We present experimental results from high-resolution studies of the energy and angle distributions for the breakup products that arise from the dissociation of fast-moving ${}_{}{}^4{}_{}{}^{}\mathrm{He}$${\mathrm{H}}^{+}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$${\mathrm{H}}^{+}$ in thin carbon foils. These results are compared with calculations based on a model for the polarization "wakes" induced in foils by the passage of fast charged projectiles. We also describe measurements on the transmission of such fast molecular ions through thin foils and present results on the transmission probabilities, energy losses, and angular distributions of the transmitted ions. A mechanism is proposed to account for these observations on molecular-ion transmission. Related studies on the foil-induced dissociation of O${\mathrm{H}}^{+}$, O$\mathrm{H}_2^{}{}_{}{}^{+}$, C${\mathrm{H}}^{+}$, $\mathrm{H}_2^{}{}_{}{}^{+}$, and ${}_{}{}^3{}_{}{}^{}\mathrm{He}_2^{}{}_{}{}^{+}$ are also briefly reported.

$K$-shell x-ray—production measurements are reported for protons, deuterons, and alpha particles incident on thin foils of copper, niobium, silver, and antimony. In the velocity range of the experiments, which correspond to 100-600 keV/u, the energy of ionization was as large as 10% of the bombarding energy. The inferred dependence of the excitation process on the projectile mass, atomic number, and energy is compared with theoretical estimates of a low-velocity ionization threshold, the binding effect, and the Coulomb-deflection effect. Precision of measurement is not great enough to discern unambiguously the threshold effect but the binding and Coulomb-deflection effects are clearly distinguished.

We present a study of electron—molecular-ion collisions. The scattering equations are solved using an iterative approach to the Schwinger variational principle. These equations are formulated using the Coulomb Green's function to properly treat the long-range Coulomb tail of the molecular-ion potential. We apply this approach to electron—hydrogen-molecular-ion collisions in the static-exchange approximation. We obtain elastic differential cross sections, and also use the continuum states from these calculations to compute the photoionization cross section of the hydrogen molecule. The iterative method used here converged rapidly in all calculations performed.

The time delay, as defined via phase shifts, does not apply to atom-atom collisions because of the semiclassical nature of the system. In this limit the contribution of one partial wave to the cross section is negligible. Therefore, we analyze time delay for the scattering amplitude and show that some new phenomena may occur, which cannot be explained by the time delay for a single phase shift. The time delay, which is averaged over all scattering angles, shows structure corresponding to several delay mechanisms. We also show that the lifetime of a resonance state, formed in a collision, may be considerably shorter than expected from the theory of resonance scattering.

A detailed calculation of the dielectronic recombination (DR) rate coefficient is presented for the system ${\mathrm{Mo}}^{31+}+e^{-}$, in which the initial states of the ion are $i_1=1\mathrm{}{s}^{2}2s^{2}2p^{6}3s$, $i_2=1\mathrm{}{s}^{2}2s^{2}2p^{6}3p$, and $i_3=1\mathrm{}{s}^{2}2s^{2}2p^{6}3d$. All possible intermediate autoionizing states and their cascade decays are included. The necessary Auger and radiative transition probabilities are computed using nonrelativistic Hartree-Fock wave functions. Various angular-momentum-averaging schemes are examined, and a simple and general procedure applicable to all open- and closed-shell targets is developed. In this, the orbital and spin angular momenta of the Auger-active electron pair is held fixed while all other angular momenta are averaged. As expected, the main contribution to the DR rate comes from the excitation of $2p$ electrons (a $\Delta n\ne 0$ process). The overall DR rates for $i=i_2$ and $i=i_3$ are ∼30% less than the rate for $i=i_1$. The overall DR rate for $i=i_1$ is slightly greater, at 3 keV, than the rate for the ion ${\mathrm{Mo}}^{32+}$.

Energy-flux integrals for Sommerfeld's half-plane problem are computed in the asymptotic region. Interferences of the geometrical optics solution and of the diffracted field are shown to be finite and related to each other in an interesting way that might lead to a useful formulation of the optical theorem for infinitely extended obstacles.

