$K\alpha$ x-ray satellites following $K$-electron capture in ${}_{}{}^{55}{}_{}{}^{}\mathrm{Fe}$ and electron impact on Mn have been measured with a high-resolution spectrometer. Ratios of double- to single-vacancy-production probability are found to be $P_{\mathrm{KL}}=(2.5\mathrm{}\pm 0.5)\times {10}^{-3\mathrm{}} \mathrm{and} (9.5\mathrm{}\pm 0.9)\times {10}^{-3\mathrm{}}$ for capture and impact, respectively. An evaluation of vacancy rearrangement in the $L$ shell before satellite emission has been carried out with the use of published level widths. It is found that in electron impact, as distinct from $K$ capture, essentially only satellites associated with a $2p$ spectator vacancy are observed. This observation is at variance with certain commonly used satellite assignments. Energies and intensities of the satellite transitions have been calculated in intermediate coupling and coordinations are proposed for the stronger lines.

The electron-impact excitation and dissociation cross sections for the $C{}_{}{}^1{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$, $c{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$, $B^{\prime }{{}_{}{}^1{}_{}{}^{}\Sigma _u^{}{}_{}{}^{}}^{+}$, and $E\left(F\right)\mathrm{}{{}_{}{}^1{}_{}{}^{}\Sigma _g^{}{}_{}{}^{}}^{+}$ states of ${\mathrm{H}}_2$ have been calculated within the distorted-wave approximation. The distorted waves are obtained as solutions of the static-exchange potential field of the ground electronic state. Both differential and integral inelastic cross sections are reported and compared with other calculated results and available experimental data.

Nonrelativistic many-body calculations of the fine structure of $\mathrm{nd}$ states of sodiumlike systems have been performed for $Z=11-42\mathrm{}$, taking into account the core polarization to first order in the spin-orbit coupling and to all orders in the Coulomb interaction. The results agree well with the experimental data available, and, in particular, the transition from inverted- to normal-level ordering appears at the right place, around $Z=15\mathrm{}$. The alternative approach of evaluating the fine structure by means of relativistic central-field calculations—introduced by Luc-Koenig—is analyzed in detail, using the Pauli approximation and a graphical form of perturbation theory. Provided the self-consistent Hartree-Fock potential is used for the core, it can be shown that the relativistic method is (to order ${\alpha }^2$) equivalent to a nonrelativistic calculation, where the core polarization is included to all orders of the Coulomb interaction. In the calculation of Luc-Koenig a local core potential is used, in which case this equivalence is only partial. In order to be able to make accurate comparisons with our many-body results, we have performed relativistic calculations using the full Hartree-Fock potential of the core.

The spontaneous radiative decay to the ground state of an atomic system initially in the higher of two excited states, coupled in a radiationless fashion by an external field, is investigated by the method of multiple-time-scale perturbation theory. The coupled differential equations of motion for the probability amplitudes are solved to second order, while the usual secular behavior of conventional time-dependent perturbation theory is eliminated in terms of two natural time scales: a fast time scale corresponding to the reciprocal of the level transition frequency and a slower time scale associated with the inverse of the radiation linewidth. Expressions are obtained to this order for the energy shifts and decay characteristics of the excited states and the energy distribution of the final-state photons, quantities previously determined by Fourier analysis and contour integration and by the phenomenological approach of Weisskopf and Wigner. A detailed comparison of these various methods of solution includes conditions under which the present results agree to second order with the previous calculations.

A new procedure is suggested to improve the convergence of the complex-rotation method. Calculations are carried out for the $\mathrm{He}2s2s{}_{}{}^1{}_{}{}^{}S$ and $2s2p{}_{}{}^1{}_{}{}^{}P$ resonances. With a relatively small and simple wave function, one obtains a width which is stable to six digits over a wide range of rotational angles and nonlinear parameters. The results are compared with those of the most accurate theoretical calculations and experiments. The feasibility of applying this method to more complicated systems as well as multichannel problems is also discussed.

Photoelectron branching ratios and angular distributions have been measured for the six outermost levels of S${\mathrm{F}}_6$ in the range $16\le h\nu \le 30$ eV with the use of synchrotron radiation. These results are discussed in the framework of the large variety of experimental and theoretical studies of S${\mathrm{F}}_6$ with the dual objective of resolving the long-standing problem of the ordering of the valence shells and of gaining some insight into the role of shape-resonant behavior in the low-energy photoionization continua of S${\mathrm{F}}_6$. These objectives are met with partial success in that we tentatively conclude the valence configuration $5a_{1g}^{2}4t_{1u}^{6}1t_{2g}^{6}3e_g^4(1\mathrm{}{t}_{2u}^6+5\mathrm{}{t}_{1u}^6)1\mathrm{}{t}_{1g}^6{}_{}{}^1{}_{}{}^{}A_{1g}^{}{}_{}{}^{}$ is most consistent with the available body of evidence and that it is plausible to invoke channel interaction near the strong resonant feature at $h\nu \sim 23-24$ eV to help account for some of the apparently contradictory evidence. Further experimental and theoretical work is suggested to clarify these issues.

