The effect of level degeneracy on saturated absorption in a resonant medium is considered using a simple but realistic three-level system to model $J=1\mathrm{}\to J=0\mathrm{}$ atomic transition. Assuming homogeneous broadening and exact resonance, an analytic nonperturbative expression for the medium susceptibility is obtained and used to study propagation of an arbitrarily polarized optical field. Optical saturation affects considerably Zeeman-coherence-induced circular dichroism. The analysis may find application in high-resolution spectroscopy and other branches of nonlinear optics.

Recent computer simulation studies have shown that diffusion-limited particle-cluster aggregation leads to structures with a considerably smaller effective fractal dimensionality than particle-cluster aggregation via linear particle trajectories. Here it is shown that Brownian motion has a much smaller effect on the structure of aggregates formed as a result of cluster-cluster aggregation. In particle-cluster diffusion-limited aggregation, it is the particle trajectory which prevents the particles from penetrating and filling in the fractal cluster. In cluster-cluster aggregation, the clusters cannot penetrate each other by means of any trajectory so the particle trajectory is of much less importance.

All-electron configuration-interaction calculations for the species Li, ${\mathrm{Li}}^{+}$, and ${\mathrm{Li}}^{-}$ in the presence of a distant negative charge (of charge -1) have been performed and, from the energies, the ground-state static dipole polarizabilities have been determined. The results (in atomic units) for Li and ${\mathrm{Li}}^{+}$, 164 and 0.188, respectively, are in good agreement with earlier predictions based on other methods. For ${\mathrm{Li}}^{-}$ we find that electron correlation practically halves the value of the dipole polarizability, reducing it to 650; previous values have ranged from 800 to 1910. In addition, for purposes of comparison and as a prelude to future calculations on small lithium clusters, we have carried out a valence-electron calculation (using a pseudopotential for the two core electrons) for the neutral atom; the results indicate that for lithium species core-core and core-valence electron correlation does not significantly affect the polarizability.

Using a local-width resonant model, the cross sections for dissociative attachment of low-energy electrons to a rovibrationally excited ${\mathrm{H}}_2$ molecule in its ground electronic state are obtained. There are 294 such rovibrational levels. Only the contribution of the ${}_{}{}^2{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ resonant state of ${\mathrm{H}}_2^{-}$ to the attachment process is investigated. Assuming a Maxwellian distribution for electron energies, the dissociative attachment cross sections are converted into attachment rates for various rovibrational levels of ${\mathrm{H}}_2$. A significant enhancement of attachment rates occurs for endoergic reactions only, and the maximum possible rate for attachment to the ground electronic state of ${\mathrm{H}}_2$ is about ${10}^{-8\mathrm{}}$ ${\mathrm{cm}}^3$/sec. Using the same energy distribution for electrons, the average energy carried by the ${\mathrm{H}}^{-}$ ions is calculated for all possible rovibrational levels. More energetic ions are formed when the attachment process is exoergic, and even the most energetic ${\mathrm{H}}^{-}$ ions have energies less than 0.5 eV. Furthermore, the attachment rates and the average ion energy appear to depend roughly on the total internal energy and not on the exact fraction of internal energy in rotational or vibrational modes.

The expressions for atomic potentials obtained from Slater basis functions are presented. Angular and radial factors are separated, and short- and long-range terms are identified. Long-range terms are retained, and a simplified (but faithful) representation of the short-range terms is analyzed. The interactions between charge distributions placed on the same atom and both types of terms are also presented. Finally, the theoretical developments are tested on several atomic calculations and the advantages of this approach in order to calculate the electronic structure of large molecules are pointed out.

Emission cross sections have been measured for about 60 lines from the $4d^{9}5s5p$ inner-shell electron excited states and high-lying $4d^{10}\mathrm{nl}$ excited states formed by single-electron impact in the electron-energy region of 10-200 eV using a photon-counting technique. Those for the lines from the $4d^{9}5s5p$ states all show their maxima around 50 eV. Those for the lines from the $4d^{10}\mathrm{nl}$ states reach their maxima between 40 and 70 eV, and the shapes of the optical excitation functions are somewhat different for various $\mathrm{nl}$. The measured emission cross sections are of order of ${10}^{-19\mathrm{}}$-${10}^{-21\mathrm{}}$ ${\mathrm{cm}}^2$ in magnitude at 50 eV.

