In the electrodeposition of metals without mixing, transport of the ions in the electrolyte proceeds both by electrical migration and by diffusion in response to gradients of concentration. At the metallic surface, the current is determined by the potential across the double layer. In many cases, a flat interface displays only a weak morphological instability, with an amplitude that is approximately independent of the wave vector. The relevance of these results to the recent observation of "dense radial" patterns is discussed.

Measurements of the $f\left(\alpha \right)$ spectrum, which is a measure of the dimension of the set of singularities of strength $\alpha$ on the attractor, are reported for the diode resonator system at the onset of chaos from both the quasiperiodic route and the period-doubling route. For the period-doubling route a driven single diode resonator is used and quasiperiodicity is attained by driving two resistively coupled diode resonators. In the driven coupled diode resonator system, a second frequency occurs naturally, but a winding number equal to the golden mean cannot be reached. However, the system can be made to respond at a winding number approximated by the continued fraction $〈4111\dots 〉$ to an accuracy of one part in ${10}^6$. The measured $f\left(\alpha \right)$ functions are compared with those calculated for the sine-circle map (quasiperiodic route) and the logistic map (period-doubling route). We find good agreement in both cases, providing experimental evidence for the universality of $f\left(\alpha \right)$ within classes of situations representing particular routes to chaos.

A scaling description of the crossover from isotropic to anisotropic cluster growth for ordinary diffusion-limited aggregation (DLA) in two dimensions developed recently by Family and Hentschel is extended to the generalized DLA or $\eta$ model. The dependence of various exponents necessary to characterize the anisotropic growth on the local-growth probability exponent $\eta$ of the generalized DLA is obtained explicitly. The $\eta$ dependence of the exponent $\beta$ describing the variation of the crossover mass $N_c$ on the degree of symmetry $m$, $N_c\sim m^{\beta }$, is derived. The results indicate that the anisotropic star-shaped clusters can be easily observed for $\eta >1\mathrm{}$, while their appearance is much more difficult for $\eta <1\mathrm{}$. All our results are consistent with those of computer simulations reported so far.

A formulation giving the $q$ dimension $D_q$ of a chaotic attractor in terms of the eigenvalues of unstable periodic orbits is presented and discussed.

A new type of phase transition associated with a singularity in the spectrum of generalized entropies, or in a corresponding free energy, is shown to exist in dynamical systems. Candidates for exhibiting such transitions are intermittent chaotic systems where certain generalized entropies vanish. This new transition may coexist with one associated with the static properties of the system.

We present the results of a theoretical investigation on the configuration interaction between doubly excited ($n_1$$l_1$,$n_2$$l_2$${)}^1$,3L and singly excited (3snl${)}^1$,3L bound states below the first ionization threshold of atomic ions which are isoelectronic to the magnesium atom. The effect of configuration interaction is studied in terms of (i) the term values correction and (ii) the change in oscillator strengths for transitions involving the neighboring singly excited states due to the presence of an individual doubly excited perturber. The range and strength of each bound doubly excited state in Al ii and Si iii ${}_{}{}^1{}_{}{}^{}$,3S${\mathrm{-}}^1$,3F series are examined in detail.

Proof is given that 1/N expansions for energy levels can be interpreted in terms of the quasiclassical minimizations of corresponding Hamiltonian forms like scrH(r,p=ħ$d_0$/r) and vice versa. This mutual connection enables us to show that the fixing condition for the expansion parameter (k=N+2l-a) proposed previously is implied to first order only. In general, the a parameter should be chosen, order by order, so that the sum of corrections to the zeroth-order result vanishes. This requirement leads to algebraic equations which produce self-consistent $d_0$=k/2 evaluations. ($d_0$ denotes the underlying phase-space quantum.) Particular fixing conditions can also be proposed. First-order $d_0$ estimates are discussed in more detail by using as an example the linear-plus-Coulomb potential. We also find the covariance behavior of $d_0$ under quasiclassical symmetry transformations.

