A probability distribution for the delay time of superfluorescent pulses is calculated as a function of the Fresnel number from the solution of the linearized Maxwell-Bloch equations in three dimensions.

The Landau-Khalatnikov two-fluid hydrodynamic equations are derived for a dilute, weakly interacting, condensed Bose gas on the basis of a microscopic theory. Explicit expressions for the transport coefficients in the linearized equations are given for very low temperatures and for moderately low temperatures below the $\lambda$ point.

The anisotropy of orientational order in cholesteric liquid crystals is investigated within a mean-field model of the cholesteric phase. It is shown that this biaxiality emerges as a direct consequence of the helical structure of the phase and the chiral character of the intermolecular interactions. The dependence of the biaxiality on temperature and pitch is compared with recent NMR measurements.

Sites on a lattice are randomly denoted "good" or "bad" with probability $p$ and ($1-p$), respectively. A particle confined to the good sites executes a random walk with nearest-neighbor hopping. We give a method for obtaining the diffusion constant $D$ for all $p$, based upon the real-space renormalization group; $D$ is seen to vanish as $p$ approaches the percolation threshold $p^{*}$. We find $D$ for all $p$ on a triangular lattice and we investigate the $p\sim p^{*}$ regime, where $D$ is found to vary as ${\xi }^{-x}f\left(\frac{\omega }{{\xi }^{-y}}\right)$, $x\sim 0.48$, $y\sim 2.48$, and $\xi$ is the correlation length. Accordingly, $D$ vanishes as ${\epsilon }^{0.65}$, $\epsilon =|p-p^{*}|$, and anomalous diffusion occurs on the percolation cluster with the mean-square displacement varying as $t^{0.81}$. Further analysis of our earlier theory of the Lorentz gas (where the scatterers define a continuum percolation problem), based upon the self-consistent repeated ring approximation, is shown also to yield the scaling form of $D$ with $D\sim {\epsilon }^{0.5}$, $\epsilon =\frac{|\rho -{\rho }^{*}|}{{\rho }^{*}}$, where $\rho$ is the reduced density, and with the mean-square displacement at ${\rho }^{*}$ increasing as $t^{\frac{2}{3}}$ in two and three dimensions.

A new method of averaging the Navier-Stokes equations has recently led to an equation for the mean velocity in which the Reynolds stresses are systematically replaced by a renormalized eddy viscosity. Here we give the results for an iterative calculation of the eddy viscosity ${\nu }_n\mathrm{}\left(k\right)\mathrm{}$ on the assumption that the energy spectrum is given by $E\left(k\right)=\alpha {\epsilon }^{\frac{2}{3}}{k}^{-\frac{5}{3}}$. A renormalization-group analysis shows that ${\nu }_n\mathrm{}\left(k\right)\mathrm{}$ reaches the fixed functional form $\nu \mathrm{}\left(k\right)=2.5\mathrm{}{\alpha }^{\frac{1}{2}}{\epsilon }^{\frac{1}{3}}{k}^{-\frac{4}{3}}$.

A new method for estimating the Kolmogorov entropy directly from a time signal is proposed and tested on examples. The method should prove valuable for characterizing experimental chaotic signals.

A new general subset of coherent states, which is complete and overcomplete by just one element, is introduced. It is the union of $N$ arbitrary nonintersecting von Neumann lattices whose unit-cell areas have a harmonic mean of $\mathrm{Nh}$. First applications are given in the problems of crystal electrons in rational magnetic fields, incommensurate structures in a magnetic field, and quantum dynamics.

An approximation scheme for dynamic response functions within the coupled cluster or $\exp \mathrm{}\left(T\right)\mathrm{}$ method of Coester and Kümmel is described in this paper. Particular attention is given to the relationship between the "vacuum amplitude" $〈0\left|U\right(t,-\infty \left)\right|0\mathrm{}〉$ for the time development of an exact eigenstate of a many-electron Hamiltonian in the presence of an adiabatically switched-on perturbaction, and the amplitude $〈{\Phi }_0\left|U\right(t,-\infty \left)\right|0\mathrm{}〉$ for the time evolution into an independent-particle reference state $|{\Phi }_0〉$, which is not orthogonal to $|0\mathrm{}〉$. The latter amplitude plays a prominent role in the time-dependent coupled-cluster calculation of response functions.