The consequences of the assumption that, under prescribed experimental conditions, the ions emerge randomly excited from the foil are examined using the maximum entropy principle. For that purpose constraints are identified by examining the time-resolved intensity of the electromagnetic radiation emitted by the ions after the foil. This leads to the most likely level or multiplet population density matrix compatible with the experimental information. The main consequences of the foil excitation mechanisms are accounted for by incorporating the framework of atomic structure into our information-theoretical approach. In the case of transitions in individual Rydberg series it is shown that for large $n$ and a given $l$ the level population functions decrease as $n^{*-3\mathrm{}}$ and depend universally on the kinetic energy of the incoming beam. It is also shown that the identification of the radiation from the emerging ions in terms of one-electron states leads, according to the maximum entropy principle, to a unique factorized representation of the probability that an ion has a given configuration immediately after the foil. This representation is used for a derivation of the charge distribution which for heavy ions is shown to be approximately Gaussian or chi-squared in accordance with experiments. The passage of ${\mathrm{He}}^{+}$ ions through the foil is treated as an example of a consistency test based on the information-theoretical derivation of the charge distribution. Following Levine and co-workers a surprisal analysis of level population functions is suggested as a well-established alternative to detailed models of foil excitation which usually invoke perturbation theory and consequently often have an ill-defined range of validity.

Rotational spectra have been assigned for ${}_{}{}^{83}{}_{}{}^{}\mathrm{Kr}$${\mathrm{H}}^{35}$Cl, ${}_{}{}^{83}{}_{}{}^{}\mathrm{Kr}$${\mathrm{D}}^{35}$Cl, ${}_{}{}^{131}{}_{}{}^{}\mathrm{Xe}$${\mathrm{D}}^{35}$Cl, and ${}_{}{}^{132}{}_{}{}^{}\mathrm{Xe}$${\mathrm{D}}^{35}$Cl. Additional assignments are reported for ${}_{}{}^{131}{}_{}{}^{}\mathrm{Xe}$${\mathrm{H}}^{35}$Cl. The measured rare-gas nuclear quadrupole coupling constants ${\chi }^R$ are (in MHz): ${}_{}{}^{83}{}_{}{}^{}\mathrm{Kr}$${\mathrm{H}}^{35}$Cl, 5.20(10); ${}_{}{}^{83}{}_{}{}^{}\mathrm{Kr}$${\mathrm{D}}^{35}$Cl, 7.19(10); ${}_{}{}^{131}{}_{}{}^{}\mathrm{Xe}$${\mathrm{H}}^{35}$Cl, - 4.64(5); and ${}_{}{}^{131}{}_{}{}^{}\mathrm{Xe}$${\mathrm{D}}^{35}$Cl, - 5.89(20). We find that the electric field gradient along the $a$ inertial axis at the rare-gas nuclear site in ${}_{}{}^{83}{}_{}{}^{}\mathrm{Kr}$H(D)F, ${}_{}{}^{83}{}_{}{}^{}\mathrm{Kr}$H(D)${}_{}{}^{35}{}_{}{}^{}\mathrm{Cl}$, and ${}_{}{}^{83}{}_{}{}^{}\mathrm{Kr}$H${\mathrm{C}}^{14}$N, and in ${}_{}{}^{131}{}_{}{}^{}\mathrm{Xe}$H(D)${}_{}{}^{35}{}_{}{}^{}\mathrm{Cl}$ is directly proportional to the electric field gradient at that site calculated from the electric multipole moments of the partner hydrogen halide. The proportionality constants are, for ${}_{}{}^{83}{}_{}{}^{}\mathrm{Kr}$, 78.5 and, for ${}_{}{}^{131}{}_{}{}^{}\mathrm{Xe}$, 154, using values of 0.27 × ${10}^{-24\mathrm{}}$ ${\mathrm{cm}}^2$ and - 0.12 × ${10}^{-24\mathrm{}}$ ${\mathrm{cm}}^2$ for the nuclear quadrupole moments of ${}_{}{}^{83}{}_{}{}^{}\mathrm{Kr}$ and ${}_{}{}^{131}{}_{}{}^{}\mathrm{Xe}$, respectively. This direct proportionality is attributed to Sternheimer-type quadrupolar shielding of the rare-gas nucleus by the electrons in the rare-gas atom. Within the limits of uncertainty of this experiment of $\lesssim 0.003$ electron we find no evidence for charge transfer from the Kr atom. Although less complete, the ${}_{}{}^{131}{}_{}{}^{}\mathrm{Xe}$ data are also consistent with this result.

