Differential cross sections for five transitions [$1{}_{}{}^1{}_{}{}^{}S\to n{}_{}{}^1{}_{}{}^{}S \mathrm{}(n=2,3,4\mathrm{})\mathrm{}$] and [$2{}_{}{}^1{}_{}{}^{}S\to n{}_{}{}^1{}_{}{}^{}S\mathrm{}(n=3,4\mathrm{})\mathrm{}$] of helium by positron impact are calculated in the framework of the two-potential modified Born approximation. The energy range studied is between 50 and 500 eV. The computed results are compared with the plane-wave results and the other available theoretical calculations.

An attempt is made to show that the collision matrix defining electron-spin-half-target collisions including spin-orbit interaction can be extracted by making eighteen experimental measurements at the same energy and scattering angle. In addition two simple experimental measurements are suggested which can be readily undertaken.

We have calculated the Compton cross section for scattering of circularly polarized light [$m{c}^2{\left(Z\alpha \right)}^2\ll \hslash \omega <m{c}^2$] from a bound atomic polarized electron. In this analysis the differential cross section includes corrections of order $\frac{\hslash \omega }{m{c}^2}$ and $\frac{p}{\mathrm{mc}}$, where $p$ is the electron momentum. This gives expressions for the cross section which require additional profile functions beyond the usual $J\left(p_z^{\prime }\right)$. The calculation is performed by the expansion of the quantum electrodynamic Hamiltonian to the appropriate order by means of a generalized Foldy-Wouthuysen transformation. In general, the profile functions are no longer a function only of the electron momentum component $p_z^{\prime }$ in the direction of the momentum transfer, but now they also depend on the scattering angle $\theta$. This latter dependence varies with the magnetic quantum number. We discuss the case of electron polarization perpendicular to the plane of scattering and show that for this case a single simple profile function suffices.

The lifetimes of the $2s3p{}_{}{}^3{}_{}{}^{}P_{0,1,2}^o{}_{}{}^{}$ levels in Ne VII have been measured by the observation of transitions to the $2s3s{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ level with the use of the beam-foil excitation method. The results are $\tau \left({}_{}{}^3{}_{}{}^{}P_J^o{}_{}{}^{}\right)=1.7\mathrm{}\left(1\right),1.0\mathrm{}\left(1\right), \mathrm{and} 1.9\left(1\right)\mathrm{}$ nsec for the $J=0,1, \mathrm{and} 2$ levels, respectively. The smaller value for $J=1\mathrm{}$ is due to a $J$-allowed decay channel to $2s^2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$, and implies a transition probability of 4.3(6) × ${10}^8$ ${\sec }^{-1\mathrm{}}$ for this intercombination line.

Recently Rich has pointed out that annihilation terms in the effective 4 × 4 Hamiltonian $H$ for $n=1\mathrm{}$ positronium cause the real parts of the Zeeman eigenvalues to be shifted by terms of order ${\left(\frac{{\lambda }_s}{4\pi }\Delta v\right)}^2\approx {10}^{-5\mathrm{}}$ relative to the Breit-Rabi eigenvalues. Here ${\lambda }_s$ is the annihilation rate of the singlet state and $\Delta v$ is the hyperfine interval. Rich observes that the $\Delta v$ measurements have not correctly dealt with decay. The Zeeman-resonance line shape is calculated here assuming that the non-Hermitian $H$ describes the motion of the four $n=1\mathrm{}$ levels via Schrödinger's equation. The deviations of this line shape from a Lorentzian are exhibited. The asymmetry of the line causes a shift in the line center relative to what one would obtain from a Breit-Rabi plus Lorentzian fit to a measured Zeeman-resonance curve. To take this into account, the measurement of $\Delta v$ by A. P. Mills, Jr. and G. H. Beaman [Phys. Rev. Lett. 34, 246 (1975)] should be increased by 2.5 ppm to $\Delta v$ (Mills and Beaman)=203.3875(16) GHz. When the Egan et al. measurement [P. O. Egan, V. W. Hughes, and M. H. Yam, Phys. Rev. A 15, 251 (1971)], which used a different line shape, is reinterpreted in terms of the line shape calculated here, the Egan et al. $\Delta v$ value increases by 21 ppm to $\Delta v(\mathrm{Egan} \mathrm{et} \mathrm{al}.)=203.3890\mathrm{}\left(12\right)\mathrm{}$ GHz. The weighted mean of the two corrected measurements is $\Delta v=203.3885\mathrm{}\left(10\right)\mathrm{}$ GHz.

