In the final state of a multiphoton-ionization process the ejected electron may interact simultaneously with the external laser field and with the residual atomic system. A procedure for calculating transition probabilities for such processes is described which incorporates the effects of resonances in the final continuum states of the atom. By using standard methods of scattering theory, it is shown how these resonant states may be separated out leaving a "background" amplitude which is a smooth function of the energy, and which therefore lends itself more readily to numerical evaluation. Such an evaluation may be based on the generalized Lippmann-Schwinger integral equation presented here. The constraint imposed by unitarity on the background amplitude is derived, and it is pointed out how approximations may be set up which satisfy unitarity automatically. A simplified model is described in order to illustrate this and other features of the theory and to make contact with some earlier work on this subject. Finally, a low-frequency approximation is developed in which final-state interaction effects are accounted for in a relatively simple analytical form.

Calculations of the photoionization of $5d$ and $4f$ subshells of a number of heavy elements have been performed with use of relativistic Dirac-Slater wave functions. Cross sections, branching ratios, and photoelectron angular distributions have been obtained and their systematics explored as a function of $Z$. The extent of the relativistic splitting of the zeros in the $5d\to \epsilon f$ dipole matrix elements has been investigated and the implications have been discussed. Comparisons with existing experiment and more sophisticated theory (Dirac-Fock, relativistic random-phase approximation) have been made, and the agreement was generally good.

We report on a new effect which is observed when the small polyatomic molecule ${\mathrm{NO}}_2$ is prepared under collision-free conditions into an electronically excited state. As the intensity of the exciting laser light is varied, the degree of polarization of the fluorescence light may undergo a change in sign. The analysis of the experimental results confronts us with an interesting problem concerning the time evolution of an isolated polyatomic system. In this paper we present the experimental results and a simple model which successfully describes these results. According to this model, the inversion of the polarization of the fluorescence light is a consequence of light-induced stability of the optically prepared state.

Electric field ionization of excited Na atoms by microwave fields between 12 and 15 GHz exhibits several interesting phenomena. The $\mathrm{}\left|m\right|=0\mathrm{} \mathrm{and} 1$ states may be ionized with a very low microwave field, $\sim \frac{1}{{3n}^5}$, corresponding to the point at which the $n$ and $n+1\mathrm{}$ Stark manifolds of principal quantum numbers $n$ and $n+1\mathrm{}$ intersect. The ionization occurs by an atom's making a succession of Landau-Zener transitions to higher-lying states, finally reaching the classical ionization limit. The $\mathrm{}\left|m\right|=2\mathrm{}$ states, on the other hand, ionize at a very high microwave field, $\sim \frac{1}{{9n}^4}$. Both these observations and the more familiar static or low-frequency result of ionization by a field of $\sim \frac{1}{{16n}^4}$ are all consistent with ionization in a completely classical fashion. The apparent differences are due to the dynamics of passing from zero field to a high ionizing field.

We examine the third-overtone absorption of diatomic molecules in the presence of a tunable field in near-third-overtone resonance using a one-dimensional anharmonic-oscillator model. We find that the tunable mode causes modulation of the absorption as a result of an intensity-induced quenching effect. At high intensities the absorption diminishes accompanied with the disappearance of the modulation. Our investigations also show that these effects are insensitive to the dephasing of the interaction.