We have measured energy spectra of electrons resulting from collisions of 0.4-0.5-keV ${\mathrm{Ne}}^{+}$ with solid targets of Mg, Al, and Si. We found only two peaks, in the electron-energy range 20—30 eV, corresponding to the autoionization of the ${\mathrm{Ne}}^{**}$ $2p^4({}_{}{}^3{}_{}{}^{}P,{}_{}{}^1{}_{}{}^{}D)3\mathrm{}{s}^2$ states. Unlike the spectra from gasphase collisions, the peak with the ${}_{}{}^3{}_{}{}^{}P$ core is the most intense. We interpret our results with a model involving reflection and excitation of the projectile in its collision with the surface. The excitation mechanism is similar to that of gas-phase collisions; new effects appear due to the continuum of electronic states in the solid.

The energies of fluorine $K\alpha$ x-ray satellite and hypersatellite peaks appearing in spectra for solid alkali and alkaline-earth fluorides and for gaseous HF have been compared. The energies for the solid compounds were found to be systematically lower than those for the gas. Spectra excited in thick solid targets by 80-MeV Ar ions exhibit new series of peaks located in the energy region just above the $K\alpha$ hypersatellites. These peaks have been attributed to $K\beta$ hypersatellite transitions from levels having $n\ge 3$. Both the energy deviations and the presence of $K\beta$ hypersatellites indicate that electron transfer to $n\ge 3$ levels occurs in the solids prior to $K$ x-ray emission. A mechanism for the electron transfer process is proposed and support for this mechanism is provided by a simple classical model.

A field-dependent hydrogenic basis is used to obtain the evolution of the energy spectrum of atoms in strong (∼${10}^8$ G) and uniform magnetic fields. The basis allows results to be derived analytically. Numerical values for the first 13 excited states of hydrogen are found to be in very good agreement with much more elaborate calculations of Smith et al. and of Brandi. In addition, the possibility of having a remnant type of degeneracy in the presence of the magnetic field is investigated.

The forbidden $6S\to 7S$ magnetic dipole transition amplitude in cesium has been measured by laser spectroscopy of an atomic beam in crossed electric and weak magnetic fields. The $M1\mathrm{}$ amplitude was determined by observing the change in the transition rate caused by interference with a Stark-induced $E1\mathrm{}$ amplitude. The result for the nuclear-spin-independent amplitude is -42.10(80) × ${10}^{-6\mathrm{}}$ ${\mathrm{\mu }}_{\mathrm{B}}$, the result for the nuclear-spin-dependent amplitude is 7.59(55) × ${10}^{-6\mathrm{}}$ ${\mathrm{\mu }}_{\mathrm{B}}$. These values disagree with earlier measurements but they are in good agreement with theory. The experimental approach is well suited to measuring parity-violating neutral-current interactions.

The uv absorption spectrum of Ba vapor is studied, noting its dependence on both vapor density and the intensity of illumination. Wavelength positions of the weak absorption lines, which appear adjacent to the $6snp {}_{}{}^1{}_{}{}^{}P_1^o{}_{}{}^{}$ principal series for $n\gtrsim 35$, have been identified as the $6s^2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ to $6sns{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ and $6snd{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ even-parity transitions. Experimental evidence is presented to support the interpretation of these transitions as collision-induced phenomena.

The usual description of Rayleigh scattering (the component of elastic photon-atom scattering identified with scattering from bound electrons) separates the high-energy fixed-momentum-transfer limit (generally taken to be specified in terms of the atomic form factor) from additional contributions to the amplitude, known as anomalous scattering factors or anomalous dispersion corrections. We use explicit results from a full relativistic numerical calculation of Rayleigh scattering to emphasize that several common assumptions regarding these anomalous scattering factors, still mistakenly used although previously criticized, are not entirely appropriate: (1) The anomalous scattering factors should not be identified with the difference from form factor; (2) the imaginary forward scattering factor $f^{\prime \prime }$ is not determined solely from photoeffect at high energy ($\gtrsim 2m{c}^2$); (3) the imaginary forward amplitude includes bound-bound resonance contributions below the photoeffect threshold, which are needed to ensure that the real forward scattering factor obtained from $f^{\prime \prime }$ through a dispersion relation goes to a finite value as the threshold is approached from above; (4) the imaginary anomalous amplitudes do not have the angular dependence of the form factor, but rather a weaker angular dependence, with the consequence that the imaginary amplitude can be comparable in magnitude with the real amplitude at some nonforward angles; and (5) the ratio of parallel and perpendicular anomalous amplitudes is not simply $cos\theta$.