Proton-impact excitation of fine-structure transitions in ${\mathrm{O}}^{3+}{}_{}{}^2{}_{}{}^{}P_{}^0{}_{}{}^{}$ ions is studied in a quasimolecular representation. The ${}_{}{}^2{}_{}{}^{}\Pi$ and ${}_{}{}^2{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$ states of the O${\mathrm{H}}^{4+}$ molecule formed by the approach of ${\mathrm{H}}^{+}$ and ${\mathrm{O}}^{3+}{}_{}{}^2{}_{}{}^{}P_{}^0{}_{}{}^{}$ are represented with self-consistent-field wave functions which include the effects of polarization. Accurate, close-coupled solutions of the nuclear scattering equations are obtained and used to assess the accuracy of some approximate scattering descriptions. The elastic approximation is found to overestimate the cross sections at all energies. The Coulomb-Born approximation is accurate at both high and low energies but greatly overstimates the cross sections at intermediate energies. A simple unitarity correction to the Coulomb-Born approximation reduces the errors substantially. For high partial waves, the Coulomb-Born approximation is satisfactory at all energies and cross sections for fine-structure excitation by proton impact can be calculated accurately and efficiently with the use of a combination of close-coupled and Coulomb-Born results. Cross sections accurate to within 25% can be obtained with very little computational effort by a combination of the elastic and Coulomb-Born approximations.

The close-coupled theory of atomic scattering in a radiation field can be used to calculate nonadiabatic effects on collision-broadened atomic line profiles. When the strength of the radiation field is not too large, reduced free-free dipole matrix elements, which are independent of the field strength and are analogous to the free-free Franck-Condon factors of line profile theory, can be defined in terms of the $S$-matrix elements for light-induced atomic scattering. The profile can then be calculated even when the molecular states are mixed by off-diagonal terms in the molecular Hamiltonian due to the breakdown of the Born-Oppenheimer approximation. Numerical close-coupled scattering calculations are used to calculate the profile for the asymptotically forbidden, collision-induced radiative transition $\mathrm{O}{}_{}{}^1{}_{}{}^{}S+\mathrm{Ar}\to \mathrm{O}{}_{}{}^1{}_{}{}^{}D+\mathrm{Ar}+h\nu$. The profile was calculated in two ways: (1) with the use of the normal Born-Oppenheimer approximation for the final states and (2) with the use of the new technique to treat the nonadiabatic mixing among the ${}_{}{}^1{}_{}{}^{}\Sigma$, ${}_{}{}^1{}_{}{}^{}\Pi$, and ${}_{}{}^1{}_{}{}^{}\Delta$ final states. The Coriolis interaction mixes the Hund's case-($a$) $\Lambda$ states asymptotically to give Hund's case-($e$) states. The central and red-wing parts of the profile which originate primarily from large internuclear separations are strongly affected by this mixing. The calculated profile which takes this mixing into account agrees well with the experimental profile but differs significantly from the Born-Oppenheimer profile. The differences are explained in terms of intensity borrowing and Hund's case-($e$) selection rules.

A microwave bridge has been used in conjunction with an ArF excimer laser to measure the coefficient $\alpha$ for two-photon ionization of Xe at 193 nm. The bridge permits the measurement of ${\nu }_m$, the collision frequency for momentum transfer, and the display of the temporal history of the absolute electron density. Although considerably larger than previous estimates, the value of $\alpha$ reported here (4×${10}^{-32\mathrm{}}$ ${\mathrm{cm}}^4$ ${\mathrm{W}}^{-1\mathrm{}}$) is in agreement with the recent theoretical calculations of McGuire.

Expressions for the incoherent-scattering function and the inelastic-scattering cross-section differential with respect to the solid angle for detection of scattered x rays from atomic, molecular, and condensed-matter targets are derived in the relativistic impulse approximation for Compton scattering. It is shown that the incoherent-scattering functions, defined as an integral over Compton profiles, can be computed easily by means of a "linear" approximation. Numerical results for Al, Fe, and Pb are compared with available experimental values and with the Waller-Hartree theory.