The two-photon x-ray emission spectra of inner-shell transitions in metallic Mo have been studied using large-area energy-dispersive Si(Li) detectors and fast, computer-controlled, time-coincidence electronics. The discrete energy-summation spectrum displays a peak at 17.1 keV corresponding to the expected $2s\to 1s$ transition, as well as a second, more intense peak at 19.7 keV. Based upon very recent analytical H-atom calculations by Florescu, this latter peak is tentatively identified as due primarily to $3d\to 1s$ transitions. The continuous two-photon spectrum has also been measured on an absolute intensity scale and compared with a frozen-orbital calculation based upon direct summation of the second-order perturbation expansion for the relevant matrix elements. For the $2s\to 1s$ transition, excellent quantitative agreement is found using the self-consistent-field Hartree-Fock wave functions of Clementi and Roetti. The same calculation predicts that the $3s\to 1s$ transition is of negligible relative amplitude. Because the calculational method is inapplicable to $d$ states, a simple closure approximation is developed which is found to be reasonably good for both the $2s$ and $3s$ two-photon transitions, but apparently fails for the $3d$ transition since it predicts a result which is relatively much too small. Our data are the first for inner-shell transitions and it is anticipated that further developments in both instrumentation and in theory will yield a new, rich, multiphoton inner-shell spectroscopy.

It is demonstrated that correlated Gaussian geminals can be used with the same computational effort as products of Gaussian orbitals in the iterative solution of the two-electron integral Schrödinger equation in momentum space. The most accurate energies $E_{\frac{1}{2}}$ and wave functions ${\phi }^1$ ever constructed directly in momentum space are reported for ${\mathrm{H}}^{-}$,He, and ${\mathrm{Li}}^{+}$.

Lifetimes of $n=2\mathrm{}$ levels in two-, three-, and four-electron ions ${\mathrm{Fe}}^{24+}$, ${\mathrm{Fe}}^{23+}$ and ${\mathrm{Fe}}^{22+}$ have been determined using the beam-foil method. The measured decay at 271 Å confirms our identification of this line with the $2s{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-2p{}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ heliumlike Fe xxv. Oscillator strengths derived from the $2s{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}-2p{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2},\frac{3}{2}}^{}{}_{}{}^{}$ resonance transitions in lithiumlike Fe xxiv results are in good agreement with multiconfiguration Hartee-Fock (MCHF) length gauge calculations. Strong cascading from $2p^2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ and $2p^2{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ have been measured and used in the analysis of the complex decay of the resonance transition in berylliumlike Fe xxiii, removing the discrepancy between the experimental and theoretical $f$ value which has been observed for the $2s^2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}-2s2p{}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ transition in some ions of the Be sequence. Experimental lifetimes and oscillator strengths are compared with theoretical data from MCHF and other relativistic calculations.

The dielectronic recombination (DR) rate coefficient ${\alpha }^{\mathrm{DR}}$ is explicitly calculated for Mo, Fe, and Ar target ions of the Na isoelectronic sequence (11 electrons). This work is an extension of a previous study of DR for ${\mathrm{Mo}}^{31+}$ ions. Both $\Delta n\ne 0$ and $\Delta n=0\mathrm{}$ transitions are considered in detail, with full $\mathrm{LS}$ coupling. The radiative and Auger cascade effects are found to be important, especially for high Rydberg states, and are included in the final rate-coefficient estimate. Scaling of ${\alpha }^{\mathrm{DR}}$ with ionic charge and free-electron temperature is discussed.

The optical Bloch equations which incorporate the phenomenological population $\left(T_1\right)$ and dipole dephasing $\left(T_2\right)$ times have been tested recently by optical free-induction-decay (FID) measurements on an impurity-ion crystal ${\mathrm{Pr}}^{3+}$:${\mathrm{La}}_3$ at 1.6 K. At low optical fields, the observed ${\mathrm{Pr}}^{3+}$ optical linewidth is dominated by magnetic fluctuations arising from pairs of fluorine nuclear flip-flops where the condition $T_1\gg T_2$ prevails. At elevated fields, this nuclear broadening mechanism is quenched and the Bloch equations are violated with $T_2\to T_1$. In this paper, a microscopic theory appropriate for a low-temperature impurity solid is presented which reveals the above features both for optical and radio frequencies, and a simple physical interpretation of this line narrowing phenomenon is given. Modified Bloch equations of a novel form are derived to second order and yield analytic FID solutions over the entire range of optical-field strength. A discussion of the earlier NMR theories is given, pointing out similarities and differences.