We have measured the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ $2^{3}P-3^{3}D$ (5875 Å) and $2^{1}P-3^{1}D$ (6678 Å) lines by Doppler-free intermodulated fluorescence spectroscopy, and also the spin-forbidden $2^3{P}_{1,2}-3^1{D}_2$ (5874 Å) and $2^1{P}_1-3^3{D}_2$ (6679 Å) lines as observed in Doppler-limited fluorescence spectra. The positive column of a low-pressure discharge was the source of the excited He atoms. The wave number of the tunable dye laser inducing the fluorescence was measured relative to an iodine-stabilized He-Ne laser by photographic Fabry-Perot interferometry. The results are $\sigma (2^3{P}_0-3^3{D}_1)=17013.762\mathrm{}08\left(9\right)\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, $\sigma (2^3{P}_1-3^3{D}_2)=17014.705\mathrm{}78\left(9\right)\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, $\sigma (2^3{P}_1-3^1{D}_2)=17018.123\mathrm{}8\left(4\right)\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, $\sigma (2^1{P}_1-3^3{D}_2)=14\mathrm{}966.65204\left(10\right)\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, and $\sigma (2^1{P}_1-3^1{D}_2)=14\mathrm{}970.06984\left(10\right)\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$. The $2^{3}P-3\mathrm{}{}_{}{}^3{}_{}{}^{}D$ results are compared with two other recent determinations. A value of 1325.4(2.0) MHz obtained for the $3^3{D}_1-3^3{D}_2$ interval by combination of our results with the accurately known $2^3{P}_0-2^3{P}_1$ interval is consistent with several previous measurements. The measurements of the spin-forbidden lines give a more accurate connection between the low triplet and singlet terms of this spectrum. We have reevaluated several term separations (directly from our measurements or by combining them with other recent results) for comparison with available calculations. The $2^{3}S-2^{3}P$ separation in combination with previous calculations gives an experimental value of -0.177 6(5) ${\mathrm{cm}}^{-1\mathrm{}}$ for the Lamb-shift contribution to this separation, as compared with Ermolaev's theoretical value of -0.173 ${\mathrm{cm}}^{-1\mathrm{}}$. Comparison of our value for the $2^{3}P-2^{1}P$ intersystem separation with theory indicates that the absolute value of the Lamb shift of $2^{1}P$ is probably less than 0.01 ${\mathrm{cm}}^{-1\mathrm{}}$, this result being supported by a similar comparison for our $2^{1}P-3^{1}D$ measurement. Our value of 102 200(3) MHz for the nonrelativistic $3^{3}D-3^{1}D$ separation, combined with a previous result for the corresponding separation in ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, yields experimental values for the mass-polarization contributions to the $3^{3}D-3^{1}D$ separations in ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$: The values are -243(18) and -322(24) MHz, respectively. We give new parametric values for the other ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ $1s3d$ interactions (three magnetic fine-structure interactions and the exchange energy) and for the singlet-triplet mixing coefficient.

The thermally averaged collision-broadened line shape is written in terms of a detuning-dependent broadening rate ${\gamma }_c\left(\Delta \right)$ which is evaluated numerically for van der Waals potentials using classical straight trajectories. The results are presented in terms of reduced variables that make it easy to calculate the line shape for any system with arbitrary van der Waals coefficient and temperature. The results show how the line shape makes a smooth transition from a Lorentzian profile in the impact region to the dramatically asymmetric far line wings. The transition zone is characterized by $\left|\Delta \right|T_d\sim 1$, where $\Delta$ is the frequency detuning from resonance and $T_d$ is a characteristic collision duration. The lowest-order correction to the Lorentzian line shape due to finite collision duration describes the dominant behavior for $\left|\Delta \right|T_d\sim 1$. The numerical results are compared with analytic approximations and recent experiments. Averaging over a thermal distribution of relative velocities is shown to alter the line-shape asymmetry substantially, improving agreement between theory and experiment. The temperature dependence of the overall line shape is presented and discussed.

