Relativistic kinematics with an 800-MeV ${\mathrm{H}}^{-}$ beam at the Clinton P. Anderson Meson Physics Facility (LAMPF) at Los Alamos allows the observation, with very little background, of resonant structures in the photodetachment spectrum of ${\mathrm{H}}^{-}$ in intense electric fields. We report studies of the ${}_{}{}^1{}_{}{}^{}P$ resonances near $n=2\mathrm{}$ in ${\mathrm{H}}^{-}$ in electric fields as high as 1.3 MV/cm. The splitting of the ${}_{}{}^1{}_{}{}^{}P$ Feshbach resonance can be explained by Stark mixing with a nearly degenerate ${}_{}{}^1{}_{}{}^{}S$ resonance. For field values above those required to quench the Feshbach resonances a ${}_{}{}^1{}_{}{}^{}D$ state is observed, apparently induced by Stark mixing with the ${}_{}{}^1{}_{}{}^{}P$ shape resonance. The systematics of the behavior of these resonances are compared with the results of a simple perturbation model.

Simple expressions are obtained which permit systematic estimates of the rate coefficients for direct radiative recombination (DRR) of fast electrons with atomic ions of various ionic species. The analysis utilizes a set of cross sections obtained through numerical calculations combined with the use of an interpolation scheme to smoothly connect reduced cross sections (apart from normalizations) of the bremsstrahlung tip region and the low-lying DRR region. It is shown that these numerical cross sections can be reproduced by the predictions of a modified semiclassical Kramers formula with an appropriate effective charge $Z_{\mathrm{eff}}$, which is larger than the effective charge which reproduces the energy levels of the states into which capture occurs. In accord with this modified Kramers formula, the numerically obtained total cross sections are shown to scale with $\frac{Z_{\mathrm{eff}}^2}{K}$ for each isoelectronic sequence, and with a parameter ${\left(n_0\right)}_{\mathrm{eff}}$ which characterizes each isoelectronic sequence. Using these scaling properties, simple analytic expressions are obtained for recombination rate coefficients, for the rate of electron kinetic-energy loss, and for the rate of radiated power loss, assuming a classical Maxwell-Boltzmann thermal distribution of continuum electrons.

Two-pulse photon echoes on the $2{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}-2\mathrm{}{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ transition in lithium vapor are generated using laser excitation pulses with angular separations of 0.70 and 1.40 mrad. The observed degradation of echo intensity with angling of the excitation pulses is in agreement with theory. The largest echoes radiated by the lithium sample contained ${10}^9$ photons; the smallest echoes detected contained only an average of 0.04 photons. This intensity range of greater than ${10}^{10}$ represents measurements made over more than 15 natural lifetimes of the $2{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ state despite the degradation due to angling. Modulation of the echo signal due to the hyperfine structure of the $2{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ state is also observed.

Natural radiative lifetimes in the $5s^2\mathrm{ns}{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ and $5s^2\mathrm{nd}{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2},\frac{5}{2}}^{}{}_{}{}^{}$ ($n\le 20$) sequences of indium have been measured using pulsed laser excitation of an atomic beam. The uv pulses were produced by a YAG-pumped, or alternatively, an excimer-pumped dye-laser system. While the $S$-state lifetimes show a normal ${\left(n^{*}\right)}^3$ behavior, the $D$ sequences are strongly perturbed. The lifetimes of the $5s5p^2{}_{}{}^4{}_{}{}^{}P$ states were found to be $J$ dependent.

Muonic x-ray spectra have been measured for ${\mathrm{N}}_2$, S${\mathrm{F}}_6$, and Ar at pressures up to 20 atm at room temperature and in the liquid or solid state, and for ${\mathrm{O}}_2$ at 20 atm and CO, NO, and a ${\mathrm{N}}_2$+${\mathrm{O}}_2$ mixture at 10 atm. Relative intensities of the higher members of the muonic Lyman series of N decrease monotonically with decreasing pressure (density). A similar effect is observed for F in S${\mathrm{F}}_6$, where some effect was also noted for the S x rays. A gas-pressure dependence in Ar was not observed in the pressure range covered. The density effect can be modeled approximately by a muonic-atom cascade code in which the $K$-electron refilling width is related to the gas density, which determines the frequency of collision of the atom with neighboring atoms or molecules. The difference in behavior between ${\mathrm{N}}_2$ or S${\mathrm{F}}_6$ and Ar at comparable pressures provides evidence for the "Coulomb explosion" that is expected to occur when a negative muon is captured by a polyatomic molecule.

