A hybrid second-order model, in which the first-Born-approximation amplitude is evaluated by using an improved choice of the target continuum-state wave function and the second-Born-approximation amplitude in the usual way, is used to obtain the triple-differential cross sections for the ionization of helium. The results are compared with the recent data of Jung et al. in the coplanar asymmetric geometry at an incident electron energy of 600 eV and are found to be in very good agreement.

A calculation of 〈$r^2$〉 for Ne from 35-keV electron scattering data is given. The result is compared with the former experimental value given by the diamagnetic susceptibility. The scattering result agrees with the theoretical calculations involving configuration-interaction wave functions but differs from the experimental value.

We present numerical calculations of the photoionization of atomic hydrogen in the presence of a strong dc electric field, using three-photon excitation with two-photon resonance with intermediate Stark states. The systematics of the dependence of the cross section on the intermediate Stark states is calculated for the n=2 to n=9 manifolds. Our results indicate that one can use ‘‘charge-shape tuning’’ to selectively excite and enhance Stark-induced giant dipoles near E=0 in hydrogen without the excitation of the overlapping continuum. Frequency selectivity can be used to excite from 1s (spherical charge) an intermediate whose charge is focused along the field followed by another excitation to the giant dipoles. Charge tunability can be achieved by controlling the degree of focusing by choice of the field and intermediates.

The influence of the vessel form, the aspect ratio Γ, and the heating gradient on the wavelength-selection mechanism in a hexagonal pattern, corresponding to Bénard-Marangoni convection, are studied experimentally. The pattern changes in an almost continuous way and shows a wavelength increase when Γ becomes greater. The wavelengths for a container where Γ>70 and for an infinite extended layer are nearly identical.

The condition for stabilizing the universal drift mode by superimposing an external high-frequency Trivelpiece-Gould mode is investigated based on a new mode-coupling process (plasma-maser effect). The energy up-conversion from the universal drift mode to the high-frequency rf field stabilizes the low-frequency drift mode. Under suitable conditions, the new method based on plasma-maser interaction is effective at a smaller relative magnitude of the rf field than the one based on a ponderomotive force in a narrow sense.

A coupled system of nonlinear evolution equations describing the combined effects of diffusion and reactions, e.g., fusion reactions or electron-ion recombinations, is transformed into a system of coupled similarity equations in one, two, and three dimensions. A description of the evolution of the coupled system for special though physically relevant situations, e.g., the diffusion of an ignited high-density fusion plasma (thermal-thermal reactions) of tritium and deuterium, is obtained in terms of a particular similarity solution.

We have studied two aspects of chaotic behavior in stimulated Raman scattering. The route to chaos in this nonlinear optical process has been shown to be period-doubling bifurcations. The fractal dimension of the Raman strange attractor has been calculated for different values of damping of the Stokes mode.

The production of (2$s^2$${)\mathrm{}}^1$S, (2$p^2$${)\mathrm{}}^1$D, and (2s2p${)\mathrm{}}^1$P states formed by double capture into projectile autoionizing states was measured with high resolution using 0° Auger spectroscopy in 150–500-keV ${}_{}{}^3{}_{}{}^{}\mathrm{He}_{}^{2+}{}_{}{}^{}$+He collisions. Absolute cross sections for these states were determined to lie approximately between ${10}^{\mathrm{-}18}$ and ${10}^{\mathrm{-}21}$ ${\mathrm{cm}}^2$, the production of the (2$s^2$${)\mathrm{}}^1$S state being dominant. An extension of a continuous distorted-wave independent-particle model to the calculation of double-electron-capture cross sections was found to overestimate our results by a large factor, ranging between 6 and 75.

We show that in relativistic heavy-ion collisions the independent-electron model can be used to predict cross sections for multiple inner-shell ionization in a single collision. Charge distributions of 430- and 955-MeV/amu ${\mathrm{U}}^{90+}$, ${\mathrm{U}}^{89+}$, ${\mathrm{U}}^{83+}$, and ${\mathrm{U}}^{68+}$ beams emerging from thin solid targets were used to obtain single- and multiple-electron stripping cross sections. The probabilities of stripping electrons from the K, L, or M shells were calculated using the semiclassical approximation and Dirac hydrogenic wave functions. The data generally agree with theory. An influence of the Auger effect is seen in ${\mathrm{U}}^{68+}$ collisions.

