Diffusion-limited aggregation generates clusters in which the density decay is determined by the same exponent throughout the cluster. We find that although the power law describing the density falloff is homogeneous throughout the cluster, the amplitude of the power-law decay about the center of the cluster is different from the amplitude elsewhere in the cluster, at least in two dimensions. The ratio of these two amplitudes is not sensitive to the details of the aggregation process.

By employing space-time dilatation invariance of the Hopf equation for the characteristic functional, it is shown that statistical-dynamical self-similarity must be featured in the free decay of inertia-dominated incompressible-fluid turbulence. The experimentally established decay law $u^2$∝$t^{\mathrm{-}6/5}$ and integral scale dependence L∝$t^{2/5}$ follow deductively and without any additive assumption from a Gaussian normal probability distribution over velocity fields at the initial instant t=0.

A novel Hamiltonian approach to generate all possible histories of Eden clusters is presented. It yields a field-theoretic formulation which is local and Markovian. The method may be generalized to other kinetic-growth and aggregation processes.

The theory of rf-driven plasma currents is applied to the lower-hybrid experiments on the Princeton Large Torus, Princeton University, tokamak. Particular emphasis is placed on those experiments in which the plasma current was varying. The comparison between theory and experiment is made with respect to the efficiency with which rf energy was converted to poloidal magnetic field energy. Good agreement is found irrespective of whether the current was increasing, constant, or decreasing.

We propose a new phenomenological rule for the weight function in the position-space renormalization-group approach for the calculation of the fractal dimension in models of geometrical disorder in order to avoid strong corrections to scaling due to surface effects. In our scheme the radius of gyration is used as a characteristic measure of the spatial extent of the clusters. In addition, an optimization parameter is introduced. Application to diffusion-limited aggregation in two dimensions shows that our method gives good estimates even when relatively small cells are used.

The recent experiment by Grangier, Aspect, and Vigué on interference in the emission from fragments of electronically photodissociated molecules is treated as a special case of cooperative fluorescence (CF) from products of various molecular processes. This general analysis relates time-resolved features of the CF to characteristics (such as orbital symmetry) of the dissociating parent molecule (PM) suggests various PM state preparations (including formation of subradiant states), and discusses the persistence of CF in systems of nonidentical fragments. The diagnostic potentialities of such studies are emphasized.

We review the proposal that relationships between physical spectra of certain atoms can be considered as evidence for a phenomenological supersymmetry. Next, a comparison is made between the supersymmetric and the hydrogenic approximations. We then present the calculation of low-Z alkali-metal-atom transition probabilities between low-n states, using supersymmetric wave functions. These probabilities agree more closely with accepted values than do those obtained with use of the hydrogenic approximation. This shows that, in simple radial Schrödinger theory, supersymmetry is a concept providing insight into the true, fermionic, many-body physics of these atoms.

The electron distribution for nuclearites and heavy atoms is computed by a generalized Thomas-Fermi formalism, which takes into account the relativistic change of mass with velocity. The relativistic equation is solved numerically by exploiting the finite nuclear-charge distribution rather than by using perturbation theory. The greatest discrepancy with the usual nonrelativistic calculation appears for nuclearites with a radius $R_N$∼${10}^{\mathrm{-}2}$ Å.

A study is made of finite-nuclear-size corrections to the Uehling potential for the ground state of hydrogenlike atoms (Z=1 and 80). The exact relativistic correction is compared to the results of perturbation theory and to nonrelativistic results based upon the approximations of Zemach. Perturbation theory and the nonrelativistic approximation are consistent with the exact calculation at Z=1, but not at Z=80. In the nonrelativistic approximation, this size correction is (1/2)α(Zα${)}^5$(R/${\mathrm{hlambda}}_e$${)}^2$mc ${}_{}{}^2{}_{}{}^{}$, where R is the rms radius of the nucleus.

Fourier transforms of the von Neumann density operators could be regarded as functions on a Lie group whose infinitesimal generators correspond to dynamical variables characterizing a given quantum system. Called ‘‘characteristic functions’’ in this paper, they are discussed with a view to reformulating quantum statistical mechanics in a group-theoretical formalism. It is shown that these characteristic functions allow a universal differentiating procedure for calculating averages of arbitrary ordered noncommuting observables and satisfy the same criterion of non-negative definiteness as the Fourier transforms of the everywhere non-negative probability distribution (the characteristic functions in classical probability theory). The group-theoretical characteristic-function formalism is especially useful in providing easy reductions of the dynamics of complicated quantum systems to the evolutions of a set of quantum variables that are of particular interest. As examples of applications, the following results are derived: (a) a hierarchy of equations of motion for subsystems of a given N-body quantum system (a quantum analog of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy), (b) an equation of motion for centers of mass of two interacting quantum systems, and (c) the behavior of spin fluctuations of an ideal spin gas in the thermodynamic limit.

The Wentzel-Kramers-Brillouin eigenvalue condition is developed in an expansion in $Z^{\mathrm{-}1/3}$ to lowest order in the limit in which the atomic number Z becomes very large. The energy levels are studied explicitly for finite orbital angular momentum l quantum numbers. The nature of the resulting level spectrum is illustrated and its connection with the solutions of Schrödinger’s equation by Latter, for a closely related potential, is briefly discussed. It is pointed out that to get the complete level spectrum near the continuum, for large Z, the case of l of order $Z^{1/3}$ will eventually require consideration. Finally, a few general results are established, one of which predicts the maximum value of l for which a bound state can occur for a given value of Z.

