We introduce a new and extremely simple model for coagulation in which the reaction kernel $K_{\mathrm{ij}}$ in the Smoluchowski equation corresponding to the model can be adjusted exactly. For the special case of a constant $K_{\mathrm{ij}}$, we deduce that for spatial dimension $d>\mathrm{}{d}_c=2\mathrm{}$, the exact solution of the Smoluchowski equation is valid (mean-field theory). For $d<\mathrm{}{d}_c$, fluctuations give rise to dimension-dependent kinetic exponents and a novel nonmonotonic cluster size distribution.

Thermal measurements probe time dependence in a convecting helium layer with cylindrical geometry and aspect ratios $\Gamma \equiv \frac{\mathrm{radius}}{\mathrm{height}}$ in the range $2.4<\mathrm{}\Gamma <22\mathrm{}$. For all $\Gamma$, there is a first transition at a Rayleigh number $R_1>R_c$ where convection begins at $R_c$. Time dependence occurs for $R>\mathrm{}{R}_1$ when $\Gamma \gtrsim 4$. The character of the transition at $R_1$ is identified over the full range of $\Gamma$. As $\Gamma$ becomes large $\frac{R_1}{R_c}\to 1.09$, a value which is difficult to reconcile with predictions for the expected skewed varicose instability.

An effective interface dynamics is derived for a Stefan-type moving-boundary-value problem corresponding to electrostatic aggregation in two dimensions. With the help of conformal-mapping techniques the problem may be reduced to a many-body-type problem described by a system of ordinary differential equations. The method allows one to show that the Mullins-Sekerka instability in this case leads to generation of cusp singularities in the interface in a finite time.

It is shown that $S_X$, the partial molal entropy of electrons in material $X$, is given by $S_X=-F{\alpha }_X$, where $F$ is Faraday's constant and ${\alpha }_X$ the absolute thermoelectric power of $X$. This result depends on three propositions. (1) The Kelvin relations are valid for all thermoelectric materials. (2) Under isothermal conditions, the Peltier effect is truly reversible. (3) For a degenerate free-electron Fermi gas, the thermoelectric power is proportional to the entropy.

A coupled-channel analysis of electron-positive ion recombination is carried out, with full treatment of the coupling between radiation and autoionization continua. The cross section for this process reduces in the appropriate limits to the expressions for radiative and dielectronic recombination. The coupling to the radiation continuum leads to a modified Fano profile for the autoionizing resonances. The more complete, combined expressions derived here may be of interest for recent experimental studies of recombination and their comparison with theoretical results.

First-passage times $T_p$ for $n$-variable metastable systems vanish as the control parameter $\mu$ approaches its spinodal value ${\mu }_{c1\mathrm{}}$, with $T_p\sim {|\mu -{\mu }_{c1\mathrm{}}|}^{{\theta }_p}$ typically. The barrier height-to-noise ratio is the small parameter. The general results for the exponent ${\theta }_p$ agree with the exactly soluble $n=1\mathrm{}$ case where ${\theta }_p=\frac{1}{2}$, and are applied to the $n=4\mathrm{}$ two-mode laser, where ${\theta }_p=2\mathrm{}$ is predicted.

The triple-dipole (Axilrod-Teller) and the exchange three-atom potentials are compared for a number of specific arrangements of three argon and xenon atoms. For these configurations, total potentials are constructed, taking a Lennard-Jones (6-12) potential for each pair. It is found that for all arrangements the exchange three-atom potential is by far the more important correction to the two-body interaction. Qualitatively, the changes with respect to the two-body potential are more pronounced for xenon than for argon.

A reciprocity theorem is stated which applies to a dielectric medium at rest polarized by one or the other of two systems of charges. Its formulation is similar to the Betti-Maxwell reciprocity theorem for elastic media.