Two-step polarization-labeling spectroscopy of diatomic molecules is described. Formulas for relative transition intensities are derived, and their use in determining angular momenta of molecular states is discussed. The experimental apparatus and procedure used to identify twenty-four new ${}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$, ${}_{}{}^1{}_{}{}^{}\Pi _g^{}{}_{}{}^{}$, and ${}_{}{}^1{}_{}{}^{}\Delta _g^{}{}_{}{}^{}$ states in ${\mathrm{Na}}_2$ are described. The states are identified as low-lying members, $n=3\mathrm{} \mathrm{to} 14$, of several molecular Rydberg series, and the dependence of their properties on principal quantum numbers is shown. These results are extrapolated to yield constants for the ground state of $\mathrm{Na}_2^{}{}_{}{}^{+}$.

By using a characteristic Green's function for an exactly solvable Schrödinger equation with an approximation to the central potential of Hermann and Skillman, the cross section for nonresonant two- and three-photon ionization of Ne, Ar, Kr, and Xe were calculated in $\mathrm{jl}$ coupling. Expressions for cross sections in $\mathrm{jl}$ coupling are given. Comparison with the Ar two-photon cross section of Pindzola and Kelly, calculated using the many-body theory, the dipole-length approximation, and $\mathrm{LS}$ coupling shows a disagreement of as much as a factor of 2. The disagreement appears to arise from distortion introduced by shifting the Green's-function resonances to experimental values.

The energies and intensities of the $L\alpha$ satellite lines are calculated for elements ${}_{}{}^{40}{}_{}{}^{}\mathrm{Zr}$, ${}_{}{}^{45}{}_{}{}^{}\mathrm{Rh}$, and ${}_{}{}^{47}{}_{}{}^{}\mathrm{Ag}$. The cascade model used includes $L_1{L}_3{M}_{4,5}$ Coster-Kronig transitions followed by photon emission between the states of the $L_3{M}_{4,5}$ and $M_{4,5}^2$ hole configurations. The relativistic intermediate-coupling method is used for both steps in our model which includes relaxation with regard to the satellite energies. Theoretically constructed spectra are compared with recent experimental results, and good overall agreement with respect to both the energy and the intensity distribution is obtained. However, on a detailed level there are discrepancies between the experimental and theoretical shapes. These are mainly due to solid-state effects since the Coster-Kronig intensities are rather sensitive to changes in the energy of the ejected electron. The energies of satellite lines are also calculated for ${}_{}{}^{56}{}_{}{}^{}\mathrm{Ba}$ for which $L_1{L}_3{M}_{4,5}$ transitions are energetically forbidden. Comparison with experiments shows that for heavier elements the direct double ionization to states of the $L_3{M}_{4,5}$ configuration has also a significant effect on these satellite spectra.

The probability $P_{\mathrm{KK}}$ of double $K$-shell-vacancy production per $K$-shell internal conversion of the 192-keV $E4\mathrm{}$ transition in the decay of ${}_{}{}^{114m}{}_{}{}^{}\mathrm{In}$ has been determined by means of a hypersatellite $K{\alpha }^H$-x-ray—$K$-x-ray coincidence experiment using an intrinsic Ge and a NaI(Tl) detector, and by means of a direct measurement of the $K{\alpha }_1^H$- and $K{\alpha }_2^H$-x-ray components with a curved-crystal spectrometer. The results are in good agreement: $P_{\mathrm{KK}}=(10.8\mathrm{}\pm 0.9)\times {10}^{-5\mathrm{}}$ and $P_{\mathrm{KK}}=(9.6\mathrm{}\pm 0.8)\times {10}^{-5\mathrm{}}$, respectively. The average value is $P_{\mathrm{KK}}=(10.2\mathrm{}\pm 0.6)\times {10}^{-5\mathrm{}}$. For the intensity ratio of the $K{\alpha }_1^H$- and $K{\alpha }_2^H$-x-ray components we obtained 1.57±0.17, and for the energy shifts of the two components we obtained, respectively, 566.8±1.4 and 560.2±1.3 eV.

We report the observation of coherent bremsstrahlung in the range 1-25 keV from electrons incident at small angles to prominent crystal planes of thin silicon and gold crystals. We also find x radiation produced by electrons making transitions between bound quantized axial-channeling orbits in silicon and gold. We find no radiation above 1 keV from any bound planar-channeling states for either silicon or gold at electron energies up to 3.0 MeV.

We have detected coherence in a superposition of excited states by collecting photoelectrons. The superposition state is prepared by one laser pulse, and the photoelectrons are produced by a delayed laser pulse. We have described the experiment by the extension of a simple model and found the agreement with the data to be quite good.

