An exact method of solution to the time-dependent wave equation for a system interacting with a sinusoidal field, which formally treats time and the phase of the field on an equal footing, is used to discuss (1) the importance of averaging the properties of a system over the phase of the applied field and (2) the nature and behavior of the characteristic exponents derived from the Floquet solution (with particular emphasis on the frequency-sweep experiment). The results for the Zeeman tuning experiment are used to resolve recent discrepancies in the literature which relate to the validity of Shirley's important result for the two-level average induced transition probability involving the derivative of the characteristic exponents with respect to the Zeeman splitting parameter ${\omega }_0$. The explicit calculations included in this work are for the single-photon two-level problem. Important implications can be inferred from them with respect to both the importance of phase averaging and the usefulness of the characteristic exponents as a quantitative means of obtaining resonance frequency shifts and half-widths for multiphoton and multilevel problems.

Starting from quasiseparability of the mean-square radius of both electrons in the electron-hydrogen system, we calculate adiabatic potentials and coupling matrices for ${}_{}{}^1{}_{}{}^{}S$ states. From these data we obtain the lowest post-adiabatic potential which is energy dependent. This potential is used to compute the ground-state energy of ${\mathrm{H}}^{-}$ and the elastic scattering phase shift of $e-\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$. Results are excellent.

The nonrelativistic asymptotic behavior of the third Born amplitude is determined for electron capture from a hydrogenlike ion or atom by a bare ion incident with a very high velocity. It is assumed that the incident ion is scattered through only a narrow range of angles, of the order of the electron/proton mass ratio. The result for the asymptotic form of the amplitude differs from two previous results. However, for the asymptotic contibution of the amplitude to the forward cross section (i.e., to the cross section integrated over the narrow forward cone) I obtain the same result as obtained previously.

The $L{\gamma }_{2,3}(L_1{N}_{2,3}$) x-ray emission spectra from ${}_{50}{}^{}{}_{}{}^{}\mathrm{Sn}$, ${}_{52}{}^{}{}_{}{}^{}\mathrm{Te}$, and ${}_{53}{}^{}{}_{}{}^{}\mathrm{I}$, excited by direct electron bombardment, were measured with a double-crystal monochromator. The spectral profiles are similar to their $4p$ energy-level-region x-ray photoelectron spectra (XPS), with base widths of about 50 eV. The origin of these unusual line profiles is attributed to many-body effects in their final states which are comparable to their respective XPS final states.

A standard perturbation expansion in the atom-radiation-field interaction is used to calculate the two-photon excitation cross section for the $1s^{2}2s^{2}2p^4{}_{}{}^3{}_{}{}^{}P$ to $1s^{2}2s^{2}2p^3\left({}_{}{}^4{}_{}{}^{}S\right)3p{}_{}{}^3{}_{}{}^{}P$ transition in atomic oxygen. The lowest-order summation over bound and continuum intermediate states is handled by solving the equivalent inhomogeneous differential equation. Higher-order electron-correlation effects are also examined.

We demonstrate the possibility of one-photon emission processes for relativistic electrons moving in static periodic magnetic fields. The electrons are in Dirac-Bloch states. For particular magnetic-field arrays, we present the wavelength formula including harmonics which arise from "umklapp" processes. We also discuss the polarization states for the emitted radiation. The strength of the emitted radiation is related to the static magnetic field.

We follow in detail the spontaneous decay of fully excited samples of two and three resonant two-level atoms separated by distances much smaller than a wavelength. We include both the static dipole-dipole interaction and an in rinsic detuning (inhomogeneous broadening) of the atoms. We find that the Coulomb interaction may have both a decohering and a recohering effect. The decohering effect is seen in three atoms not equivalently placed. Here the Coulomb interaction diminishes super-radiance by subjecting the different atoms to different frequency shifts. The recohering effect is seen in all cases and consists in a protection of super-radiance against an inhomogeneous broadening far in excess of the inverse radiation time. Both effects have analogs in small many-atom samples studied in previous literature.