The zeros in dipole and quadrupole matrix elements of photoeffect from the $n{s}_{\frac{1}{2}}$ subshells of uranium approach common positions as $n\to \infty$. This is an illustration of the more general feature that for sufficiently large $n_0$ photoeffect cross sections and angular distributions from $\mathrm{nJL}$ subshells, aside from the bound-state normalization factor which scales the cross section, are the same for all $n>\mathrm{}{n}_0$ ($J$, $L$ fixed) except for energies very close to threshold. This behavior can be expected for all subshells and all elements and for all multipole matrix elements.

Successive stages of a photoemission process are examined with regard to their influence on the spin correlation between the escaping electron and the residue. The process $hv+{\mathrm{K}}^{-}\to \mathrm{K}\left(4p{}_{}{}^2{}_{}{}^{}P\right)+e$ is studied but its treatment has general application. Unresolved fine structures in the residue's spectrum affect this correlation not only near the emission threshold but also by introducing interference beats with long wavelength along the escape trajectory. A coincidence experiment which observes spin polarization simultaneously with the polarized atomic fluorescence should display this interference pattern.

An investigation is made of dissipative system with spin-dependent interaction potential. A general solution of the Schrödinger equation is obtained and the special cases $\alpha t\gg 1$ and $\alpha t\ll 1$ are discussed in more detail. It is shown that at time $t\gg \frac{1}{\alpha }$ there are two stationary states, one with energy $V_0$ and another with energy $-V_0$. It is also shown that, for a potential independent of the $z$ component of the spin operator, the existence of friction causes the $z$ component of the spin density to go to zero and the $x$ component and the $y$ component to be periodic in space regardless of the initial conditions. The wave function of an electron injected into a crystal is calculated. The result shows that the wave function has two parts, one oscillating in time and another exponentially decaying in time.

We present a model calculation for two-photon autoionization of ${\mathrm{H}}_2$ to the $X{}_{}{}^1{}_{}{}^{}\Sigma _g^{}{}_{}{}^{}$ state of ${\mathrm{H}}_2^{+}$. The theory is based on a formulation that allows for strong-field effects. It is shown that, as a result of such effects, the autoionization profile will in general exhibit qualitatively new behavior at laser intensities needed for two-photon ionization. The magnitude of these effects depends significantly on the presence of resonance with intermediate states. The notion of autoionization width and $q$ parameter are generalized to include this new behavior. Detailed calculations are reported for intensity effects on the line profile, the role of intermediate resonances, and the separate contribution of the vibrational states of ${\mathrm{H}}_2^{+}$ as final states. The feasibility of observation with currently available sources is discussed.

The relative intensities of $K$-shell photoelectron satellites near their respective thresholds in Ne and Ar have been measured using synchrotron radiation. The Ne satellites were found to be 25-40% smaller than in the high-energy limit. The $2p\to 3s$ "conjugate shakeup" state of ${\mathrm{Ne}}^{+}$ was not observed, in contrast to predictions of many-body perturbation theory. The asymmetry parameter of the neon Auger group was found to be equal to zero at the $1s\to 3p$ resonance at 867 eV. This result may indicate that the $3p$ Rydberg electron is essentially decoupled from the core in the Auger decay process. In argon, a $K$-shell satellite was observed at 24.6(3) eV with 6% intensity relative to the main line, confirming a theoretical prediction by Dyall. Tentative evidence was obtained that this branching ratio increases with energy in the first 90 eV above threshold.

The effects of amplitude, phase, and frequency fluctuations in the exciting laser field on the intensity correlation of resonance fluorescence from a single two-level atom are investigated. Numerical results are presented for both weak and strong excitation with narrow-band and broadband laser fields having Lorentzian or Gaussian line shapes.