It is shown for the particular example of a berylliumlike atom that the Hartree-Fock 2s inflection point does not occur at the node of the wave function, as it must for a central potential. Local exchange approximations, therefore, cannot be expected to be capable of exactly modeling the effect of the exchange interaction.

Differential cross sections for the electron-capture process in proton-hydrogen collisions at incident proton energies of 25, 60, and 125 keV are calculated with use of the eikonal approximation in which the distortion by the internuclear interaction is included. The results agree very well with experiments. Capture into excited final states is appreciable, particularly at low energies.

We outline a statistical model for the cross section characterizing the integrated intensity of the redistributed radiation resonantly scattered from a localized scattering center coupled to a thermal bath. The theory exploits a formal analogy between the resonant scattering of light and nuclear scattering in the compound-nucleus regime. Using statistical models developed for the nuclear problem, we express the cross sections describing the quasielastic scattering and the redistributed Raman scattering in terms of parameters which can be extracted from measurements of the coherent-scattering cross sections.

In a previous paper [G. Birnbaum et al., Phys. Rev. A 29, 595 (1984)] the collision-induced rototranslational absorption spectra of ${\mathrm{H}}_2$-He were computed from first principles, with the assumption of isotropic interaction. Here, we study the effects of the anisotropy on the basis of a distorted-wave approximation. Computed spectral intensities and shapes of the rotational lines differ from the previous results by less than the numerical uncertainties of the computations (∼1%), except in the far wings where intensities are increasingly greater than comparable results based on isotropic interaction.

A relativistic dispersion relation, accurate to order of ${\alpha }^2$$Z^2$, is presented for the real part of x-ray atomic anomalous scattering factor f’.

The index of refraction of a free-electron-laser (FEL) pulse is derived directly, independently of the general FEL analysis, by considering the propagation of an electromagnetic wave along an electron beam that is penetrated by a static magnetic field.

In contrast to coherent states ‖α〉 which have zero Hanbury Brown and Twiss Effect [i.e., $g^{\mathrm{}\left(2\right)\mathrm{}}$(0)=1], it is shown that generalized coherent states ‖n,α〉 are antibunched for ‖α${\Vert }^2$<(1/2). The range of values for α (real) in terms of the squeezing parameter r (real) for the squeezed coherent state ‖α,r〉 in order to exhibit bunching and antibunching are obtained. The conditions and the exact range of values for r and α for a given n for generalized squeezed coherent states ‖n,α,r〉 to exhibit bunching and antibunching are also obtained.

A nonlinear Schrödinger equation is derived which governs the nonlinear interaction of the adiabatic particle motion with finite-amplitude ion-acoustic waves in an unmagnetized plasma. It is found that the ion-acoustic waves remain modulationally stable and that the nonlinear wave can propagate in the form of dark envelope solitons.

A complex Lorenz system for convection due to interchange instability in collisional plasmas is derived from the classical two-fluid equations, including, among others, the effects of magnetic field curvature, finite ion gyroradius, and compressibility. The correspondences and differences between the presently derived system and the Lorenz system are discussed. For a wide regime of physical parameters the system is found to evolve towards a nonlinear equilibrium, but chaotic behavior is observed for the regime in which the real Lorenz system is chaotic.

We give an averaging solution for the conductivity of a two-phase mixture with enhanced interface conductivity. The results obtained are in qualitative agreement with the measured dependence of the conductivity of an ionic conductor (LiI or AgI) on the content of insulating material (${\mathrm{Al}}_2$${\mathrm{O}}_3$).

Perturbations of the relativstic quantum plasma are studied using Wigner-function techniques. In addition, a generalized fluctuation-dissipation theorem is given that relates the perturbed Wigner function to the fluctuations of the Wigner function at thermal equilibrium. As a consequence, the relativistic quantum version of the fluctuation-dissipation theorem is obtained and analyzed.

The solution of various diffusion problems, in both continuous and discrete systems, can be expressed in terms of a Laplace transform of the exponential function of a fractional power. In this Brief Report the need for a complete asymptotic analysis of these functions is discussed in the context of one-dimensional diffusion with random trapping sites and the necessary asymptotic analysis is carried out.

Due to fluctuations around the metric entropy of chaotic dynamical systems there exists a spectrum of invariant dynamical scaling indices, complementary to the range of invariant static scaling indices which have been discovered and applied recently. The basic scaling behavior in both cases is shown to be rooted in the thermodynamic formalism of dynamical systems. An explicit simple example of these ideas is given, stressing their use in characterizing complex behavior.

If the time evolution of an irreversible process is described by a completely positive quantum-dynamical semigroup a systematic formulation in terms of coherence vectors is of particular advantage since the time change of their length and relative scalar product determines, to a large extent, the relative entropy with respect to a unique final state and, ultimately, the total entropy production. As examples, general exact formulas for two-level systems are given and, in arbitrary dimensions, for a weakly irreversible process close to the central state, a first-principles derivation of the phenomenological Onsager coefficients is outlined.

In a sine-Gordon system with loss and applied ac driver, a breather can be maintained as a persistent entrained oscillation if the driver is strong enough. The threshold field is determined by a perturbation method and compared to numerical experiments. Excellent agreement is found.

We establish the identity of the persistence length of an easily bendable polymer with the critical length for the onset of elastic instability toward bending induced by the root-mean-square twist. For a polymer of arbitrary bending stiffness the identity remains approximately valid; the ratio of persistence length to critical length is always within 20% of unity.

In a recent article [Phys. Rev. A 31, 2107 (1985)] Leasure and Balint-Kurti claim to give a more efficient algorithm than any previously available for determining matrix elements of the Hamiltonian in valence-bond calculations. Actually, an algorithm of no significant difference and the same efficiency has been available since 1972 and has been applied to valence-bond calculations.

The computational effort needed for the evaluation of Hamiltonian matrix elements between nonorthogonal Slater determinants is analyzed.

We demonstrate that the equations presented by Leasure and Balint-Kurti are a reformulation of prior results.

In our paper [S. C. Leasure and G. G. Balint-Kurti, Phys. Rev. A 31, 2107 (1985)], we presented a new procedure for calculating Hamiltonian matrix elements between Slater determinants constructed from nonorthogonal orbitals. This is the central problem of valence-bond theory.