This paper presents a global ab initio approach, called the electronic ab initio quantum-defect theory (EAQDT), to molecular photoionization spectrum calculations. This method first obtains the ab initio electronic parameters by the hereafter developed electronic iterative-variational eigenchannel approach (EIVEA). Then these electronic parameters are used in the calculation of the final state and the corresponding photoionization cross section by the multichannel quantum-defect theory (MQDT) [Jungen and Atabek, J. Chem. Phys. 66, 5584 (1977)]. In EIVEA, an elaborate $N$-electron correlated final-state wave function is introduced. This wave function allows us to take into account the ionic-core relaxation, many ionic cores and electronic autoionizing interactions. In calculating the transition probability we also use an electron-correlated initial state. Compared with the standard MQDT, the EAQDT is free from the use of semiempirical parameters and therefore has a wider applicability. This method is applied, as a test, to the low-resolution photoionization spectrum of ${\mathrm{H}}_2$. In the energy range between threshold and 23 eV studied here, where electronic autoionization does not take place, we obtain a theoretical cross section which bears comparison with the experimental one above 17.5 eV.

Various form-factor theories used to predict Rayleigh-scattering cross sections of gamma-ray photons are examined. For energies above the $K$ threshold comparisons are made with more accurate numerical calculations, for a high-$Z$ element (Pb), primarily at small momentum transfers [up to $x\equiv {\lambda }^{-1\mathrm{}}sin\left(\frac{\theta }{2}\right)=10\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$, where $\lambda$ is the photon wave-length] but also for larger momentum transfers. Nonrelativistic form-factor predictions generally are in good agreement with the numerically obtained theoretical values, in contrast to poorer predictions obtained with relativistic form factors. However, we also observe that a modified relativistic form-factor theory predicts the theoretical Rayleigh-scattering amplitudes still more accurately, to higher momentum transfers. Comparison with available experiments for Pb at energies from 145 to 1408 keV and momentum transfers $x\le 10$ ${\mathrm{\AA }}^{-1\mathrm{}}$ indicates no systematic pattern of discrepancy between theory and the significant scatter among different experimental results.

An improved scheme is presented for calculating multiconfiguration self-consistent-field wave functions of electronic systems for which the symmetry group is simply reducible. Our formulation is based on expansion of the orbitals in a basis set, but is otherwise entirely general. The MCSCF equations are derived from a multistate variation principle. In the algebraic development extensive use is made of shell and term replacement operators, permitting a transparent formal development in which symmetry properties are fully exploited. The resulting scheme is manifestly quadratically convergent in the general case. Sufficient detail is presented to provide the basis for efficient computer implementation.

The time-dependent theory of Courtens and Szöke is generalized using the approach of Burnett et al. to derive time-dependent spectral intensities of resonance fluorescence from atoms driven by a pulsed laser in the presence of collisions. These results are valid both for laser detunings inside and outside the usual impact region of the spectrum, including Zeeman degeneracy effects. We apply this theory to a simple but important example ($J=0\mathrm{}$ to $J=1\mathrm{}$) to obtain quantitative predictions for the observable scattered-light spectrum which can be directly compared with recent experiments.

The variable-charge Coulomb-projected Born approximation proposed by Schaub-Shaver and Stauffer is used to analyze the electron-impact excitation of the $2{}_{}{}^1{}_{}{}^{}S$ state of helium. Differential and integrated cross sections for the transition are calculated and compared with the other available theoretical calculations and experimental measurements.

We present a fully-quantum-mechanical theory of the intracavity interaction of coherent light with semiconductors. Interaction is assumed to occur via excitons. Using a master-equation approach we include such effects as exciton-lattice and exciton-exciton interactions. In the two cases of high and low exciton densities, steady-state analysis reveals bistability and hysteresis in the system. Bistability of a dispersive and absorptive nature in both exciton number and output intensity, dependent on input intensity is found. The bistability displayed in the high-density case agrees qualitatively with the experimental curves obtained by Gibbs et al. for GaAs. As yet the low-density bistability has not been experimentally observed.

A study of the photoionization of calcium in the relativistic random-phase approximation is reported. Predictions of photoionization cross sections, angular distribution asymmetry parameters, and spin-polarization parameters for the $4s$, $3p$, and $3s$ subshells are made with emphasis on the energy region above the $3p_{\frac{3}{2}}$ threshold where multiconfigurational effects are not expected to be very important. Autoionization resonances below the $3s$ threshold and between the $3p_{\frac{3}{2}}$ and $3p_{\frac{1}{2}}$ thresholds are analyzed using the relativistic multichannel quantum-defect theory.