We present a study of the evolution to chaos for the acousto-optic bistable device. We numerically solve the difference-differential equation describing the system which shows excellent agreement with the experiment. We analyze the influence of noise—additive and multiplicative—on the bifurcation sequence and on the onset of chaos. It is shown experimentally that both types of noise create a gap in bifurcation sequence. In addition we present a comparison between theory and experiment of the time evolution of the signal.

The suitability of degenerate four-wave mixing (DFWM) as a source of squeezed-state (two-photon coherent state) light is investigated, both theoretically and experimentally. In previous semiclassical theory, which neglected pump quantization and loss in the nonlinear medium, Yuen and Shapiro [Opt. Lett. 4, 334 (1979)] showed that such states would be generated by 50%-50% combination of the transmitted probe (TP) and the phase-conjugate (PC) output beams of DFWM. Here the effects of quantum fluctuations in the amplitudes and phases of the pump beams are calculated in a traveling-wave finite-interaction-length DFWM configuration. It is shown that in the limit of strong pump beams and weak nonlinear coupling, the classical-pumps assumption of Yuen and Shapiro is valid. With use of this assumption, loss in the nonlinear medium is incorporated into the model by coupling the interacting modes to a set of reservoir modes. It is shown that loss presents an absolute limit on the degree of squeezing that can be achieved with DFWM. Also, for comparison with experimental work, the photoelectron statistics of the TP, PC, and 50%-50% combination modes are calculated for lossy DFWM; significant deviations are found from the predictions for lossless operation. Quantum-noise measurements on the PC and TP beams generated in sodiumvapor DFWM are described. The mixer is pumped and probed by the nearly transform-limited pulses produced by a continuous-wave-oscillator-pulse-amplifier chain dye laser at 589 nm wave-length. The normalized second-factorial moment $g_2$ of the PC and TP beams is determined from photoelectron-counting measurements. Inability to simultaneously achieve high DFWM reflectivity and acceptably low scattered-plus-fluorescent background, coupled with low photomultiplier quantum efficiency, restrict the experiment to a DFWM regime wherein theory predicts Poisson statistics. Experimental $g_2$ values corroborate this prediction, indicating that systematic and excess noises have been eliminated. No attempt was made to measure the quantum statistics of the 50%-50% combination mode.

Recent work on the perturbation theory for the central-field Dirac equation is extended to include potential coupling of the anomalous-magnetic-moment type. A combination of general parity-conserving central fields is also considered. A method of transforming such a general perturbation to a specific type of perturbation is also demonstrated. All corrections to the energies and wave functions, including corrections to the positions of the nodes in excited states, are expressed in quadrature in a hierarchical scheme, without the use of either the Green's function or the sum over intermediate states.

Coherent propagation of intense short laser pulses through degenerate absorbing media is investigated with the use of an atomic-iodine laser-absorber self-resonant combination. Four degenerate systems, the ${}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}-{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$, $F=3\mathrm{}\leftrightarrow F^{\prime }=4\mathrm{}$, $\Delta M_F=0,\pm 1$ and $F=2\mathrm{}\leftrightarrow F^{\prime }=2\mathrm{}$, $\Delta M_F=0,\pm 1$ transitions, are studied under various conditions. Theoretical analysis based on the "pulse-area—pulse-energy" approach shows different pulse propagation behaviors for three typical types of degeneracy. Experimental results give good agreement with theoretical predictions. It is concluded that self-induced transparency exists in any degenerate two-level system, provided that suitable polarization of radiation is used. The usefulness of self-induced-transparency phenomena for measurements of transitional dipole moment and homogeneous relaxation time is also demonstrated.

A solution to the Boltzmann equation is found that extends to large gradients and fields the classical Chapman-Enskog approximation developed by Spitzer and collaborators for electron transport in a fully ionized gas. The extended solution is used to calculate correction factors to the classical transport coefficients of a nonuniform plasma that depend on the temperature-gradient scale length as a parameter. These factors lead to inherently flux-limited heat flow with values in close agreement with Monte Carlo and numerical Fokker-Planck calculations.