The method of adiabatic switching (AS) is applied to the problem of a hydrogen atom in a strong magnetic field, i.e., the quadratic Zeeman effect (QZE). The QZE is one of the simplest realistic physical problems exhibiting classical chaos which presents conceptual and computational obstacles to the implementation of many semiclassical quantization methods, while the highly nonseparable nature of the problem makes exact quantum treatments problematic. The AS method is straightforward, mainly involving integration of Hamilton’s equations of motion, and in addition, unlike most other trajectory-based semiclassical methods, works even in mildly chaotic volumes of classical phase space. In AS, a zeroth-order classical torus is quantized and then the perturbation is switched on adiabatically using a time-dependent or time-independent switching function which is incorporated into the Hamiltonian. A central problem in AS is the choice of the most appropriate zeroth-order tori. Based on a comprehensive study of the classical dynamics of the QZE it is shown that the best zeroth-order tori for AS are those obtained by quantizing the zeroth-order Hamiltonian (i.e., the hydrogen atom) and simultaneously an adiabatic invariant found by Solov’ev. AS is performed for a wide variety of magnetic fields and energies including states lying in mildly chaotic regions of phase space where Solov’ev’s invariant is no longer conserved. Results are generally in excellent agreement with exact quantum results, and additionally the method is self-diagnostic, yielding large standard deviations in energies should it begin to fail. However, AS is seen to break down in the strongly chaotic regions of phase space where the quantum levels display multiple avoided crossings (strongly n-mixing regime). Application of AS to the QZE leads to a number of new developments in the theory of AS, including AS in extended phase space where the Hamiltonian is explicitly independent of time.

The consistencies of calculated term values (ionization energies) for various 1snl terms having n=5–8, l=1–5 are tested by microwave-spectroscopic and other available data. The most accurate n P, n D, and n F term values obtained from published variational calculations are generally found to be consistent, within the estimated uncertainties, with more accurate n G and n H energies from core-polarization theory [R. J. Drachman, Phys. Rev. A 26, 1228 (1982)]. The n ${\mathrm{}}^3$D and n ${\mathrm{}}^1$D term values from variational calculations [A. Kono and S. Hattori, Phys. Rev. A 34, 1727 (1986)] are confirmed within uncertainties as small as ${10}^{\mathrm{-}4}$ ${\mathrm{cm}}^{\mathrm{-}1}$ (n=8), although the ${}_{}{}^1{}_{}{}^{}\mathrm{D}$ values are systematically too large by amounts within the uncertainties. The ionization energy $E_I$ has accordingly been reevaluated by using only the calculated n ${\mathrm{}}^3$D term values (n=4,5) and available experimental measurements: The resulting $E_I$ value is 198 310.772 27(40) ${\mathrm{cm}}^{\mathrm{-}1}$ with respect to the 2 ${}_{}{}^3{}_{}{}^{}S$ level at 159 856.077 60 ${\mathrm{cm}}^{\mathrm{-}1}$.

The available data and calculated term energies allow determination of the entire 1snl excited energy-level system with much improved accuracy for the higher levels. Calculated energies are used instead of experimental results in several cases involving apparently underestimated experimental uncertainties. The levels are given explicitly through n=8. Experimental term values based on the new $E_I$ value are combined with calculated term values not including QED contributions to obtain ‘‘experimental’’ Lamb shifts for a number of n S and n P terms. The experimental Lamb shifts of the 2 ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$–2 ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ and 2 ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$–2 ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ separations are also reevaluated. Results of comparisons of these experimental shifts with various calculated Lamb shifts vary from agreement within 0.3% experimental uncertainties (for the 2 ${}_{}{}^3{}_{}{}^{}S$ shift and shift of the 2 ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$–2 ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ separation) to relatively large discrepancies for the higher n S terms (∼50% for 5 ${}_{}{}^3{}_{}{}^{}S$). Two-electron QED contributions calculated for 2 ${}_{}{}^3{}_{}{}^{}S$, 2 ${}_{}{}^1{}_{}{}^{}S$, and 2 ${}_{}{}^1{}_{}{}^{}P$ [G. W. F. Drake and A. J. Makowski, J. Phys. B 18, L103 (1985)] are confirmed within uncertainties of about 35% by the data in each case, the level of confirmation for 2 ${}_{}{}^3{}_{}{}^{}S$ and 2 ${}_{}{}^1{}_{}{}^{}P$ being subject to additional uncertainties from as-yet uncalculated contributions.

Simple expressions are given for the cross sections and rate coefficients for populating the excited levels with n=3 in neonlike ions through the mechanism of inner-shell ionization of sodiumlike ions by electron impact. It is shown how configuration and intermediate-coupling mixing effects are easily included. Illustrative numerical results for the rate coefficients for inner-shell ionization of Na-like iron, selenium, and molybdenum are given and compared with the rate coefficients calculated by Hagelstein and Jung [Atom. Data Nucl. Data Tables 37, 121 (1987)] for populating these same excited levels by the alternative mechanism of electron-impact excitation from the ground level of the neonlike ions.

We investigate the effects of inner-shell ionization of sodiumlike ions on the kinetics of neonlike selenium, using a simple model that separates the calculation of the excited-state kinetics from that of the ionization balance. Our model includes collisional and radiative transitions between the neonlike states, inner-shell ionization of sodiumlike states, and dielectronic recombination from fluorinelike ions. By examining the relative importance of these various population mechanisms, we demonstrate that inner-shell ionization of sodiumlike ions has a significant effect on the inversion kinetics of neonlike selenium, although it is not sufficient alone to account for the discrepancy with experimental observation.

