed in our experiment the photoionization occurs from states with vibrational wave functions very similar to those of the ${\mathrm{H}}_2^{+}$ core. As a consequence, the autoionizing states appear as nearly symmetric resonances, rather than the highly asymmetric Beutler-Fano profiles observed from the direct photoexcitation from the ground state of ${\mathrm{H}}_2$. Our experiments show that the J=1 np states are broader than the J=3 np states converging to the same limit, suggesting that the two states autoionize into the ɛp and ɛf continuum, respectively. We compare our observations with a theoretical analysis using a multichannel quantum defect theory. The J=1 states reveal the profound effect caused by the perturbation of the autoionizing Rydberg series converging to the lowest vibrational and rotational state of ${\mathrm{H}}_2^{+}$ by low-n states converging to higher vibrational states of the ${\mathrm{H}}_2$-ion core.

Recent studies by DeVoe and Brewer [Phys. Rev. Lett. 50, 1269 (1983)] have shown that the conventional optical Bloch equations markedly fail to describe the optical saturation behavior of the $D_1$ line in the solid ${\mathrm{Pr}}^{3+}$:${\mathrm{LaF}}_3$. In this paper we extend these studies to another solid, ruby, using free-induction-decay observations obtained by pulse excitation of the $R_1$ line at 693.4 nm with an ultranarrow-linewidth dye laser. Comparison of the results with Gauss-Markov and random-telegraph-dephasing theories shows approximate agreement for a fluctuation correlation time ${\tau }_c$=$T_2$, the dephasing time. This result is remarkably similar to that obtained for ${\mathrm{Pr}}^{3+}$:${\mathrm{LaF}}_3$. However, for theoretical and experimental reasons, we conclude that the theories do not consistently explain the current as well as other data. A qualitative discussion of another dephasing model is given.

We present a theory of nondegenerate multiwave mixing in a squeezed vacuum. The probe absorption and coupling coefficients are derived using a standard Fourier-series method. We average the coefficients over pump spatial holes and solve the coupled mode equations to find the four-wave-mixing reflection coefficient. Reflectivity peaks and dips are found to be narrower than in an unsqueezed vacuum. Both the absorption and the reflectivity provide sensitive ways to measure the amount of squeezing in the vacuum.

We measure the statistical distribution of buildup times for the field of a single-mode ${\mathrm{CO}}_2$ laser when cavity losses have rapidly changed from a large to a small value. The ratio between the average buildup time and its statistical spread is shown to be a sensitive test of the quantum fluctuations in the off state. This method operates as a ‘‘statistical microscope,’’ permitting the accurate determination of a small mean photon number in the infrared region by optical amplification, and a discrimination of the initial mean photon number from noise contributions along the amplification process. Following the buildup, the laser pulse decays on two time scales. The faster one, due to the radiation coupling, can be fitted by a Toda oscillator model; the slower one, due to the collisional dynamics of the excited population, provides a quantitative evaluation of two distinct population decay rates, one within the rotational manifold and the other one out of the vibrational band.

Pressure-induced effects in nonlinear optics and spectroscopy are studied using a nonstandard-dressed-atom formalism for a set of two-level atoms. We consider a two-level atom interacting with two radiation fields whose frequencies differ by δ and undergoing dephasing collisions with a perturber bath. The atom-field detunings are large compared with all relaxation rates in the problem. The system is described by a Hamiltonian of an atom dressed by a single-mode field with a coupling constant slowly varying in time at frequency δ. We show that the collisionally aided excitation of the initially unpopulated dressed states is modulated in time. All the characteristics of the pressure-induced effects are deduced from the properties of this time-modulated excitation. Apart from already known phenomena (pressure-induced extra resonances in four-wave mixing, pressure-induced phase shifts, etc.) that are reinterpreted using this approach, we present a new effect that can be described as fluorescence beats. Finally, we show that this approach gives a firm basis for use of a model involving collision-induced gratings and we interpret the pressure-induced effects in the context of this model.

We carry out numerical simulations of the evolution and steady-state properties of a dye laser operating near resonance. The model we use is fully two dimensional (i.e., it includes the intensity and the phase of the radiation) and does not involve the usual low-intensity expansions commonly used in the literature. The equation for the complex electric field is driven by white additive noise (quantum fluctuations due to spontaneous emission) and by colored multiplicative noise (fluctuations of the gain parameter). We note that the simulations agree with the experimental results of Zhu, Yu, and Roy [Phys. Rev. A 34, 4333 (1986)] for parameter values used in their experiments. We compare the simulation results with predictions of the ‘‘best Fokker-Planck equation’’ (BFPE) for the steady-state distribution of the laser intensity and find remarkable quantitative agreement for large ranges of parameters values, even for values that are in principle beyond the range of validity of this equation. We conclude that the BFPE can be safely invoked to make predictions for this system.

In a highly nonlinear thin film, the presence of the diffracted beams from the pump-probe-beam-induced refractive-index grating modifies considerably the energy coupling between the pump and the probe beams. Using coupled amplitude and phase equations, the roles of various factors such as phases and phase shifts, phase modulations, pump-beam intensity, intensity ratio, interaction length, and losses in the medium in the multiwave-mixing processes are clearly identified. We also present experimental results on the dependence of the probe gain on the pump-probe-beam ratio, the pump intensity, and on the interaction length, using a nematic liquid-crystal film as the nonlinear medium.