The x-ray absorption spectrum of neodymium exhibits discontinuities which are the results of multielectronic excitations in the $L$ atomic shells of the elements. The observed discontinuities were identified as being the results of $2s^{-1\mathrm{}}+2\mathrm{}{p}_{\frac{1}{2}}^{-1\mathrm{}}$, $2s^{-1\mathrm{}}+2\mathrm{}{p}_{\frac{3}{2}}^{-1\mathrm{}}$, $2p_{\frac{1}{2}}^{-1\mathrm{}}+2\mathrm{}{p}_{\frac{3}{2}}^{-1\mathrm{}}$, $2p_{\frac{1}{2}}^{-2\mathrm{}}$, and $2p_{\frac{3}{2}}^{-2\mathrm{}}$ double excitations. Two discontinuities which correspond in energy to the simultaneous creation of three electronic vacancies were noted. The measured energies and the results of relativistic Hartree-Fock-Slater calculations for double-vacancy excitations are in good agreement. The magnitude of these discontinuities is difficult to determine with reasonable certainty, but it is only a few percent of the discontinuity and the $L_3$ absorption edge of the element.

$m_J$ mixing in $4{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ and $4{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ potassium atoms as well as atomic multipole relaxation induced in K-K and K-Ar collisions were investigated by methods of atomic fluorescence spectroscopy. K vapor, pure or mixed with Ar, was placed in a kG magnetic field and irradiated with a single Zeeman component of 7665- or 7699-Å resonance radiation, causing the selective excitation of the ${}_{}{}^2{}_{}{}^{}P_{\frac{1}{2},-\frac{1}{2}}^{}{}_{}{}^{}$ or ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2},-\frac{3}{2}}^{}{}_{}{}^{}$ substate. Collisions of the excited atoms with ground-state K or Ar atoms caused $m_J$ mixing which was monitored by analysis of the resulting fluorescent spectrum with a scanning Fabry-Perot interferometer. Intensity measurements on the fluorescent Zeeman components in relation to ground-state atomic densities yielded the following multipole relaxation cross sections ${\Lambda }_J^{\mathrm{}\left(L\right)\mathrm{}}$: K-K (${10}^{-12\mathrm{}}$ ${\mathrm{cm}}^2$): ${\Lambda }_{\frac{1}{2}}^{\mathrm{}\left(1\right)\mathrm{}}=5.7\mathrm{}\pm 0.9$, ${\Lambda }_{\frac{3}{2}}^{\mathrm{}\left(1\right)\mathrm{}}=8.1\mathrm{}\pm 1.4$, ${\Lambda }_{\frac{3}{2}}^{\mathrm{}\left(2\right)\mathrm{}}=11.4\mathrm{}\pm 2.0$, ${\Lambda }_{\frac{3}{2}}^{\mathrm{}\left(3\right)\mathrm{}}=9.8\mathrm{}\pm 1.5$; K-Ar (${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$): ${\Lambda }_{\frac{1}{2}}^{\mathrm{}\left(1\right)\mathrm{}}=65\mathrm{}\pm 10$, ${\Lambda }_{\frac{3}{2}}^{\mathrm{}\left(1\right)\mathrm{}}=175\mathrm{}\pm 25$, ${\Lambda }_{\frac{3}{2}}^{\mathrm{}\left(2\right)\mathrm{}}=230\mathrm{}\pm 35$, ${\Lambda }_{\frac{3}{2}}^{\mathrm{}\left(3\right)\mathrm{}}=190\mathrm{}\pm 30$. The $Q_J(m\leftrightarrow m^{\prime })$ cross sections for $m_J$ mixing were derived from the ${\Lambda }_J^{\mathrm{}\left(L\right)\mathrm{}}$ as well as the cross sections for multipole decay ${\sigma }_J^{\mathrm{}\left(L\right)\mathrm{}}={\Lambda }_J^{\mathrm{}\left(L\right)\mathrm{}}+{\sigma }_J^{\mathrm{}\left(0\right)\mathrm{}}$. The experimental results are in good agreement with theoretical calculations.

Nonadiabatic contributions to the core polarization in calcium Rydberg states have been investigated experimentally by microwave spectroscopy of $F$ and $G$ states. Transitions $4snf{}_{}{}^1{}_{}{}^{}F_3^{}{}_{}{}^{}\to 4sng{}_{}{}^1{}_{}{}^{}G_4^{}{}_{}{}^{}$ have been measured for $n=23-25\mathrm{}$. The transition frequencies are in good agreement with calculations based on a dynamical model of the core interaction, but differ by approximately a factor of 2 from the usual adiabatic treatment. The dipole core polarizability of calcium (the polarizability of ${\mathrm{Ca}}^{+}$) is found to be ${\alpha }_1=87\mathrm{}\left(2\right)\mathrm{}$ (atomic units). The quantum defect for the $4sng{}_{}{}^1{}_{}{}^{}G_4^{}{}_{}{}^{}$ series is 0.0310(5). General formulas are presented for the quantum defects of the high-angular-momentum states.