Energies were computed for the $2s3p$ levels in the Be isoelectronic sequence from $Z=10\mathrm{} \mathrm{to} 26$. Multiconfiguration wave functions of form ($2s3p$,$2p3s$,$2p3d$)were obtained from the program MCHF77. The Pauli relativistic corrections were calculated and the 2×2 spin-orbit-interaction matrix was diagonalized to obtain the ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ interval and mixing coefficient. Results agree with observations and with other self-consistent-field calculations at $Z=10, 23, \mathrm{and} 26$. The avoided crossing of the two $J=1\mathrm{}$ levels is found to occur at $Z=21\mathrm{}$. Finally, the radiative-decay probabilities of the mixed $J=1\mathrm{}$ levels were calculated; results are compared with other calculations and checked against a recent experiment in Ne VII.

The role of the Aharonov-Bohm effect is analyzed for the bound states of a charged particle in the superposition of two fields: A uniform magnetic field plus the vector potential of a solenoid. Exact solutions are given for a solenoid of zero size and the corrections due to finite size are discussed. It is shown that a series of new "betatron resonances" appear in the spectrum, dependent on the flux quantum number $f=\frac{e\Phi }{\mathrm{hc}}$. The fundamental betatron resonance remains narrow and unshifted for solenoid radii large enough to broaden and shift the cyclotron resonance.

A new approach to the one-particle Green's functions $\mathit{G}$ for finite electronic systems is presented. This approach is based on the diagrammatic perturbation expansions of the Green's function and of the dynamic self-energy part $\mathit{M}$ related to $\mathit{G}$ via the Dyson equation. The exact summation of the latter expansion is reformulated in terms of a simple algebraic form referred to as algebraic diagrammatic construction (ADC). The ADC defines in a systematical way a set of approximation schemes ($n\mathrm{th}$-order ADC schemes) that represent infinite partial summations for $\mathit{M}$ and (via the Dyson equation) for $\mathit{G}$ being complete through $n\mathrm{th}$ order of perturbation theory. The corresponding mathematical procedures are essentially Hermitian eigenvalue problems in restricted configuration spaces of unperturbed ionic configurations. Explicit equations for the second-, third-, and fourth-order ADC schemes are derived and analyzed. While the second- and third-order schemes can be viewed as systematic rederivations of previous approximation schemes, the fourth-order ADC scheme represents a complete fourth-order approximation for the self-energy and the one-particle Green's function which was hitherto not available.

A method is developed for predicting the stopping power of crystals toward swift channeled ions, based on a semiempirical treatment of the dielectric response of the medium. Random stopping power is also obtained. Theoretical results are compared with the experimental channeled stopping power of gold as a function of ion velocity and position within channels. It is shown that the theory is accurate when the velocity of the ion equals at least twice the root-mean-square velocity (estimated from binding energies) of most of the electrons near its path.

The neutralization-ionization method using two gas targets was employed to study the sequence ${\mathrm{H}}_3^{+}$ → ${\mathrm{H}}_3$ → ${\mathrm{H}}_3^{+}$. The existence of long-lived states of the neutral molecule ${\mathrm{H}}_3$ ($\tau \gtrsim 3\times {10}^{-7\mathrm{}}$ s) is demonstrated, any ambiguity due to the presence of HD molecules being definitively removed. Dissociation cross sections of the molecular ion in argon have been measured and the dissociation cross section of the neutral molecule, the electron-capture, and the electron-loss cross sections have been estimated. The capture cross section for ${\mathrm{H}}_3^{+}$ is extremely small (∼1 b at 1 MeV) and decreases very rapidly with the velocity of the incident ion beam. It is suggested that these measured cross sections concern the formation of ${\mathrm{H}}_3$ Rydberg states in a narrow band of $n$ and $l$ values.

We have measured the rate coefficient [$k=5.6\mathrm{}\times {10}^{-12\mathrm{}}$ ${\mathrm{cm}}^3$/s (±37%)] for associative ionization occurring in collisions between two $\mathrm{Na}\mathrm{}\left(3P\right)\mathrm{}$ atoms, by measuring the current resulting from excitation of Na vapor by cw-laser radiation. The major source of uncertainty in measurements of this type is in the determination of the number density and spatial distribution of excited atoms. Here we have measured the excited-atom density by three methods, and we have studied the spatial distribution of excited atoms in detail. Our rate coefficient at $T\sim 650$ K is compared to other experimental results.

A theory of the ionization of inner-shell electrons during ${\beta }^{+}$ decay is obtained by modifying a theory of inner-shell ionization during ${\beta }^{-}$ decay presented previously. The theory includes the contributions of both the shakeoff and direct-collision mechanisms and yields results whose relative accuracy is of order $Z\alpha$. Numerical results for the $K$-shell ionization probability are presented for several nuclides, including ${}_{}{}^{58}{}_{}{}^{}\mathrm{Co}$, ${}_{}{}^{64}{}_{}{}^{}\mathrm{Cu}$, and ${}_{}{}^{65}{}_{}{}^{}\mathrm{Zn}$; they demonstrate that, contrary to the ${\beta }^{-}$ case, the direct-collision mechanism plays an essential role in inner-shell ionization during ${\beta }^{+}$ decay, confirming a conjecture by Law. When compared with the results of recent experiments, they are found to give significantly better agreement than do the results of previous theoretical work.