Single and multiple ionization of He, Ne, and Ar has been studied experimentally by impact of fast protons and antiprotons. The single-ionization cross sections obtained with protons and antiprotons are found to be the same. The double-ionization cross sections obtained with antiprotons, however, are much larger than those obtained with protons at equal velocity. This difference is found for all three gases but the effect is largest for He and Ne, where the difference is about a factor of 2 at 1 MeV/amu. The difference is discussed in terms of interference between two collision mechanisms which both result in double-electron escape. Experimental information on the magnitude of the interference term is obtained by inclusion of double-ionization data, partly obtained in this work, for fast electron and α-particle impact. For triple ionization of Ne, we also find that antiprotons yield much larger cross sections than protons do. Identical cross sections, however, are found for triple ionization of Ar with protons and antiprotons. This is believed to be due to the fact that triple ionization of Ar is mainly a consequence of a single vacancy produced in an inner shell followed by electronic rearrangement. This observation supports the interpretation that the observed charge effect is due to an interference effect in the outermost shell.

A molecular study of the excitation reactions H(1s)+H(1s)→H(1s)+H(2s) and H(1s)+H(1s)→H(1s)+H(2p) is presented for the first time in the range of impact energies 1–9 keV, using a common translation factor to account for the momentum-transfer problem. As a consequence of this study, we explain in detail the collisional mechanisms involved and point out several new features that may explain the discrepancies between the available experimental data and all previous theoretical calculations, and among the latter. Preliminary results for the cross sections are also presented to show the influence of the form chosen for the common translation factor.

The continuum-distorted-wave–eikonal-initial-state model is used to study single ionization of helium by proton, antiproton, and multiply-charged bare ions (${\mathrm{He}}^{2+}$, ${\mathrm{Li}}^{3+}$) impact. Total cross sections are calculated and compared with experimental data. Comparison with calculations using the first Born approximation show that binding and polarization effects are intrinsically taken into account.

We report on distorted-wave calculations of the electron-impact ionization cross sections and rate coefficients for the Na-like ions ${\mathrm{Ti}}^{11+}$, ${\mathrm{Cr}}^{13+}$, ${\mathrm{Fe}}^{15+}$, and ${\mathrm{Ni}}^{17+}$. The cross sections for direct ionization out of the 3s, 2p, and 2s subshells were determined using the configuration-average, distorted-wave approximation. In addition, excitation-autoionization contributions originating from inner-shell excitations of the type 2$s^2$2$p^6$3s→2$s^2$2$p^5$3snl (n=3,4,5) and 2$s^2$2$p^6$3s →2s2$p^6$3snl (n=3,4) were calculated by employing the distorted-wave approximation and configuration-interaction, bound-state wave functions. Near threshold, the total-ionization cross sections in all four ions are enhanced by approximately a factor of 5 through excitation autoionization. These excitation-autoionization contributions are large, even though they have been substantially reduced by radiative decay to the bound states of the initial ion. Furthermore, although electron correlation has a minimal effect on the excitation cross sections, the magnitude of the branching ratios for autoionization is quite sensitive to configuration interaction in the autoionizing levels. This is especially true for the 2p→3d excitations, where configuration interaction between 2$p^5$3s3d and 2$p^5$3$p^2$ can increase the magnitude of the autoionizing rates for levels within the 2$p^5$3s3d configuration by as much as three orders of magnitude. Thus, for example, in the case of the 2p→3d excitation in ${\mathrm{Ni}}^{17+}$, correlation increases the overall branching ratio for autoionization from 0.27 to 0.53.

The range-energy (RE) relations for Au ions in CH and Au in the energy interval 10≤E/A≤150 MeV are reported. Bevalac beams of ${\mathrm{Au}}^{61+}$, ${\mathrm{Au}}^{35+}$, and ${\mathrm{Au}}^{11+}$ at E/A=50 MeV were used to investigate the dependence of dE/dx, hence effective charge $z^{\mathrm{*}}$, of Au ions in matter as a function of target material and initial charge of incident Au ions. The essential finding of this experiment is that the measured ranges of the Au ions are typically within 2% of those predicted by the Barkas-Berger RE relation. The experimental RE relations for Au in CH and Au can also be reproduced with equal precision by assuming that dE/dx is given by the product of the rate of energy loss for protons and an empirically derived expression for $z^{\mathrm{*}2}$, each quantity being dependent on the target material, via the adjusted ionization potential $I_{\mathrm{adj}}$ and the velocity β of the ion.