We have made molecular-dynamics computer simulations of dense krypton gas ($10.6\times {10}^{27}$ atoms/${\mathrm{m}}^3$ and 296 K) using reasonably realistic pair potentials. Comparisons are made with the recent experimental data[P. A. Egelstaff et al., Phys. Rev. A 27, 1106 (1983)] for the dynamic structure factor $S(q,\omega )$ over the range $0.4<q<\mathrm{}3.0\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$. For $q<\mathrm{}1.6\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$ the influence of the attractive part of the potential is important and shorter-ranged many-body forces are found to play a role. Additional (less significant on a relative scale) effects are found in the region $q~2.7\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$. Some suggestions for future work are made.

In order to interpret the spectral-line intensities emitted from various plasmas, a collisional-radiative-model program has been constructed for heliumlike ions. In this model a population of 61 excited levels is considered, and excitation, deexcitation, ionization and three-body recombination by electron collisions, spontaneous transition, radiative recombination, and dielectronic recombination have been included. For these processes, the most reliable rate coefficients, experimental or theoretical, have been employed. A detailed account is given of the program along with the review of the rate coefficients adopted. As an example of its applications, line-intensity data for theta-pinch plasmas are analyzed; for oxygen the three sets of experiments are consistent with the present calculation. For the case of carbon, however, the intensity ratio cannot be interpreted consistently on the assumption of the ionizing-plasma model. Rather, it is strongly suggested that the plasma has a significant contribution from the recombining-plasma component.

In recent experimental investigations of the ionization of Rydberg atoms in low-frequency electromagnetic fields, ionization rates have been measured which depend strongly on the intensity of the oscillating fields but only weakly on the frequency. In an attempt to understand this ionization mechanism, an analogous, one-dimensional system is considered consisting of a surface-state electron bound to the surface of liquid helium by its image charge. A complete classical analysis of the behavior of this nonlinear oscillator in a microwave field is presented which shows that above a critical field strength the electron dynamics become chaotic and the electron diffuses in energy until it ionizes. Analytic estimates for the classical thresholds and rates for stochastic excitation and ionization are determined as functions of the microwave-field amplitude and frequency. Since the microwave frequencies and field strengths required for stochastic ionization of this one-dimensional "hydrogen" atom are readily available, this system provides an opportunity to thoroughly explore the manifestations of classical chaos in a quantum system.

A two-dimensional relaxational model equation is studied numerically to investigate the role of lateral boundaries and nonlinear terms in pattern formation. The model reduces in perturbation theory to the same amplitude equation as the one derived from the three-dimensional Boussinesq equations for thermal convection. State-of-the-art numerical methods are described that solve the initial-boundary-value problem efficiently and accurately in large rectangular cells and for long times, for both rigid and periodic boundary conditions. The results of simulations for different aspect ratios, Rayleigh numbers, and initial conditions are discussed in detail. The interaction of defects, the effect of lateral boundaries on the growth and saturation of linear instabilities, and the origin of the long-time scales needed to reach a stationary state are studied. Wave-number selection is investigated using spatial Fourier analysis, and evidence is presented that the band of stable wave numbers is not uniformly occupied as a pattern evolves from random initial conditions of all length scales. These results are in good agreement with many of the observed experimental features of pattern formation in small- and large-aspect-ratio cells, and show some new features that have not yet been seen.

Emission for bremsstrahlung and direct radiative recombination is studied in typically non-Maxwellian plasmas, as found in the critical-density region of laser-produced plasmas. The strong departure of the spectrum from its Maxwellian counterpart is described by a general representation (which is rigorous for hydrogenic plasmas) by means of calculated reduced emissivity coefficients. This departure leads us to reconsider a current temperature diagnostic.