Recently published Stark broadening data of potassium ns-4p and nd-4p lines have been reexamined. Newly derived data are compared with theoretical results obtained from a simple approximative formula. The experiment agrees with theoretical results, in average, within ±20%.

When our experimental Stark widths of potassium ns-4p and nd-4p lines are reanalyzed, we find good agreement with theory.

Recently Talukdar et al. [Phys. Rev. A 29, 1865 (1984)] found that the so-called ‘‘half-off-shell’’ Coulomb T matrix $T_{\mathrm{Cl}}$(p,k;$k^2$) were to be (i) singular at p=0 for l>0, and (ii) increasing for increasing l. We point out that both these results are incorrect: (i) From the simple closed formula $t_{\mathrm{Cl}}$(p,k;$k^2$)=(2γ/πp) exp(3πγ/2)$Q_l^{i\gamma }$($p^2$+$k^2$ )/2pk), 0<p<k , one can see by inspection that $t_{\mathrm{Cl}}$(p,k;$k^2$)=O($p^l$), for p→0, precisely as the Coulomb-potential matrix element and the off-shell Coulomb T matrix. (γ is Sommerfeld’s parameter and $Q_l^{i\gamma }$ is Legendre’s function of the second kind.) (ii) For all p≠k, $t_{\mathrm{Cl}}$(p,k;$k^2$) tends exponentially to zero as l tends to infinity: as $l^{\mathrm{-}1/2}$ exp[-l‖ln(p/k)‖].

We present a direct measurement of the velocity dependence of the associative-ionization (AI) cross section for collisions between Na${(}^3$P) atoms in the energy range 0.08–0.29 eV in a crossed-beam experiment using a Doppler-shift velocity-selection technique. The AI cross section at first decreases, reaches a minimum at about 0.15 eV, then sharply increases with collision energy. Interpretation of the results in terms of a semiclassical theory of AI indicates that more than one potential surface of Na${(}^2$P${+\mathrm{}}^2$P) must be involved in the AI process.

The correlations within a layer at a distance R from the origin of large diffusion-limited aggregates were investigated by determining the tangential correlation function $c_R$(θ) as a function of the angle θ. We find that for θ≪1$c_R$(θ) decays algebraically with an exponent ${\alpha }_{\perp }$=0.41±0.04, which is different from the corresponding value obtained for the radial correlations, indicating that the aggregates are internally anisotropic. This fact has an effect on the results obtained for the fractal dimension in the form of the appearance of a correction-to-scaling term.

The behavior of Rydberg atoms in a recent experiment involving selective excitation in combined ac and dc electric fields is shown to be consistent with the predictions of a one-dimensional model incorporating only the extreme level of each Stark manifold. For low microwave powers, the excitation is resonant and is described qualitatively by multiphoton perturbation theory. For higher powers, an alternative stochastic theory predicts rapid ionization at all frequencies, as observed experimentally.

Longitudinal excitation discontinuities (kinks) that arise from partial-sample switching in increasing absorption bistability are predicted theoretically and observed in a sharp-cut color filter. The kinks give rise to a sawtooth output temporal dependence for a triangular input shape. Kinks are an emphatic illustration of the local nature of increasing absorption bistability.

A nonequilibrium, bistable flow driven by exponentially correlated Gaussian noise is considered. An approximate, nonlinear Fokker-Planck–type equation, modeling effectively the long-time dynamics of the bistable, non-Markovian flow is constructed, and the mean sojourn time is evaluated in the limit of weak noise. Keeping the noise strength constant, the mean sojourn time is predicted to undergo an exponential increase with increasing noise correlation time. Representing the bistable, colored noise dynamics with an electronic circuit, the mean of the sojourn time and the sojourn-time distribution have been measured experimentally. The experiments confirm the exponential increase for the mean sojourn time and close quantitative agreement with this newly proposed theoretical approach is found. In contrast, previous approximation schemes which expand around the Markovian theory (zero noise correlation time) would predict for this case an exponentially decreasing mean sojourn time upon increasing the noise correlation time, in marked disagreement with the present measurements.

The long-time behavior of diffusion-controlled trapping by randomly distributed static traps with a finite size is investigated theoretically. Two significant finite-size effects, the increase of an effective trap density, and the decrease of an effective dimensionality, are clarified. The trapping in the presence of strong attractive interactions between particles and traps, that by polymers or generally random fractals, and the occurrence of a crossover in several systems, are discussed in some detail.

An amplitude equation for a codimension-two bifurcation point is studied in the presence of a periodically modulated Rayleigh number. The boundary limits of the convective state and flow patterns above threshold are calculated. It is found that the system exhibits chaotic behavior close to the codimension-two point. The Lyapunov exponent associated with these trajectories is calculated.

The Rayleigh-Ritz variational principle can be modified to generate upper bounds to the exact ground-state energy even when the local repulsive core of a two-body interaction V is replaced by the corresponding T or G matrix calculated for a negative energy (-ω). One obtains this result by adding a suitable counterterm to the resulting regularized Hamiltonian and selecting ω as an additional variational parameter.