A finite-dimensional-matrix technique valid for computation of complex eigenvalues and eigenfunctions useful for discussing time evolution in both dc and ac Stark fields is presented. The complex eigenvalue parameters are those of appropriately analytically continued, time-independent Stark Hamiltonians as obtained via the complex scale transformation $r\to r{e}^{i\theta }$. Such a transformation distorts the continuous spectrum away from the real axis, exposing the Stark resonances, and also allowing use of finite variational expansions employing $L^2$ basis functions chosen from a complete discrete basis. The structure of the dc and ac Stark Hamiltonians is discussed and extensive convergence studies performed in both the dc and ac cases to fully document the utility of the method. Sudden and adiabatic dc Stark time evolution is used to illustrate the power of finite-dimensional-matrix methods in describing complex, multiple-time-scale time evolution. The relationship between the ac Stark Hamiltonian used (a time-independent truncated Floquet Hamiltonian) and continued-fraction perturbation theory follows easily via use of matrix partitioning, and provides a particularly straightforward derivation of these results. Finally, some illustrative calculations of off-resonant generalized cross sections are given at low and high intensities, indicating that the method works satisfactorily at intensities the order of internal atomic field strengths. A more detailed discussion of time evolution in two-, three-, and four-photon ionization processes appears in the following paper by Holt, Raymer, and Reinhardt.

The two-level model of multiphoton ionization is reviewed within the context of an exact theoretical framework. Parametrization of the complex dressed states arising in a generalized Floquet analysis gives numerical values for the effective two-level parameters for two-, three-, and four-photon ionization of ground-state atomic hydrogen with the ($m_l=0\mathrm{}$) intermediate resonant states $2p$, $2s$, and $3p$, respectively. Detailed time dependences of the ionization process are given for responses to a linearly polarized, monochromatic, single-mode laser turned on suddenly with respect to near-resonant states, but adiabatically with respect to all others. Appropriate expressions for time-independent ionization rates are obtained during specific time intervals. The $K$ index ($K=\frac{\partial \ln N}{\partial \ln I}$), of interest in recent experiments, is understood within the framework of a simple model. Application to four-photon ionization of the metastable ${}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ state of hydrogen illustrates the breakdown of the two-level model, as the number of "near-resonant" levels is a function of the field strength.

Radiationless transitions filling vacancies in atomic $M_1$, $M_2$, and $M_3$ subshells have been calculated relativistically with Dirac-Hartree-Slater wave functions for ten elements with atomic numbers $67\le Z\le 95$. Results are compared with those of nonrelativistic calculations and experiment. Relativistic effects are found to be significant. Limitations of an independent-particle model for the calculation of Coster-Kronig rates are noted.

A study of the detailed structure of the bound odd-parity Rydberg states of barium has been undertaken using a cw dye laser in combination with an atomic beam. Special attention has been paid to the $6snf$ configurations, of which the hyperfine structure has been analyzed in terms of a small set of parameters. In addition to an effective Slater-exchange integral, an effective spin-orbit interaction, and a contact hyperfine parameter, a new parameter representing two-body magnetic effects, has been introduced. The introduction of this new parameter is discussed in some detail. Good agreement between the calculated and experimental hyperfine energies is achieved in this way.

Detection of argon dimers by means of Raman scattering is reported. This first observation of dimers by Raman scattering in a supersonic expansion provides a new technique for the study of the low-lying excitations of dimers and perhaps larger clusters, useful in determining interatomic potentials, etc. Spectra were recorded at low temperature and density in a supersonic expansion of pure argon. Both the pure rotational and the much weaker vibrational Raman transitions were observed for the lowest two vibrational states of the dimer. Raman transition frequencies were determined from the spectra. Theoretical spectra were generated with the use of the polarizability approximation. By using a classical point-dipole-induced dipole model in the calculation of the matrix elements and assuming a thermal distribution over the dimer levels, we could reproduce the rotational spectra to within experimental uncertainty.

Results of a systematic study of the formation of dimers in a supersonic free-jet expansion of argon as studied by Raman scattering are presented. By seeding the expansion with ${\mathrm{N}}_2$, measurements of temperature and density were obtained in the part of the flow field where dimers were observed. Temperature was also measured in the remaining part of the expansion showing large deviations from the behavior of an isentropic expansion due to condensation. The condensation was observed directly by Rayleigh scattering as well. From the Raman spectra it was shown that the dimers can relax their internal energy rapidly enough to come into thermal equilibrium with the translational degrees of freedom. By relating the intensity of dimer transitions to that of the simultaneously measured ${\mathrm{N}}_2$ $J=0\mathrm{}\to 2$ Raman transition, we were able to measure the concentration of dimers in the expansion. The measurements were compared to the predictions of equilibrium theory for a chemical equilibrium between dimers and monomers. The predictions of two- and three-body collision dimer-formation models were also tested.