As one progresses along the isoelectronic sequence of Cs, the ground state changes from $6s_{\frac{1}{2}}$ (Cs, ${\mathrm{Ba}}^{+}$) to $5d_{\frac{3}{2}}$ (${\mathrm{La}}^{2+}$) to $4f_{\frac{5}{2}}$ (${\mathrm{Ce}}^{3+}$, ${\mathrm{Pr}}^{4+}$). The relativistic Hartree-Fock and model-potential calculations reported here are aimed at obtaining a better understanding of variations in the ordering of the states as the ion charge increases. The $5d$ and $4f$ orbitals are found to "collapse" as the increasing Coulomb and exchange attractions overcome centrifugal repulsion. Valence-core electron exchange is found to be crucial for the proper ordering of the states as well as for reliable fine-structure splittings. Furthermore, the collapse of the $5d$ and $4f$ orbitals greatly enhances the sensitivity of the properties of these states to small perturbations, so that even details of the exchange interaction, including nonlocal effects, as well as core-relaxation and -polarization effects, are required in order to compute accurate ionization potentials and fine-structure splittings.

The evolution of a quantum state is altered when a small perturbation is added to the Hamiltonian. As time progresses, the overlap of the perturbed and unperturbed states gives an indication of the stability of quantum motion. It is shown that if a quantum system has a classically chaotic analog, this overlap tends to a very small value, with small fluctuations. On the other hand, if the classical analog is regular, the overlap remains appreciable (on a time average) and its fluctuations are much larger.

A method is given for deriving model Hamiltonians which describe the behavior of a subsystem in interaction with a set of different particles. The formalism is illustrated by reducing the Jaynes-Cummings Hamiltonian for an interacting fermion-boson system, to a fermion-only Hamiltonian. The conditions are discussed under which such elimination of degrees of freedom is possible.

A simple theory for establishing the stability or instability of positron-atomic systems against dissociation is presented. The theory consists of assuming that Morse-potential parameters for protonic diatoms are transferrable to the corresponding positronic molecules, and making appropriate reduced-mass modifications in the calculation of binding energies. The surprisingly good reliability of the method is established by appealing to the well-known positronium affinities of atomic hydrogen and fluorine. Positronium (Ps) binding is found for about half of the 42 atoms tested. In addition, instability is indicated for all nine positron-atom systems tested, and stability is indicated for seven of eight negatively charged systems tested; e.g., Ps${\mathrm{O}}^{-}$.

We describe a general method of applying point canonical transformations to the path integral followed by the corresponding new-time transformations aimed at reducing an arbitrary one-dimensional problem into an exactly solvable form. Our result is independent of operator-ordering ambiguities by construction. The method is used in getting the exact path-integral solutions of the Coulomb- and Morse-potential problems.

Exact second-Born-approximation elastic scattering amplitudes are computed for a dipole excitation pseudostate model of electron scattering by ground-state atomic hydrogen. Calculations at 15, 25, and 35 keV incident energy show a forward peak in the differential elastic cross section. The optical theorem is exactly satisfied by these calculations, and the magnitude of the forward peak is determined primarily by physical values of the atomic static polarizability and oscillator strength. In the energy range considered, the computed peak is smaller by a large factor than the magnitude required to interpret recently observed experimental data in terms of single elastic collisions of electrons with ground-state atoms.

The $R$-matrix theory of Wigner is applied to the description of charge exchange. By making use of the correct coordinates for each arrangement, the boundary conditions are properly satisfied. Unphysical long-range couplings do not appear, and the use of "electronic traveling factors" is avoided. The wave function for different arrangements are nonorthogonal, and are essentially equivalent to the "intersecting waves" of Delos [Phys. Rev. A 23, 2301 (1981)]. It is shown under appropriate simplifying assumptions that the $R$-matrix formalism reduces to the high-energy two-state approximation of Kramers and Brinkman. The main task of the $R$-matrix theory is the determination of the matrix elements of the Hamiltonian between basis functions belonging to different arrangements. This is achieved by methods of functional transfer combined with appropriate simplifications arising from the smallness of $\frac{m}{M}$. This leads to the central result that the transformation of a highly oscillating nuclear radial function from one arrangement to another brings with it a highly oscillating function of the electronic coordinates of the new arrangement. This causes off-diagonal elements of the Hamiltonian matrix to decrease rapidly as the energy increases. Consequently the cross section for charge transfer also decreases with increasing energy.