The zero-core-contribution model is extended to calculate absolute photodetachment cross sections taking into account the fine-structure levels and higher electronic states of the anions and neutral atoms. Comparisons are made with experimental data involving 20 different anions with $p$ outermost occupied orbitals. Very good agreement is obtained.

A model is presented for the dynamical evolution of superfluorescence from an optically pumped three-level system. The full propagation, transverse, and diffraction effects are taken into account. With the use of a previously developed algorithm, a computational simulation was constructed from this model and results are presented and discussed. In particular, it is shown that the injected coherent pump-pulse initial characteristics, such as on-axis area, temporal and radial width and shape, can have significant deterministic effects on the superfluorescent pulse delay time, peak intensity, temporal width, and shape. Thus, by specifying certain initial properties of the injected pump pulse, the superfluorescent pulse can be shaped and altered. The results predict the conditions under which an injected light pulse of a given frequency can be used to generate, shape, and control a second light pulse of a different frequency via a nonlinear medium, thus demonstrating a new aspect of the phenomenon of light control by light.

We examine the coherence properties and photon statistics of stationary light obtained by the superposition of nonstationary emissions occurring at random times, in accordance with a homogeneous Poisson point process. The individual emissions are assumed to be in a coherent, chaotic, or $n$ state. The statistical nature of the emission times results in fluctuations of the relative contributions of different emissions at a given time. This is manifested by an additional positive term, exhibiting particlelike properties, in the normalized second-order correlation function. Thus, the photon-counting variance is increased. For coherent emissions, interference between the randomly delayed emissions produces additional wavelike noise. In the limit when the emissions overlap strongly, the field exhibits the correlation properties of chaotic light, regardless of the statistics of the individual emissions. In the opposite limit, when emissions seldom overlap, the light intensity is describable by a shot-noise stochastic process, and the detected photocounts show an enhanced particlelike noise, which has its largest value when the counting time is long. In that limit, the photocounts obey the Neyman type-$A$ and generalized Polya-Aeppli distributions, when the individual emissions are coherent and chaotic, respectively. When the individual emissions correspond to the $n$ state, the Poisson emission times result in bunching which reduces or eliminates the inherent antibunching associated with the $n$ state.

We derive, solve, and analyze the linearized master equation and evaluate the spectrum for absorptive optical bistability in the high-$Q$ cavity when the incident laser has jitter or frequency fluctuation. The fluctuations are treated as a time-dependent Gaussian process whose properties are determined by the individual laser's characteristics. With our results we can explain the qualitative results of machine simulations and provide criteria for the magnitude of fluctuations in optical bistability in terms of laser and cavity parameters.

The equations of motion for an inhomogeneously broadened laser operating off resonance in the neighborhood of threshold are solved. It is shown that the effects of detuning cannot be described just by a frequency-dependent laser pump parameter, but that the laser characteristics are modified in other ways also. The relative intensity fluctuations and the correlation time of the laser are calculated as a function of mean intensity and frequency, and it is shown that both are affected by detuning. These theoretical conclusions are then confirmed quantitatively by direct photoelectric counting and two-time correlation measurements of a He:Ne laser.

The relationship between the squeezing and photon-number fluctuations in the output of a degenerate parametric oscillator is investigated. The addition of a second driving field at the idler frequency allows the direction of the squeezing to be changed. The squeezing may appear in the amplified quadrature. Photon antibunching or bunching may occur depending on whether the quadrature carrying the coherent excitation is squeezed.

The results of measurements of energy losses of 35-, 100-, and 250-GeV particles channeled through a 2-cm Ge crystal are reported. The energy losses are correlated with the incoming and outgoing particle angles, relative to the channel axis, and the results are compared with existing theories.

The Rayleigh number for convective instability of a horizontal layer of fluid to two-dimensional disturbances depends on the wavelength of the disturbance. In a finite rectangular domain with stress-free boundaries, there are critical lengths at which instability to two different sets of rolls occurs simultaneously. This paper gives a nonlinear analysis of this multiple-bifurcation problem. We present a complete characterization of the transitions which occur for lengths near critical. For small values of the Prandtl number the transition between the two sets of rolls occurs via a new type of solution which is represented by the superposition of the two sets of rolls with comparable amplitude. For higher Prandtl numbers the transition is an abrupt one, and is accompanied by hysteresis.