Photoelectron spectra of atomic mercury have been taken using photon energies between 50 and 270 eV. The relative cross sections, subshell branching ratios, and angular distribution asymmetry parameters of the $4f$, $5p$, and $5d$ subshells are reported. In addition, the $4f$ asymmetry parameter was measured up to 600 eV. These quantities show dramatic effects accompanying Cooper minima in the $5d$ and $5p$ subshells and a large centrifugal barrier in the $4f\to \epsilon g$ channel. Comparisons are made with relativistic random-phase approximation and Dirac-Slater calculations. Intershell correlations appear responsible for features in the measured $4f$ asymmetry parameter at the $4d$ threshold and in the calculated $5d$ branching ratio at the $5p$ threshold.

A radio-frequency ion trap has been used to store ${\mathrm{Si}}^{2+}$ ions created by electron bombardment on Si${\mathrm{H}}_4$ or Si${\mathrm{F}}_4$. The lifetime of the metastable $3s3p{}_{}{}^3{}_{}{}^{}P_1^o{}_{}{}^{}$ level, measured by direct observation of the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$-${}_{}{}^3{}_{}{}^{}P_1^o{}_{}{}^{}$ decay at 189.2 nm, was 59.9±3.6 μs; $A=(1.67\mathrm{}\pm 0.10)\times {10}^4$ ${\mathrm{s}}^{-1\mathrm{}}$. The uncertainties indicate the 90%-confidence limit. Statistical uncertainty dominated. The measured value agrees with calculated values to within their quoted accuracies. Our result therefore confirms the calculated data which have been used heretofore in determinations of electron densities in astrophysical plasmas such as the solar transition zone.

The smallness of Be and its valence structure are attractive characteristics for the rigorous application and testing of the flexibility and utility of many-body theories. Recently, a number of results of many-electron calculations have been published on the $1s$ binding energy (BE) and the Auger width ($\Gamma$) of the hole state. They show considerable dispersion. We have studied these properties and the fluorescence yield (${\omega }_K$) of ${\mathrm{Be}}^{+} 1s2s^2{}_{}{}^2{}_{}{}^{}S$ by applying a general theory of autoionizing states which is based on projected function spaces and justifies the variational calculation of localized relativistic or nonrelativistic correlation and the subsequent inclusion of the continuum. Two computational methods have been employed: The first method (A) aims at the accurate calculation of the total energy of initial and final states. In the case of Be, its ground-state energy is known accurately. The excited-state energy is computed in this work variationally and includes the effect of the continuum. The resulting correlated square-integrable wave function ${\Psi }_0$ of the hole state is then employed for the calculation of the Auger width and the radiative transition probabilities to the lower discrete states $1s^{2}2p$ and $1s^{2}3p{}_{}{}^2{}_{}{}^{}P_{}^o{}_{}{}^{}$. We find that the angular correlation increases the decay rates whereas inclusion of radial and spin-polarization correlation eventually decreases them by a factor of 2 from the Hartree-Fock (HF) value. Nonorthonormality (NON) is taken into account explicitly; we show that radiative decay does not arise only from correlation effects. The second method (B) is based on the consistent analysis of electronic structure and aims at the calculation of only those one- and two-subshell correlations which contribute to the BE the most. The validity and generality of the second method—which has been applied before to a number of atoms in the periodic table—is demonstrated once again. Our results are, with method A, a BE of 123.732 eV, $\Gamma =0.023\mathrm{}$ eV, and ${\omega }_K=1.2\mathrm{}\times {10}^{-4\mathrm{}}$ and, with method B, a BE of 123.82 eV. The BE's include an empirical relativistic correction of 0.027 eV. An Auger-spectroscopy measurement has yielded a BE of 123.6±0.1 eV. Our value for ${\omega }_K$ is closer to the available experimental values from the solid state (≅3.3∼${10}^{-4\mathrm{}}$) than a previous many-electron calculation, by a factor of 5.

Unfocused linear polarized laser light is used to explore ionization mechanisms in the region near three-photon resonances in Xe. In Xe-Ar and Xe-Kr mixtures at elevated concentrations, processes involving dimer absorption of third-harmonic photons are shown to play an important role in determining ionization yields, and a method for using the observed ionization to measure vacuum ultraviolet absorption is described.