In noncoherent transfer, a photon undergoes multiple scattering with frequency changes, the frequency profile $\phi \left(0\mathrm{}\le \phi \le \Lambda \right)$ after each scattering is prescribed, the mean free path varies like ${\phi }^{-1\mathrm{}}$, and there is a small probability of destruction $\epsilon$. In contrast with the coherent (monochromatic) case, diffusive behavior is not obtained as $\epsilon \to 0$. The scaling law of the intensity of radiation can be obtained with a technique suggested by the renormalization-group approach to critical phenomena. The equation of transfer for "core" photons (say, $\Lambda \ge \phi >\frac{1}{2\Lambda }$) is solved in terms of "wing" photons ($\frac{\Lambda }{2}\ge \phi >0\mathrm{}$). The solution is substituted wherever core photons appear in the equation for the wing photons. A closed equation for wing photons is thus obtained. After rescaling of the variables (wave number and $\phi$) it resembles the original equation ($\phi$ again runs from 0 to $\Lambda$) but has a nonlocal scattering operator. The procedure is iterated and the successive equations are found to approach a fixed form with suitable choice of the rescaling factors. This choice fixes the scaling law. It depends only on the asymptotic behavior of the profile at large frequencies. Known results for the dependence of the "thermalization length" on $\epsilon$ are recovered.

Integral Compton-scattering cross sections of 662-keV $\gamma$ rays from $K$-shell electrons in Y, Zr, Mo, Ag, Cd, and Sn have been determined. The results, when compared with theory, suggest that the $K$-shell electrons in the elements under investigation behave as free electrons.

Relativistic, multipole, and screening effects on photoelectron angular distributions are examined using the numerical partial-wave single-electron-transition code previously applied to total cross sections. We present data on the development of relativistic and higher-multipole corrections to the nonrelativistic dipole approximation, showing that these effects are not well described by such simple factors as $1+4\beta cos\theta$ and in fact persist to threshold in high-$Z$ elements. We trace the disappearance of screening effects on the distribution with increasing energy as screening becomes simply a multiplicative normalization effect on the total cross section, and so discuss ways to parametrize angular-distribution data. Finally, we compare theory with existing experiments, including a comprehensive comparison with all experiments at 100-eV energies and above.

The lifetimes of sixteen levels of Kri belonging to the $4p^{5}5p$ and $4p^{5}6p$ configurations have been measured by the delayed-coincidence method. The results are compared with other experimental values and with theoretical calculations using $\mathrm{jK}$ coupling and using intermediate coupling. From cascade components, lifetime values for some levels belonging to the $4p^{5}4d$ configuration can be inferred.

Detailed dispersion curves of second-order coherent anti-Stokes Raman scattering (CARS) (${\omega }_4=3\mathrm{}{\omega }_1-2\mathrm{}{\omega }_2$) are reported for benzene with the laser frequency difference ${\omega }_1-{\omega }_2$ near the 992-${\mathrm{cm}}^{-1\mathrm{}}$ Raman line. The results are compared with the first-order CARS (${\omega }_3=2\mathrm{}{\omega }_1-{\omega }_2$) dispersion curves. Several experimental parameters were manipulated in order to distinguish between a direct six-wave mixing process, which depends on the fifth-order nonlinear susceptibility ${\chi }^{\mathrm{}\left(5\right)\mathrm{}}$ and a cascaded four-wave mixing process involving ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$ twice. The observed characteristic interference line shape, the dependence on laser power, and the concentration dependence of the effect indicate that the cascaded process dominates. Additional evidence for the cascaded mechanism is derived from second-order CARS experiments using three incident laser frequencies. It is shown theoretically that if simultaneous phase matching occurs for both first- and second-order CARS, then the electric-field amplitude of the cascaded four-wave mixing should dominate the direct six-wave mixing by a factor of the order of $\frac{1}{\lambda }$, where $l$ is the interaction length and $\lambda$ is the second-order anti-Stokes wavelength. The second-order CARS reported here is to be distinguished from a possible "overtone" coherent Raman process which would require the frequency separation of the two lasers to be twice the Raman fundamental.