We compute in the framework of a multifractal model for three-dimensional fully developed turbulence the number of degrees of freedom N as function of the Reynolds number R. $N— depends on the whole spectrum of singularities h related to the anomalous scaling of the velocity differences. On the other hand, we have also considered what is the total number $N_T^{\mathrm{*}}$ of equations needed in a computer simulation since N just has theoretical relevance. We stress, however, that the main features of intermittency can be described by an effective number N${̃}^{\mathrm{*}}$ which is much smaller than $N_T^{\mathrm{*}}$ because N${̃}^{\mathrm{*}}$ neglects very improbable events. We show that $N_T^{\mathrm{*}}$∝$R^3$ while we get from a fit of experimental data that N${̃}^{\mathrm{*}}$∝$R^{2.3}$ is of the same order of N∝$R^{2.2}$. .AE

Bubble fields generated in a liquid (water) irradiated with sound of high intensity are investigated by high-speed holographic cinematography at framing rates up to 69?0 holograms per second. The period-doubling route to chaos found previously in the sound output from the liquid also shows up in the bubble oscillations. This observation confirms the view that the nonlinear acoustic response of the liquid is mediated by the bubbles and their nonlinear oscillations.

We consider the factorization of two vector constants of the motion ${\mathrm{C}}^{\pm }$, which were recently introduced for the Coulomb problem [O. L. de Lange and R. E. Raab, Phys. Rev. A 34, 1650 (1986)]. The operators ${\mathrm{C}}^{\pm }$ are quantum-mechanical analogs of the classical conserved vectors (1∓iL^×${)\mathrm{A}}_c$ where L is the orbital angular momentum vector and ${\mathrm{A}}_c$ is the Laplace-Runge-Lenz vector. It is shown that ${\mathrm{C}}^{\pm }$ can be factored in two different ways to yield operators which, apart from their dependence on the constants of the motion ${\mathrm{L}}^2$ and H, are linear in either p or r. In this way we obtain 16 abstract operators. The properties of these operators are investigated and the following observations are made: (i) Twelve are ladder operators for the quantum numbers l, and l and m, in the eigenkets ‖lm〉 of ${\mathrm{L}}^2$ and $L_z$. In linearized, differential form six of these operators are ladder operators for the spherical harmonics in the coordinate representation, while the other six are the corresponding operators in the momentum representation. (ii) Two operators factorize an operator related to the Hamiltonian. In linearized, differential form they are the two ladder operators for the radial part of the coordinate-space wave functions which were discovered by Schrödinger. (iii) Two operators yield a factorization which is related to Hylleraas’s equation. In linearized, differential form they are ladder operators for the radial part of the momentum-space wave function.

A novel approach to energy-density-functional theory, based on point transformations in coordinate three-dimensional space, is advanced. These point transformations are discussed in the context of one-electron densities and many-electron wave functions. In particular, the group properties of these transformations are discussed and it is shown by incorporating some of the topological properties of the one-electron density, as discussed by Bader et al., that the n-representability conditions for densities may be reformulated. This is done in this paper for atoms. As a simple application of this method, the local-density approximation is obtained by computing the point transformation for a slowly varying density. Also the relationship between this method and the one based in equidensity orbitals is discussed.

The theoretical aspects of the β-decay process in ${\mathrm{T}}_2$ as they relate to neutrino-mass experiments are discussed. We present new results from stabilization method calculations for the resonance states of the daughter ${\mathrm{HeT}}^{+}$ ion. The probabilities for this system to be found in various final shake-off states after the ${\mathrm{T}}_2$ decay have been calculated. The β-decay energy spectra are generated using probability distributions of various accuracies. It is shown that, if the actual neutrino mass were 30 eV, one would obtain masses of 6 and 25 eV using spectra of the bare tritium nucleus and the tritium atom, respectively, for analyzing the data. If the nuclear motion effects were neglected, the obtained mass would be 30 eV but the end-point energy would be shifted by 1.5 eV. For a 30-eV mass the accuracy of our calculations is much better than necessary: Substituting our data by those obtained with a very poor basis set changed the neutrino mass only by about 1 eV. For a 1-eV mass, however, the less accurate calculation would introduce a substantial error. In particular, including the effects of nuclear motion is important to correctly determine a 1-eV mass. The accuracy with which resonance states of the daughter ion are determined has practically no influence on the final result. We argue that most solid-state effects will lead to corrections small compared to the expected experimental errors.