By observing the decay in flight of laser-excited atoms in a fast atomic beam with energy between 60 and 150 keV, lifetimes of the $\mathrm{Li}2{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ and $\mathrm{Na}3{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ are measured to be (27.29±0.04) and (16.40±0.03) nsec, respectively (uncertainties are one standard deviation).

The problem of predissociation in a strong electromagnetic field is investigated in the context of a double-resonance scenario. A nonperturbative approach is followed. Numerical examples are given to show how the line shape is modified. The results are also discussed in connection with the possibility of a photocatalytic effect.

The theory of photon-number statistics in resonance fluorescence is treated, starting with the general formula for the emission probability of $n$ photons during a given time interval $T$. The results fully confirm formerly obtained results by Cook that were based on the theory of atomic motion in a traveling wave. General expressions for the factorial moments are derived and explicit results for the mean and the variance are given. It is explicitly shown that the distribution function tends to a Gaussian when $T$ becomes much larger than the natural lifetime of the excited atom. The speed of convergence towards the Gaussian is found to be typically slow, that is, the third normalized central moment (or the skewness) is proportional to $T^{-\frac{1}{2}}$. However, numerical results illustrate that the overall features of the distribution function are already well represented by a Gaussian when $T$ is larger than a few natural lifetimes only, at least if the intensity of the exciting field is not too small and its detuning is not too large.

The dipole autocorrelation function for spectral line broadening is treated in a quantum theory which rigorously satisfies the fluctuation-dissipation theorem on a microscopic level. The basic approximation in the theory is the binary-collision approximation. In the present paper, the two-body interaction is decomposed into one part which commutes with the internal coordinates and another part which does not. The theory, as developed, is appropriate for broadening mechanisms for which the noncommuting term may be treated within the framework of perturbation theory, while the commuting term is to be treated exactly. The theory gives, at long times, a result for the dipole autocorrelation function consistent with the well-known impact approximation. At short times, an autocorrelation function of Gaussian form, with renormalization of the initial-state occupancy is obtained. It is found that the qualitative features discussed above are unaltered in higher-order perturbation theory. The results are consistent with the requirement that all time derivatives of the autocorrelation function at $t=0\mathrm{}$ exist. This further satisfies the requirement that all moments of the line-shape function in the frequency domain exist, hence that the line-shape function decays "exponentially" sufficiently far in the wings.

Self-pulsing of a single-mode laser has been studied with the use of the inhomogeneously broadened 3.51-μm transition in xenon. Time-averaged intensity power spectra, average power output, and real-time observations of intensity fluctuations have been recorded for various detunings of the Fabry-Perot cavity. Two forms of self-pulsing have been observed, both of which can be explained in terms of the phase locking of several frequencies which simultaneously exist in the same spatial mode, made possible by the rapid variations of the index of refraction in the high-gain medium. One form of such mode splitting occurs in the wings of the atomic response due to the variations in the inhomogeneously broadened anomalous dispersion. The second form can occur anywhere in the tuning range of the laser as it is caused by distortions induced in the dispersion by the hole-burning effects of the oscillating mode. The pulsation frequency of this induced mode splitting varies with cavity tuning, shows a dip at the atomic line center, and may be absent for detuning of one or two homogeneous linewidths away from center. The instabilities have shown subharmonic bifurcations of the pulsation frequencies. Both high-$Q$ pulsation frequencies and broad bands of frequencies in the power spectra have been observed for various operating conditions.

A general calculation is presented for the transient coherent off-resonance response of the well-known three-level system coupled to oscillating fields through two allowed transitions. Exact closed-form results are obtained for field envelopes of constant pulse amplitude and for adiabatic variations. Arbitrary off-resonance parameters and coupling matrix elements apply with the restriction that nonsecular terms in the rotating frame can be neglected.

A model for optical bistability in a ring cavity which exhibits periodic self-oscillation and period-doubling bifurcations leading to aperiodic behavior—"optical turbulence"—is discussed. For two two-dimensional maps describing cavity dynamics in an adiabatic limit (Ikeda's model), period-doubling sequences are studied numerically and found to be consistent with Feigenbaum's conjecture of universality. In the dispersive limit unstable regions are mapped as a function of round-trip losses and cavity detuning. From analytic expressions for this parameter dependence minimum power requirements for self-oscillation are estimated. A new instability for absorptive systems in a detuned cavity is identified.