The acceleration of trapped electrons in the relativistic plasma waves (wake fields) produced by specially shaped charged-particle beams is described by physical, analytic, and two-dimensional simulation models. The effects of competing instabilities, imperfect bunch shapes, transverse dynamics, and dephasing of trapped particles are considered.

A one-parameter generalization of the diffusion-limited-aggregation (DLA) model, originally suggested by Witten and Sander, is studied. On changing the parameter, the resulting aggregate geometry changes from a fractal DLA-like structure to a compact one. Along the way, geometrical structures bearing a striking resemblance to viscous fingers and a variety of aggregates found in nature are obtained.

The multiterm spherical-harmonic representation of the velocity distribution function of ‘‘reacting’’ charged-particle swarms in a gaseous medium is discussed from a general viewpoint, using spherical tensors throughout, in contrast to the traditional mixed spherical-Cartesian notation usually employed in analysis of the hydrodynamic regime. The resulting hierarchy of kinetic equations generated from the Boltzmann equation has a universal validity, applicable to all experimental arrangements, as do the associated transport and reaction-rate coefficients. The structure of these equations and the nature of the eigenvalue problem associated with them are discussed generally, independently of any numerical technique adopted for their solution, of which the moment method of Lin, Robson, and Mason [J. Chem. Phys. 71, 3483 (1979)] is just one possibility.

We have calculated charge-transfer cross sections for collisions of ground-state ${\mathrm{N}}^{2+}$ ions with atomic hydrogen for barycentric collision energies up to 5.4 keV/amu. The calculations were done using a combination of close-coupled and unitarized distorted-wave techniques after an expansion in ${\mathrm{NH}}^{2+}$ molecular states. In addition to the entrance channel, we included a single product channel dissociating to ${\mathrm{N}}^{+}$(2s2${\mathrm{p}}^3$${,}^3$${\mathrm{D}}^{\mathrm{o}}$)+${\mathrm{H}}^{+}$, both within the ${}_{}{}^3{}_{}{}^{}\mathrm{\Pi }$ symmetry. Our results are in good agreement with recent experimental measurements of state-to-state charge-transfer cross sections except at higher energies, where increasing population of the ${\mathrm{N}}^{+}$(2s2${\mathrm{p}}^3$${,}^3$${\mathrm{P}}^{\mathrm{o}}$) level was observed. The charge- transfer excitation process leading to the ${}_{}{}^3{}_{}{}^{}\mathrm{P}_{}^{\mathrm{o}}{}_{}{}^{}$ ${\mathrm{N}}^{+}$ state is not well described by the Landau-Zener approach.

A triple infinite sum of formulas expressed as an expansion in Legendre polynomials is generated by use of computer algebra to represent the potential from the midpoint of two Slater-type orbitals; the charge density that determines the potential is given as the product of the two orbitals. An example using 1s orbitals shows that only a few terms are needed to obtain four-figure accuracy. Exact formulas are obtained for multipole moments by means of a careful study of expanded formulas, allowing an ‘‘extrapolation to infinity.’’ This Löwdin alpha-function approach augmented by using a C matrix to characterize Slater-type orbitals can be readily generalized to all cases.

We calculate the binding energies of atoms and molecular chains in ${10}^{12}$ G magnetic fields using the Hartree-Fock method. For Z>2 (4) at 1×${10}^{12}$ (5×${10}^{12}$), the isolated atom is energetically favored over the molecular chain.

The critical potential parameter $T_c$=($Z_c$${)}^{1/2}$ expressed as a biquadratic function of the nodal and orbital quantum numbers is incorporated into two analytic eigenvalue formulas. The first uses an explicit modification of the Morse-potential eigenvalue formula. The second uses an analytic simplification of the zeroth-order approximation of Imbo, Pagnamenta, and Sukhatme. Both procedures are validated with large sets of eigenvalues obtained by numerical solutions of Schrödinger’s equation for three related short-range potentials whose shapes differ widely.

A recently developed impact-parameter method is applied to electron-impact dissociation processes involving the A${\mathrm{}}^1$Π state of HCl. Calculations were performed for initial vibrational levels of the X${\mathrm{}}^1$${\Sigma }^{+}$ state up to $v_i$=2 and for rotational temperatures to 1000 K. The cross sections increase by approximately 50% from $v_i$=0 to $v_i$=2. The dependence on rotational temperature is small except for an anomalous enhancement at 0 K that the theory predicts for Π states. Since the predicted cross sections are an order of magnitude larger than those for photodissociation, electron-impact dissociation processes will play an important role in lasers involving HCl.

Absolute cross sections for the emission of Balmer-α and Balmer-β radiation have been measured for H+Kr and H+Xe collisions. Measurements were made for H-atom energies from 2.5 to 0.04 keV. The polarizations of the emitted radiations were also determined and, for H-atom energies above 0.2 keV, the contributions to these emissions from decay of the long-lived 3s and 4s excited states of hydrogen were resolved. The results are discussed in comparison with similar data for H-atom impact on the other rare-gas atoms.