The Fokker-Planck equation approach to forward four-wave mixing developing from the initial coherent states is adopted to obtain a set of recursive relations for the expectation values of the normally ordered field operators. This set of equations is closed, in accordance with the model of the generalized superposition of coherent and chaotic fields, to provide differential equations for unknown quantities in this model. A numerical solution of these equations enables one to determine the photon number distribution, its factorial moments, squeezing variances, and entropy of radiation under discussion. Fully quantum-mechanical features of radiation such as its sub-Poisson behavior and squeezing of vacuum fluctuations are preserved in this approach. The validity of this approximation is discussed and numerical results are provided.

The statistical properties of nonlinear oscillators modeling dissipative forward four-wave mixing are investigated, adopting the Fokker-Planck equation approach. The photon statistics are shown to be insensitive to the nonlinearities and are formulated in terms of the superposition of coherent and chaotic fields. The only approximation in describing the squeezing properties consists in the way of including thermal noise. The effect of the initial coherent amplitudes, that of the interplay of the coupling constants, and that of the reservoir on the squeezing properties are studied. An interesting connection between the revivals of coherent amplitudes and squeezing is pointed out.

In the 1970s the experiments of Weingartshofer et al. [Phys. Rev. Lett. 39, 269 (1977) and Phys. Rev. A 19, 2371 (1979)] have shown that the Kroll-Watson cross section for Rutherford scattering in the presence of an intense laser field is correct. In a recent paper [Phys. Rev. A 38, 2525 (1988)], by using the Volkov solution to the minimally coupled Dirac equation, we had shown that the spin of the electron would give a contribution to the heating rate of a plasma in the intense laser light. We had also developed the concept of the quasifree states of the electron from a kinematical point of view. Using these concepts, we show that the Rutherford cross section has to be modified due to the spin of the electron and also due to the high intensity of the laser radiation at the region of interaction. A new coupling (decoupling) scheme is presented separating the kinematical factors from the dynamical ones. When the electron’s momenta are perpendicular to the polarization plane of the laser field (small-angle scattering), it is discovered that the net number of photons absorbed or emitted in a single scattering process is limited to less than or equal to 2. We develop a mathematical transformation in the Appendix to reduce the infinite sum over products of Bessel functions into a single finite integral so that the ratio of our cross section to that of Rutherford can easily be computed and the results are plotted for various ranges of the parameters involved.

The thermodynamics of the relativistic shock wave in which electron-positron pairs are produced in the post-shock matter is studied in the temperature range 5×${10}^9$ K≲T≲${10}^{12}$ K, where the baryons are nonrelativistic and electron-positron pairs are the only leptons created. The post-shock matter with pairs in thermodynamic equilibrium are classified according to whether or not the energy density of the radiation (the pairs and the photons) exceeds that of the baryons. The post-shock matter without pairs in thermal equilibrium is also considered in the case where it is composed of a relativistic two-temperature electron-ion plasma. The relevant time scales for such processes as temperature relaxation, pair production, and cooling are examined in order to establish the temperature region where such a plasma can exist. Analytic relations between the pre-shock and post-shock quantities are obtained in certain limits of these three cases. The shocks with and without pairs in the post-shock matter are then compared.

Recent calculations of electron impact excitation rates in heliumlike Si xiii are used to derive the electron-density-sensitive emission-line ratio R (=f/i) and temperature-sensitive ratio G[=(f+i)/r], where f, i, and r are the forbidden 1$s^2$ ${}_{}{}^1{}_{}{}^{}s$ ${}_{}{}^3{}_{}{}^{}S$, intercombination 1$s^2$ ${}_{}{}^1{}_{}{}^{}p$ ${}_{}{}^3{}_{}{}^{}\mathrm{P}_1^{}{}_{}{}^{}$,2 and resonance 1$s^2$ 1$s^2$${}^1$S–1s2p ${}_{}{}^1{}_{}{}^{}P$ transitions, respectively. A comparison of these with R and G ratios measured from x-ray spectra of the divertor injected tokamak experiment, for which the electron density and temperature have been well determined, reveals good agreement between theory and observation, with discrepancies of typically 8% in R and 5% in G. This provides experimental support for the accuracy of the atomic data adopted in the line ratio calculations. The theoretical results may be applied to the analysis of remote sources for which no independent electron density and temperature estimates exist (such as solar flares), in order to derive values of $N_e$ and $T_e$ which, on the basis of the above comparison between theory and observation, should be accurate to ±0.3 and ±0.1 in the log, respectively.

A general review of distribution functions reveals that the two- and three-point correlation functions familiar to galaxy studies may be identified with the total correlation functions relevant to the study of liquids. In this context a discussion is included of the Peebles-Groth three-point correlation function. A recently derived two-point correlation function in polynomial form is reviewed. Renormalization of this expression is found to bring it into very good agreement with the well-established $r^{\mathrm{-}\gamma }$ form (where r is intergalaxy displacement and γ is a constant).