Systematic investigations of charge-transfer reactions $\mathrm{H}\mathrm{}\left(1s\right)+A^{Z+}\to {\mathrm{H}}^{+}+A^{\mathrm{}(Z-1\mathrm{})+}\mathrm{}(n,l)\mathrm{}$ ($A^{Z+}$ being a fully stripped ion) within the multichannel Landau-Zener theory with rotational coupling included (MLZRC) are presented. Total cross-section ($\sigma$) calculations in the energy region 0.03-80 keV/amu for selected projectiles with charges $5\le Z\le 74$ are performed. Oscillations in the $Z$ dependence of $\sigma$ are observed at low collision energies in the low-$Z$ region. Above this region the $Z$ dependence of $\sigma$ is linear. The $n$,$l$ distributions of captured electrons are investigated and results for the partial cross sections ${\sigma }_n$ for a number of reactions are presented. The maxima of $n$ distributions appear at $n_m\approx Z^{\frac{3}{4}}$ (in accordance with other theoretical predictions) and have a weak velocity dependence. Validity and limitations of the MLZRC model and the obtained results are discussed.

The relativistic plane-wave Born-approximation calculations have been performed for $K$-shell ionization by proton impact. The $K$-shell ionization cross sections have been obtained by the use of relativistic hydrogenic (Dirac) wave functions for target electrons. The ratio of the relativistic cross section to the nonrelativistic one is evaluated and compared with various approximate correction methods for the electronic relativistic effects. Similar comparison is made for the $K$-shell ionization cross sections corrected for binding-energy and Coulomb-deflection effects. These results are also compared with the experimental data.

Total electron-capture cross sections have been measured for collisions of ${\mathrm{Fe}}^{q+}$ ions ($3\le q\le 14$) with H and ${\mathrm{H}}_2$ at energies in the 10-95 eV/amu range. The cross sections increase approximately linearly with increasing ionic charge $q$, and, for atomic hydrogen, can be represented by the empirical formula: $\sigma =q\times {10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$ with an rms deviation of ±26%. For ${\mathrm{Fe}}^{5+}$ and ${\mathrm{Fe}}^{6+}$, for which higher-energy data exist, the cross sections are found to be essentially energy independent over the range $17<E<\mathrm{}2000\mathrm{}$ eV/amu. The cross sections for an atomic H target average 26% larger than for ${\mathrm{H}}_2$. Agreement with generalized theoretical models is within a factor of 2 or better.

Absolute electron-transfer cross sections have been measured for ${\mathrm{H}}^{+}$ and ${\mathrm{H}}^0$ in collisions with Ca and Sr metal vapor targets for energies between 1 and 70 keV. The measurements include cross sections for single- and double-electron capture by ${\mathrm{H}}^{+}$ and single-electron capture and loss by ${\mathrm{H}}^0$. The single-electron capture cross section for ${\mathrm{H}}^{+}$ incident has been calculated using the binary-encounter approximation, and agrees with experiment to within a factor of 2 for energies between 2 and 70 keV. The electron-detachment cross section for ${\mathrm{H}}^{-}$ in collisions with Ca and Sr is determined from the present measured data and previously measured charge-state equilibrium fractions. The high-and low-energy structure in the cross sections for single- and double-electron capture by ${\mathrm{H}}^{+}$ are discussed in terms of the importance of inner-shell capture at high energies and a molecular picture at low energies, and the cross sections are compared to those for Mg and Ba targets published in a previous paper. The cross section for single-electron capture by ${\mathrm{H}}^0$ rises at low energies; that for electron detachment from ${\mathrm{H}}^{-}$ decreases at low energies in agreement with theoretical predictions of Olson and Liu. This situation is discussed as the mechanism responsible for large negative-ion equilibrium yields at low energies for alkaline-earth targets.

An optical potential for taking account of the continuum in a coupled-channels calculation of electron scattering from atoms and ions must reproduce the total ionization cross section. This is tested here for a range of atoms and ions, using a momentum-space formulation based on the orthogonalized Born-Oppenheimer approximation to the ionization amplitude. The theory is quite acceptable as a fast calculation of total ionization cross sections, particularly at higher energies where distorted-wave methods are cumbersome. It compares quite satisfactorily with distorted-wave calculations for ions at lower energies near the maximum of the cross-section curve.