Experiments are described which show that the fraction of electrons from high Rydberg states which contaminate the traditionally measured convoy-electron spectrum for fast oxygen ions emerging from thin carbon foils is small (<3%). Field ionization of the high Rydberg states is also found to be approximately independent of the direction of the field, although quantum beats indicate coherent Rydberg-state excitation.

Auger-electron production in collisions of slow ${\mathrm{Al}}^{+}$, ${\mathrm{Si}}^{+}$, ${\mathrm{P}}^{+}$, ${\mathrm{S}}^{+}$, ${\mathrm{Cl}}^{+}$, and ${\mathrm{Ar}}^{+}$ ions incident on Ar and ${\mathrm{CH}}_4$ targets has been investigated. Total cross sections for projectile L-shell, Ar L-shell, and C K-shell Auger-electron production have been determined experimentally. For a number of cases, vacancy-production cross sections have been deduced by combining the present data with the results of previous x-ray measurements. The latter cross sections are found to be consistent with the predictions of the molecular-orbital model of atomic collisions.

Conspicuous effects from a weak post-collision interaction have been identified in triply differential cross sections for the ionization of helium by fast electrons at asymmetric kinematics. A classical correction to an accurate first Born approximation is in good agreement with experimental data, showing the important influence of correlation after the collision.

The photoelectron (PE) angular distribution for the resonant two-photon autoionization of ${\mathrm{H}}_2$ through the lowest autoionizing state of ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{}{}_{}{}^{}$(1${\mathrm{\sigma }}_{\mathrm{u}}^2$) symmetry has been studied. It is found that at low laser intensities the spontaneous decay of the intermediate resonant state (different vibrational levels of the $B^1$${\Sigma }_u$ state) can modify the PE angular distribution significantly, whereas at higher intensities, this effect is washed out by the other intensity-dependent competing channels.

A Fabry-Perot interferometer with a hybrid Stark structure has been employed to measure the frequencies of some rotational transitions of ${\mathrm{CH}}_3$F and ${\mathrm{CH}}_3$OH in the ground vibrational state. The measurements are performed at fixed source frequency by sweeping the Stark field, and the zero-field frequencies are obtained by extrapolation of many different components. The results are ν(K=1)=153 207 755.95(0.83) kHz and ν(K=2)=153 199 847.83(0.40) kHz for the J=3←2 lines of ${\mathrm{CH}}_3$F and ν=76 509 651.3(3.3) kHz for the (5,0)←(4,1) $E_1$ transition of ${\mathrm{CH}}_3$OH.

Photoelectron angular distribution asymmetry parameters for photoionization to each of the three term levels of the ${\mathrm{Cl}}^{+}$ ion are calculated above the ${}_{}{}^1{}_{}{}^{}\mathrm{S}$ ionic threshold with use of the open-shell transition-matrix method. Comparison is made with frozen-core Hartree-Fock asymmetry parameters and with the multiconfiguration Hartree-Fock results of Fielder and Armstrong. The calculated asymmetry parameters are used to estimate partial-cross-section branching ratios at 584 Å from the relative experimental photoelec- tron intensity measurements of Kimura, Yamazaki, and Achiba.

The spectrum of ${\mathrm{Xe}}^{3+}$ has been observed in the 570–6900-Å range. The previous analysis has been revised and extended. All levels of the ground configuration (5$s^2$5$p^3$) and of the 5s5$p^4$ configuration are now established.

The hyperfine structure (hfs) of the 5d ${\mathrm{}}^2$$D_{5/2}$ ${}_{}{}^{135}{}_{}{}^{}$,137Ba ions has been measured by collinear fast-beam laser-rf double-resonance spectroscopy, completing the high-precision hfs data for the metastable ${}_{}{}^2{}_{}{}^{}\mathrm{D}_{3/2}^{}{}_{}{}^{}$,5/2 doublet. hfs constants, corrected for second-order hfs perturbation, are deduced and compared with the results of many-body perturbation theory. Nuclear quadrupole moments are extracted.

We calculate from the quantum regression theorem the entire photon-counting statistics for the fluorescence from a laser-driven two-level system weakly coupled to a metastable third level, and compare the result with the statistics of a dichotomic Markov process. The comparison shows, that at least in the limit of an infinite intensity of the laser in a single experiment the sequence of photon counts should display randomly alternating periods with no counts and a nonzero counting rate as if the atom executed ‘‘quantum jumps’’ to and from the metastable state.

Dehmelt’s proposal for an ultimate laser-frequency standard based on a single trapped ion is examined. Density-matrix calculations are developed for a double-resonance scheme which, under favorable circumstances, amplifies a highly forbidden and narrow electronic transition. The advantages of a pulsed excitation scheme are discussed, and the limitations of cw excitation are exposed.

A quantum-statistical theory is developed for a single-atom, three-state quantum system where a strong (1-3) and a weak (2-3) transition are driven resonantly by an incoherent field. From a second-order correlation function of the fluorescence intensity, it is concluded that a quantum jump can occur, in the sense that the single atom can undergo large fluctuations between a state of full emission in the strong transition to a state of no emission when the electron is shelved in the metastable state (2).