Differential cross sections have been calculated for the charge-transfer reaction ${\mathrm{O}}^{2+}$ +He→${\mathrm{O}}^{+}$+${\mathrm{He}}^{+}$ at center-of-mass collision energies from 1 to 100 eV. A number of features are predicted, all having semiclassical interpretations: an interference pattern resulting from inelastic scattering on multiple potential surfaces, a ‘‘rainbow’’ effect arising from the polarization in the initial channel, and a ‘‘forward glory’’ effect. At lower collision energies these features become more striking. As the energy released in the charge-transfer reaction becomes comparable to or greater than the initial relative collision energy, inelastic ${\mathrm{O}}^{+}$${(\mathrm{}}^2$P°) product ions should move to the outer fringes of the forward scattering cone.

The KLL Auger-electron yields from a number of C-, N-, and O-bearing compounds have been measured for either $H^{+}$ or ${\mathrm{He}}^{+}$ bombardment in the incident energy range of 0.6–2.0 MeV. The yields are seen to vary significantly with the chemical environment with variations of greater than 30% observed between ${\mathrm{CH}}_4$ and ${\mathrm{CF}}_4$ yields. These variations seem to be reproducible by two simple scaling laws, one based on the inelastic scattering cross sections of the various molecular components, while the second uses the effective number of valence-shell electrons about the site of the K-shell vacancy. The cross sections are reported for the ${\mathrm{He}}^{+}$-induced carbon and nitrogen Auger-electron yields from ${\mathrm{CH}}_4$, ${\mathrm{C}}_2$${\mathrm{H}}_6$, ${\mathrm{C}}_2$${\mathrm{H}}_4$, ${\mathrm{C}}_2$${\mathrm{H}}_2$, CO, ${\mathrm{CO}}_2$, ${\mathrm{C}}_2$${\mathrm{F}}_6$, ${\mathrm{CF}}_4$, (${\mathrm{CH}}_3$${)}_2$NH, ${\mathrm{NH}}_3$, ${\mathrm{N}}_2$, and ${\mathrm{N}}_2$O, as well as for the ${\mathrm{H}}^{+}$-induced carbon and oxygen Auger-electron yields from ${\mathrm{C}}_2$${\mathrm{H}}_6$, CO, ${\mathrm{CO}}_2$, ${\mathrm{N}}_2$O, and ${\mathrm{O}}_2$.

We have extended our variationally determined nonadiabatic polarization potential [Gibson and Morrison, Phys. Rev. A 29, 2497 (1984)] to the e-${\mathrm{N}}_2$ system and calculated elastic, total momentum transfer, and rotational excitation cross sections. This model potential, which requires no scaling and contains no adjustable parameters, is presented in tabular and analytic (fitted) form for possible use in future studies. We evaluated the static potential at the near-Hartree-Fock level of accuracy and included exchange effects exactly via the linear algebraic method of Collins and Schneider [Phys. Rev. A 24, 2387 (1981)]. Diverse cross sections based on this model are in excellent agreement with existing experiment. We also compare various scattering quantities calculated with our model to prior theoretical results and to newly determined numbers using two other model potentials: a cutoff phenomenological form and the correlation-polarization potential of O’Connell and Lane [Phys. Rev. A 27, 1893 (1983)].

L- and M-shell x-ray production cross sections have been measured for thin solid targets of neodymium, gadolinium, holmium, ytterbium, gold, and lead by 25-MeV ${}_{{\mathrm{}}^1{\mathrm{}}_6^2}{}^{}{}_{}{}^{}\mathrm{C}_{}^{\mathrm{q}+}{}_{}{}^{}$ (q=4,5,6) and by 32-MeV ${}_{{\mathrm{}}^1{\mathrm{}}_8^6}{}^{}{}_{}{}^{}\mathrm{O}_{}^{\mathrm{q}+}{}_{}{}^{}$ (q=5,7,8). The cross sections were determined from measurements made with thin targets (less than 2.25 μg/${\mathrm{cm}}^2$). For projectiles with one or two K-shell vacancies, the target x-ray production cross sections were found to be enhanced over those for projectiles without a K-shell vacancy. The sum of direct ionization to the continuum (DI) plus electron capture (EC) to the L,M,N,. . . shells and EC to the K shell of the projectile have been extracted from the data. The results are compared to the predictions of first Born theories, i.e., plane-wave Born approximation for DI and Oppenheimer-Brinkman-Kramers formula of Nikolaev for EC, and to the ECPSSR that accounts for energy loss and Coulomb deflection of the projectile as well as for relativistic and perturbed stationary states of inner-shell electrons.