Energy spectra of the projectile ions have been measured following electron capture by slow ${\mathrm{Ne}}^{q+}$ ions on He for $3\le q\le 8$. Both single-capture and transfer ionization were observed. The reactions are all exoergic with positive energy defects between 3.6 and 31 eV, and with crossing radii between 8 and 2.1 Å. Capture is found to selectively populate states whose crossings lie at a radius which can be calculated on the basis of a simple prescription. The total transfer cross sections range up to 55% of the geometrical ones deduced from the measured crossing radii.

The cross-section formula of Flannery [Phys. Rev. A 22, 2408 (1980)] in the semiquantal approximation for the processes referred to in the title is rewritten so as to make it more useful in practice. The formula is shown to be further simplified by taking an average over the azimuthal quantum number of a highly excited hydrogenic atom to be ionized. Numerical applications with use of the Glauber amplitude for the electron-atom inelastic scattering are made to the ionization collisions between two excited hydrogen atoms with simultaneous excitation and deexcitation of one of the atoms. The results are compared with those obtained by using the Born amplitude, and are analyzed in terms of the Glauber generalized oscillator strengths.

Relative stopping cross sections are measured for 3-MeV/u He, Li, and C ions in 2-26-μg/${\mathrm{cm}}^2$ C foils. The observed stopping cross sections for the fully stripped He and Li ions scale essentially as $Z_1^2$, in agreement with standard theory on higher-order $Z_1$-dependent effects applied to C targets. We observe nonequilibrium charge-state effects in the energy loss of C ions. Postfoil charge-state selection is used to measure the fixed-charge stopping cross sections for the fully stripped and one-electron C ions, and to extract the energy lost in the charge-change cycle ${\mathrm{C}}^{6+}$ ⇄ ${\mathrm{C}}^{5+}$ with the aid of a two-component charge-state model. The results show that charge-changing energy loss forms a significant part of the total stopping for 3-MeV/u C ions, and a significant higher-order $Z_1$-dependent effect is seen in the stopping cross section for ${\mathrm{C}}^{6+}$ ions. The standard interpretation in terms of the Bloch term and polarization theory is discussed in the light of these observations.

Pseudopotential molecular-structure calculations have been used to obtain the seven lowest ${}_{}{}^1{}_{}{}^{}\Sigma$ and ${}_{}{}^1{}_{}{}^{}\Pi$ states of CsH. These states and their associated radial and rotational coupling terms have been used to calculate the cross sections for ${\mathrm{H}}^{-}$+${\mathrm{Cs}}^{+}$ ion-pair production in $\mathrm{H}+\mathrm{Cs}\mathrm{}\left(6s\right)\mathrm{}$ and $\mathrm{H}+{\mathrm{Cs}}^{*}\mathrm{}\left(6p\right)\mathrm{}$ collisions at energies from 0.1 to 10 keV. The ion-ion mutual neutralization cross section, ${\mathrm{H}}^{-}$+${\mathrm{Cs}}^{+}$ → H+Cs, is also presented. The cross-section calculations were done with the perturbed-stationary-state method, modified to include two-electron translation factors. The ion-pair production cross section for ground-state reactants is in good agreement with experiment; collisions of H with excited ${\mathrm{Cs}}^{*}\mathrm{}\left(6p\right)\mathrm{}$ show an order-of-magnitude enhancement of the ion-pair production cross section at 100 eV. The ion-ion mutual neutralization cross section is found to be large, attaining a value of 1.3 × ${10}^{-14\mathrm{}}$ ${\mathrm{cm}}^2$ at 0.1 keV.

First-order many-body theory has been used to calculate electron-photon coincidence parameters for the $4s^{\prime }{\left[\frac{1}{2}\right]}_1^0\left({}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$ and $4s{\left[\frac{3}{2}\right]}_1^0\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$ states of argon, for the incident electron energies of 16, 20, 30, 50, and 80.4 eV. Consequences of the spin-orbit coupling in the target atom upon the interpretation of electron-photon coincidence experiments are discussed.