Superradiance has been observed in the far infrared on a pure-rotational transition in optically pumped methyl fluoride. Observed behavior included single pulses, shot-to-shot fluctuation, dependence on the pump pulse length, preferential polarization, and longitudinally asymmetric emission (the onset of swept-gain superradiance). A numerical solution of the Maxwell-Bloch equations including degeneracy, Doppler broadening, and population and polarization source terms, and taking into account all the transitions which might possibly contribute, produces results which agree well with the observations. To do this, only a single free parameter is used; this is a factor of about 10 multiplying the expected initial tipping angle (which is of the order of $N^{\frac{-1\mathrm{}}{2}}$).

For the pair of ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ levels at 3868 and 26 558 ${\mathrm{cm}}^{-1\mathrm{}}$0, the upper-state population was measured as a function of the irradiance of a resonant exciting pulse of fixed duration. The observed damped Rabi flopping showed that the two-level system was partially coherently excited. The results were compared with the prediction of an exact solution of the time-dependent Schrödinger equation for two-level systems excited by a detuned rectangular pulse. The Schrödinger equation solution, after averaging over laser irradiance fluctuations, agrees well with the data.

A time-independent single-rate theory for multiphoton ionization processes is developed to cover cases with a partially coherent (finite-bandwidth) driving laser. We use the Ornstein-Uhlenbeck fluctuating-phase model to describe the driving field, which has therefore a non-Lorentzian spectrum, and the effective two-level model to represent the atomic system. We present analytic and numerical methods that permit discussion of the effects of non-Lorentzian band-shape laser light, and we give analytically the bandwidth dependence of the rate in the wings of the ionization curve. Our model contains a simple scaling relationship that permits the rate for $N$-photon-resonant ($N+1\mathrm{}$)-photon ionization to be obtained directly from the one-photon-resonant two-photon ionization rate. We treat explicitly the cases $N=1\mathrm{}$ and $N=2\mathrm{}$.

We present a theoretical model for the interaction of a beam of two-level atoms with a resonant laser beam. It is shown that the radiation force, while averaging to zero at resonance, produces a transverse spread of the atomic velocities. If radiative damping is ignored, this spread increases linearly with time and finally saturates towards a steady value. Although the spread has a quantum-mechanical origin, we show that it is possible, in the limit $\hslash k\to 0$, to describe the phenomenon in terms of differential equations of motion for the atomic translational variables, as in the classical case. In this model it is also possible to describe the effects of radiative damping, as well as other additional effects, which may occur in a real experiment. Finally a comparison of our results with experimental data, recently obtained on an Na atomic beam, has been made. Although an order-of-magnitude fit of the experimental data could be obtained, the weights of the different causes, reducing the spread, were found to be ambiguous and have been left partly open.

The presence of a laser field is found to alter significantly the shape of the angular distribution of ejected electrons in electron-atom ionizing collisions when photon exchanges occur. Laser electric fields parallel to the primary electron transferred momentum (${\overrightarrow{\mathrm{E}}}_L\parallel {\overrightarrow{\mathrm{K}}}_{\mathrm{if}}$) increase the number of secondary electrons ejected in the backward direction (with respect to ${\overrightarrow{\mathrm{K}}}_{\mathrm{if}}$). Laser electric fields perpendicular to ${\overrightarrow{\mathrm{K}}}_{\mathrm{if}}$ double the peaks present in the field-free angular distribution and rotate them symmetrically in opposite directions from the ${\overrightarrow{\mathrm{K}}}_{\mathrm{if}}$ axis towards the ${\overrightarrow{\mathrm{E}}}_L$ axis. Calculations are presented for ionization events accompanied by one-photon absorption in a coplanar asymmetric geometry.

A review of quasiprobability methods for transforming chemical and quantum-optical master equations into Fokker-Planck equations is presented. For cases where conventional representations lead to Fokker-Planck equations with non-positive-definite diffusion coefficients; e.g., sub-Poissonian statistics, a generalization of the representation involving an extension to the complex plane enables analytic results to be obtained for certain nonlinear chemical and optical processes. Alternatively, a different integration measure may be chosen which ensures a positive distribution and Fokker-Planck equation with positive-semidefinite diffusion coefficients. This enables stochastic differential equations to be defined. These methods are applied to two-photon absorption and dispersive bistability in quantum optics where nonclassical photon statistics arise and to two models of nonlinear chemical reactions where sub-Poissonian statistics occur.