Dynamic quadrupolar polarizabilities ${\alpha }_q$(ω) for the sodium isoelectronic sequence up to Z=18 have been calculated, and analytic representations of Rydberg d- and s-state wave functions have been obtained using time-dependent coupled Hartree-Fock theory. The excitation energies are obtained from the position of the poles of a frequency-dependent functional. The estimated static limit ${\alpha }_q$(ω${)}_{\omega \to 0}$ compares well with existing static results, and the transition energies are in good agreement with the spectroscopic values. The accuracy of the excited-state wave functions is checked indirectly by evaluating quadrupolar oscillator and multiplet strengths which compare favorably with other results wherever available. Furthermore, the quantum-defect values are estimated using complete screening and compared with those obtained spectroscopically. Excellent agreement is observed.

A new approach is presented for determining the dynamical self-structure factor $S_s$(q,ω) for a multicomponent dilute gas mixture. The starting point is the three-dimensional linear inhomogeneous Boltzmann equation with a Maxwell interaction potential. It is shown that the dynamical self-structure factor can be expressed analytically in terms of a continued fraction of infinite but sparse matrices. Although other methods and approximation schemes for calculating $S_s$(q,ω) via the Boltzmann equation have been suggested so far, the method and the results presented here are new in the following sense. First, to our knowledge there does not exist an analytical solution of the Boltzmann equation covering the entire (q,ω) range for $S_s$(q,ω) and yielding in particular the correct dynamical self-structure factor $S_s$(q,ω) for both the hydrodynamical limit (q→0) and the free-gas limit (q→∞). Second, at least the example considered in this paper shows most clearly that the commonly suggested expansion of $S_s$(q,ω) in a continued fraction of scalars cannot be regarded as a useful expansion method.

We have developed a systematic approach for identifying a priori and computing accurately wave functions of a special class of doubly excited states which seem to lead in a regular way to the Wannier state at the two-electron ionization threshold. As an application, we present a variety of new and experimentally verifiable results for the ${}_{}{}^1{}_{}{}^{}\mathrm{°}$ symmetry in ${\mathrm{H}}^{\mathrm{-}}$, He, and ${\mathrm{Li}}^{+}$.

A nonorthogonal configuration-interaction procedure has been used to calculate adiabatic energy curves of ${\mathrm{ArH}}^{+}$. The basis functions are a mixture of typical molecular-orbital configurations and typical valence-bond (Heitler-London) configurations. This gives an economical description of the wave functions, allowing an easy tracing of various diabatic states through the adiabatic states and a clear identification of the asymptotic states. The results are used to rationalize the unexpectedly large production of ${\mathrm{Ar}}^{2+}$+${\mathrm{H}}^{\mathrm{-}}$ from collisions of ${\mathrm{H}}^{+}$ with Ar.

The distorted-wave approximation is used to calculate the double-electron-excitation cross section of Li${(}^2$S${\mathrm{-}}^4$P) and Be${(}^1$S${\mathrm{-}}^3$P) by electron impact. The distortion in the incident and exit channels incorporates the distortion effects of the static, polarization, and exchange potentials appropriately. The results are compared with the Born-Oppenheimer approximation.

Profiles of the singly ionized strontium resonance line at 421.6 nm (4p ${\mathrm{}}^2$${\mathrm{P}}_{1/2}$–4s ${\mathrm{}}^2$${\mathrm{S}}_{1/2}$) which are collisionally broadened by argon have been measured from the line core to near-wing region (within the distance of Δν≲50 ${\mathrm{cm}}^{\mathrm{-}1}$ from the line center). The observed broadening rate of the core is (1.87±0.25)×${10}^{\mathrm{-}20}$ ${\mathrm{cm}}^{\mathrm{-}1}$/${\mathrm{cm}}^{\mathrm{-}3}$ at 690 K. A clearly asymmetric profile has been observed in the wing region. These results are discussed by considering semiclassical impact and quasistatic theories combined with theoretical interaction potentials for the ${\mathrm{Sr}}^{+}$-Ar pair which were previously reported by the present authors.