Nuclear-motion corrections to the atomic fine-structure isotopic shift are computed by use of many-body perturbation theory. The corrections are of three different types: normal mass effects (change of length scale), electron-nucleus relativistic interactions, and higher-order cross terms between the specific-mass operator and spin-dependent interactions. Numerical results are reported and compared with experiments for the ground states of Br, ${\mathrm{Ar}}^{+}$, Cl, ${\mathrm{Ne}}^{+}$, and C. Except for ${\mathrm{Ne}}^{+}$, reasonable agreements are obtained. For the best investigated case of Cl, the theoretical and experimental shifts are, respectively, -25.4 MHz and -24.9(1.0) MHz. In all cases the electron-nucleus relativistic interaction and the cross term between the specific mass-shift Hamiltonian and the spin-orbit interaction are found to yield large and counteracting contributions. The nuclear field-shift contribution to the fine-structure isotopic effect is also investigated for ${\mathrm{Ar}}^{+}$ and found to be of minor importance.

The resonance energies for the hydrogen atom in an electric field, both the real and imaginary parts, have been calculated together from the real Rayleigh-Schrödinger perturbation series by Borel summation. Padé approximants were used to evaluate the Borel transform. The numerical results compare well with values obtained by the complex-coordinate variational method and by sequential use of Padé approximants.

Asymptotic expansions for Airy functions and more generally confluent hypergeometric functions, which are of fundamental importance in semiclassical quantum mechanics, are summable. The Stokes lines of the expansions are cuts of the Borel sums of the power series occurring in the expansions. At a Stokes line on which the function is continuous, the asymptotic expansions change discontinuously, but their composite sums do not—a fact that greatly clarifies the role of the Stokes line. On a Stokes line itself, it is still possible to evaluate the asymptotic expansion by Borel summation via analytic continuation, and as a consequence complex expansions may have real sums, and vice versa. This observation has important implications for the significance and use of asymptotic expansions recently derived for the resonances of the LoSurdo-Stark effect and for the energy eigenvalues of ${\mathrm{H}}_2$${\mathrm{}}^{+}$. For both of these problems the physical values of the expansion parameters, the electric field strength and the reciprocal of the internuclear distance, lie on Stokes lines.

The ratio of the cross section for double ionization to the cross section for single ionization of helium produced by 25- to 625-keV/amu ${\mathrm{He}}^{+}$ projectiles has been measured. The results reported here are consistently higher than the values reported by Dubois et al. Above 400 keV/amu, where charge capture is small, the ratios are about the same as those reported for ${\mathrm{He}}^{2+}$ projectiles.

A new technique is used to probe the dynamics of Penning ionization reactions involving He($2^3$S) atoms and the targets K, Rb, Cs, ${\mathrm{O}}_2$, ${\mathrm{Cl}}_2$, and ${\mathrm{CF}}_3$Cl. In this technique, the electrons on the $2^3$S atoms are spin labeled and the polarization of the Penning electrons is determined. The data indicate that, for Rb, a significant fraction of the ionization occurs through energy transfer to a core excited state followed by autoionization. The data for the molecular targets confirm that ionization via ionic channels is important.

The threshold behavior of the cross section when electron detachment leaves behind a neutral atom (or molecule) with an electric dipole moment is derived through the formalism of quantum-defect theory. The cross section is a constant with a superimposed modulation with energy which has negligible amplitude for realistic situations such as the photodetachment of ${\mathrm{H}}^{\mathrm{-}}$ accompanied by excitation. The threshold behavior for double detachment is also derived on the basis of a Coulomb-dipole description of the two electrons. It is shown that no oscillations will be observed in the cross section for this process.

A unified treatment of ion-atom collisions proposed earlier [Phys. Rev. A 31, 590 (1985)] is applied to study excitation and charge transfer in ${\mathrm{H}}^{+}$+H and ${\mathrm{C}}^{6+}$+H collisions. This method expands the time-dependent electronic wave function in terms of traveling atomic orbitals of the two collision centers at large internuclear separations which is matched to the solution in the inner region where it is expanded in terms of molecular orbitals without translational factors. The results for ${\mathrm{H}}^{+}$+H are shown to agree with recent elaborate close-coupling calculations and with experiments. For ${\mathrm{C}}^{6+}$+H collisions, the partial cross sections for capture to n=5 of ${\mathrm{C}}^{5+}$ are in better agreement with the atomic expansion calculation of Fritsch and Lin than with the molecular orbital expansion of Green et al.

We calculate the capture cross sections for ${\mathrm{H}}^{+}$+He→H+${\mathrm{He}}^{+}$, treating the passive electron explicitly in a distorted-wave formalism based on the eikonal approximation. It is found that the shape of the differential cross sections is influenced considerably by the interaction between the passive electron and the incident proton, while the integrated cross sections are much less sensitive to that. The differential cross section at 293 keV agrees well with the experimental data except at extremely small scattering angles. The forward peak is reproduced well at higher energies. The integrated cross sections are in excellent agreement with experiments for the incident energy above 250 keV.

Angular differential cross sections for the proton-impact excitation of ground-state helium ${(1\mathrm{}}^1$S) to the $2^1$S and $2^1$P states have been measured for the first time in the energy range 25 to 100 keV with use of the energy-loss technique. The data indicate that, for very small scattering angles, at 25 keV the $2^1$S differential cross section is greater than the $2^1$P differential cross section. For impact energies greater than 50 keV, the $2^1$P differential cross section clearly dominates over the $2^1$S cross section in the very small scattering angle region. The present data have been numerically summed and integrated to compare with previous absolute experimental measurements on related processes. These are in very good agreement with the present results. An eight-state impact-parameter calculation incorporating the electron-capture channel was performed and resulted in the best agreement with the experimentally determined differential cross sections.