The blackbody radiation between two parallel (distance $L$ apart) infinitely extended and perfectly conducting plates is studied. The volume-averaged temporal correlation functions of the electromagnetic field are presented in a form suitable for discussing the temporal coherence behavior for arbitrary time differences and arbitrary values of the product $\mathrm{LT}$ ($T$ being the temperature). The anisotropy of the geometric arrangement manifests itself in the components of the correlation functions parallel and perpendicular to the plates. For extremely small $\mathrm{LT}$, the component of the electric field correlations perpendicular to the plates exhibits the features of a two-dimensional radiation field whereas the component parallel to the plates exhibits the periodic motion of a single mode with decreasing amplitude. Computed curves of the degree of coherence, the phase angle, and the autocorrelation function are presented and compared with the coherence properties of the blackbody radiation in infinite isotropic space and in a cube.

Recently, the question of the origin of correlations in thermal light has again been debated. The alternative viewpoints suggest that (i) stimulated emission causes the correlations implied by Bose-Einstein statistics and exemplified by the Hanbury Brown-Twiss effect, or (ii) stimulated emission coherently amplifies any initial field, with no change in the nature of photon statistics, apart from the addition of, and interference with, spontaneous-emission noise. It is shown that two essentially different physical models have been considered previously, with many results being only approximate. For these models we obtain the evolution of the photon statistics by deriving exactly the generating function for the diagonal elements of the field density matrix and the quantum characteristic function. The source of Bose-Einstein correlations is seen to be merely the interference in the superposition of random independent fields from a chaotic source, spontaneous emission being one example. Extending the investigation to a nonlinear model, we show that, although there is no longer coherent amplification, it is still not correct to infer that this interaction, which produces the amplification, also leads to Bose-Einstein statistics.

The radiation due to the coherent excitation of the electric dipole moments of the atoms in a crystal has been studied. These dipole moments are induced by the electric field of a relativistic charged particle traveling through the crystal. In this context, coherent excitation refers to the correlation of the phases of the dipole moments which are induced by a single relativistic charged particle. The phases of dipole moments which are induced by different charged particles are, of course, uncorrelated. The electric field of the incident relativistic charged particle is analyzed into its frequency spectrum and the effect of each frequency component on the crystal is determined. Expressions for the fields far away from the crystal and the radiated energy are derived for transitions between bound states, for transitions from a bound state into the continuum, and for the case where the frequency components are much larger than the ionization potentials of the atoms divided by Planck's constant. It is shown that the generated coherent radiation is emitted in the Bragg directions. Moreover, the polar and azimuthal angular spreads, as well as the frequency width, divided by the frequency of radiation, are of the order $\frac{1}{\gamma }$, where $\gamma ={(1-{\beta }^2)}^{-\frac{1}{2}}$, $\beta =\frac{v}{c}$, $v$ being the velocity of the incident charged particle and $c$ being the velocity of light. A comparison is made with x-ray diffraction and it is shown that, for a small crystal, the radiated energy per incident charged particle is less than the radiated energy per incident photon by a factor approximately equal to $\frac{Q^2}{\hslash c}$, where $Q$ is the charge of the particle and $\hslash$ is Planck's constant divided by $2\pi$.

A mode-coupling approximation and a continued-fraction representation are used to calculate the memory kernels of the dynamical field and photon-number correlation functions near a single-mode laser's threshold. The resulting linewidths of field and intensity fluctuations versus pumping are in good agreement with Risken's numerical calculations as well as with empirical linewidth data. In addition details of the line shape are also reported. The deviations from a Lorentzian are appreciable in the proper threshold region.

The coupling mechanism of a C${\mathrm{O}}_2$ laser with a plasma has been investigated. The parametric decay instability, stimulated Brillouin backscattering, and the modulational instability were observed at theoretically predicted laser power thresholds. The modulational instability seems to be responsible for the generation of magnetic fields and fast ions.