The derivation of model Hamiltonians such as crystal-field and spin Hamiltonians requires the decoupling of electrons, which may be done by defining an appropriate equivalent Hamiltonian $H_{\mathrm{eq}}$. The connection between $H_{\mathrm{eq}}$ and the original Hamiltonian, and between the respective eigenfunctions, is explicitly given. The eigenfunctions of $H_{\mathrm{eq}}$ are linear combinations of simple products of atomic spin orbitals, the latter being chosen in such a way that its antisymmetrization leads to a linearly independent set. The problem is then reformulated in a chosen subspace (effective space) via the effective-Hamiltonian formalism. The model Hamiltonian $H_{\mathrm{mod}}$ is then obtained by projecting out the undesired degrees of freedom. If in the two-atom two-electron case one keeps in $H_{\mathrm{mod}}$ only first-order terms in the interatomic interaction, one gets the usual Heitler-London approximation. For this reason the formulation has been called the extended Heitler-London method. As an illustration the formalism is applied to the ${\mathrm{H}}_2$ molecule, where the usual Heisenberg Hamiltonian is rigorously derived and the values of the energy baricenter and magnetic exchange constant are given, up to the second order of perturbation theory.

Intermediate-coupling collision strengths are calculated for all transitions between the states 3$s^2$ ${}^1$$S_0$, 3s3p(${}^3$$P_0$,1,2, ${}^1$$P_1$), 3$p^2$(${}^1$$D_2$, ${}^3$$P_0$,1,2, ${}^1$$S_0$), 3s3d(${}^3$$D_1$,2,3, ${}^1$$D_2$), and 3s4s(${}^3$$S_1$, ${}^1$$S_0$). Calculations are carried out in a ten-state distorted-wave approximation. Resonance effects are considered by using multichannel quantum-defect theory, and relativistic effects in the target Hamiltonian are taken into account in the Breit-Pauli formulation. The important 3$s^2$ ${}^1$$S_0$–3s3p ${}^3$$P_1$ transition is found to be subject to large resonance enhancement, as previously shown by other workers for less highly charged Mg-like ions. Term coupling among the target states also affects several transitions considerably. Present results are compared with previous calculations; some significant differences are noted. The new results suggest a serious discrepancy between calculated and observed relative intensities of the 284.2-Å (resonance) and 417.3-Å (intercombination) lines for Fe xv in the Sun, but will reduce the discrepancy for this ratio for other Mg-like ions observed in tokamak plasmas.

A new approach to the variational representation of the Dirac equation is presented. The method takes advantage of the conditions satisfied by the eigenfunctions at the origin. In this way, a variational representation of the complete Dirac-Coulomb spectrum without spurious roots is obtained. Rigorous proofs of bounds for the positive and negative variational eigenvalues, as well as differential and integral properties of the variational eigenfunctions, are given. An alternative approach to the elimination of spurious roots based on constraining the basis set to satisfy the right nonrelativistic limit is also presented.

A method of describing the nonlocality of the exchange and correlation energy and potential is used in a self-consistent spinless atomic calculation. The exchange and correlation potential $V_{\mathrm{xc}(\mathrm{r}\to )}$ is analytically written and used in the calculation of the total energies and orbitals eigenvalues of the self-consistent Kohn-Sham equations for the atomic case. The results for the lighter atoms and for other examples are discussed and compared with the results obtained within the framework of the local-density approximation (LDA). We also present an analysis of the shape and asymptotic behavior of the potentials. A comparison of the outcome of the method with the results of LDA, Hartree-Fock calculations, and other approximate descriptions of nonlocality effects clearly indicates the power of the method.

With use of the Sobolev-Hölder inequalities, certain rigorous interrelationships among the leading terms in the expansions of the kinetic- and the exchange-correlation-energy density functionals have been derived. This work has also been extended to include some quasiclassical connections. All these relationships are inequalities that have been tested numerically with use of Hartree-Fock densities for 1806 neutral atoms and their ions.

Molecular-dynamics simulations on cluster formation in compressed argon and xenon gases were performed, with use of a Lennard-Jones (6,12) potential together with Axilrod-Teller three-atom interactions and those of exchange type, applying results of a recent analysis of these three-body potentials [Phys. Rev. A 30, 1593 (1984)]. Selective stabilization of clusters ${\mathrm{Ar}}_{19}$, ${\mathrm{Xe}}_{13}$, and ${\mathrm{Xe}}_{19}$ (possibly also ${\mathrm{Xe}}_{25}$) was established, predominantly as a result of the three-atom exchange potential. It is conjectured that these exchange contributions, in combination with selective stability due to cluster ionization, explain the phenomena observed in time-of-flight mass spectroscopy experiments on rare-gas-atom clusters.

It is shown that, in order to yield physically well-behaved energy curves E(R), the wave-function components used in channel-coupling-array analyses of the ungerade states of ${\mathrm{H}}_2$ must obey a boundary condition which is derived herein. A very simple ansatz, obeying this new boundary condition, is constructed for the components corresponding to the lowest-lying triplet ${\mathrm{H}}_2$ ungerade state. Even though the ansatz is very crude, the resulting E(R) differs from that of an exact calculation by at most 0.04 a.u. and is well behaved as the internuclear separation approaches zero. Since previous ${\mathrm{H}}_2$ ungerade channel-coupling-array calculations yielded energy curves that were infinitely attractive as R→0, this paper provides the theoretical basis for a practical means of eliminating this unphysical behavior.