Simple but accurate expressions for the total cross sections and energy-absorption cross sections for inelastic scattering of x rays from atomic, molecular, and condensed matter are developed. The starting point is the relativistic impulse approximation for Compton scattering of x rays. This gives the inelastic-scattering cross-section differential with respect to energy and solid-angle interval. Integration over energy of this expression up to all the shells $K$, $L$, $M$,... for the orbitals gives a simple result in the "linear" approximation [R. Ribberfors and K.-F. Berggren, Phys. Rev. A 26, 3325 (1982)]. The result is a cross-section differential with respect to solid angle. Numerical results for Al, Ag, and Pb are in good agreement with available experimental values and with the Waller-Hartree theory. It is shown that a further integration of the differential cross section with respect to the solid angle results in a simple formula for calculating the total cross section for inelastic scattering of x rays. A comparison with integrated values of the incoherent scattering function (Waller-Hartree theory) is carried out. Calculations of the (electron) energy-absorption cross-section result in a compact formula. In this case also, we make comparisons with the double-differential cross section integrated twice and with the Walter-Hartree theory.

A crossed-ion-beam-laser apparatus has been used to measure the branching ratios for photodetachment of ${\mathrm{K}}^{-}$ and ${\mathrm{Rb}}^{-}$ ions to the lowest-lying ${}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$, ${}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$, and ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ states of the resulting neutral atoms as a function of photon energy between the thresholds for producing the excited-state atoms and up to 50 meV beyond. The branching ratios are determined by measuring the total neutral-atom production and the excited-state to ground-state decay radiations. Between thresholds, the results are in good agreement with the ${\mathrm{K}}^{-}$ results of Slater and the ${\mathrm{Rb}}^{-}$ results of Frey Above the ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ threshold, our ${\mathrm{K}}^{-}$ results quickly approach constant values and do not show the energy-dependent structure observed by Falk, Leep, and Geballe. The angular distributions of the ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ decay radiations have been measured and are found to agree in magnitude with calculated expectations and to be independent of energy over the range of observation. The polarization-based multichannel quantum-defect theory of Watanabe and Greene has been fitted to the ${\mathrm{K}}^{-}$ results of Slater and the ${\mathrm{Rb}}^{-}$ results of Frey Our measurements are in agreement with these calculations.

The gyromagnetic ratio of several states in ${\mathrm{I}}_2$ is studied with the technique of polarization rotation and level crossing in doubly resonant third-harmonic generation. The level-crossing curve has a linewidth of approximately the Doppler linewidth of the corresponding non-coherent process divided by the angular momentum quantum number. In the polarization-rotation work, a rotated angle 80° is observed with little depolarization. The ratio of the angle rotated to the magnetic field of some 20 resonances can be divided into two groups: large ($\frac{\Delta \theta }{\Delta H}\sim 10$°/kG) and small ($\frac{\Delta \theta }{\Delta H}<2\mathrm{}$°/kG). A theory based on the interference between the different molecules is presented to explain the experimental data. The observed differences in $\frac{\Delta \theta }{\Delta H}$ is interpreted in terms of the difference in the transition branch in the one- and two-quantum transition. The gyromagnetic ratio of the ground state as determined by this technique is approximately -6 and that of the two-quantum excited state is approximately -20.

The delayed or time-domain four-wave-mixing experiment is treated in the regime of intense near-resonant pulses. The interaction with the radiation during both pump and probe pulses is considered to all powers of the electric field amplitude. Analytical results are obtained for an effective four-level system. These include the dependence of the coherence amplitudes on the ratio of the pump-field intensities when there is a large vibrational discrepancy between ground and excited electronic states and a general solution for the unitary time development during the probe pulse. For the first time, delayed coherent anti-Stokes Raman scattering is detected from highly dilute (10-ppm) guest molecules. Illustrative examples are presented for the system of pentacene in benzoic acid at low temperature. Vibronic-free induction decay and the effect of field inhomogeneity across the beam profile are found to be essential for understanding the observed intensity and spectral distribution of the signal beam in the region of optimum pulse intensity.

We specialize the quantum-statistical theory of optical bistability developed in "Optical Bistability. II" to a low-$Q$ cavity. From a linearized Fokker-Planck equation derived in the positive $P$ representation, the steady-state correlation matrix and spectrum of fluctuations are calculated. Expressions which normally assume a positive-definite diffusion matrix are shown to be valid for nonpositive-definite diffusion. For absorptive bistability we find agreement with results derived previously by quite different methods. More generally we extend previously published results by including atomic and cavity detunings. We compare the transmitted spectrum for dispersive bistability with that for absorptive bistability, and photon antibunching in dispersive bistability is discussed.