With use of a diabatic molecular representation in two states, resonant charge transfer in helium in the presence of a laser field has been studied within the semiclassical impact-parameter approximation. The laser-frequency dependence of the charge transfer cross section shows an anomalous-looking feature quite distinct from cases studied earlier involving excitation. An effect of the laser field on the angular distribution of the charge transfer ions is also indicated.

Solitary-wave- (SW) bearing systems described by nonlinear scalar fields are considered. It is shown that the existence of the ‘‘energy integral’’ makes it possible to determine the frequency spectrum of linear excitations of any SW, without detailed knowledge of the SW solution itself. One only needs to specify the boundary conditions which single out the desired SW. Examples and generalizations to multicomponent fields are discussed.

A kinetic calculation is presented for the electron thermal conductivity in dense plasmas, where the Spitzer-Haaumlrm theory is not valid. A simple expression is obtained for the generalized Coulomb logarithm which allows an extrapolation of classical results into the strongly coupled regime.

A scaling form for the pair correlation function of random fractals is combined with the scaling form of the percolation distribution of cluster sizes to obtain expressions for the static structure factor S(q) and first cumulant $K_1$ of the dynamic structure factor S(q,t) at the gel point. We find S(q)∼$q^{\mathrm{-}\mu }$ and $K_1$∼$q^3$ with μ=D(3-τ), where D is the fractal dimension and τ is the exponent for the distribution of cluster sizes. Special forms are suggested for the scaling functions to obtain results for the nonscaling regime.

This paper is an essential addendum to a previous paper [L. Ingber, Phys. Rev. A 29, 3346 (1984)]. Calculations are presented here to support the claim made in the previous paper that there exists an approximate one-dimensional solution to the two-dimensional neocortical Fokker-Planck equation. This solution is extremely useful, not only for obtaining a closed algebraic expression for the time of first passage, but also for establishing that minima of the associated path-integral stationary Lagrangian are indeed stable points of the transient dynamic system. Also, a relatively nontechnical summary is given of the basic theory.

The recent experiment of Morgan and Ederer on helium 2s2p ${}^1$$P^o$ has improved the agreement between theory and experiment substantially. To achieve higher accuracy in our theoretical result, we include the relativistic correction to the energy. The new result of 60.150 eV agrees excellently with the 60.151±0.010 eV of Morgan and Ederer. The wavelength for the 2p3p ${}^1$P–2s2p ${}^1$$P^o$ transition is also predicted to facilitate the observation of this ${}_{}{}^1{}_{}{}^{}\mathrm{P}_{}^{\mathrm{o}}{}_{}{}^{}$ state in an optical emission spectrum.

The propagation of nonlinear p-polarized electromagnetic surface waves in a model previously studied by Yu is studied here without restrictions on the field amplitudes. s-polarized waves are also studied. Results for the dispersion relations and field profiles are reported.

The exact renormalization approach of Ben-Avraham and Havlin [Phys. Rev. A 29, 2309 (1984)] can be generalized to obtain the thermal and magnetic exponents describing the statistics of self-avoiding walks on finitely ramified fractals. The exponents ν and γ for the two-dimensional Sierpiński gasket are equal to 0.7986. . . and 1.3752. . ., respectively.

A new family of fractals is investigated. The fractal dimension $D_f$ is found to be equal to a variable parameter of the model characterizing the strength of the screening. Thus we can make fractals with arbitrary $D_f$, and study anomalous diffusion as a function of $D_f$. Our data support a generalization we propose of the recent Aharony-Stauffer conjecture based on the spatial distribution of ‘‘growth sites’’ of a fractal.

Variational calculations with correlated basis sets have been carried out to obtain the nonrelativistic energies for the n ${}^3$S (n=2–6), n ${}^1$D (n=3–8), and n ${}^3$D (n=3–8) series in He i with estimated accuracies of ${10}^{\mathrm{-}3}$–${10}^{\mathrm{-}5}$ ${\mathrm{cm}}^{\mathrm{-}1}$. A comparison of the results with recently reevaluated experimental energy values, with the aid of available relativistic and mass-polarization corrections, suggests a value of 198 310.773(1) ${\mathrm{cm}}^{\mathrm{-}1}$ for the ionization energy for He i on an energy scale fixed by the 2 ${}^1$P value of 171 135.0000 ${\mathrm{cm}}^{\mathrm{-}1}$.

We have carried out an interferometer experiment to determine the phase shift of slow neutrons caused by the motion of a material medium. Within experimental error, we confirm the theoretical prediction of a null result for the case when the medium moves inside stationary boundaries. Upper limits on the energy dependence of neutron-nucleus potential and on the wavelength dependence of s-wave neutron scattering lengths are deduced.

A new three-photon double-resonance excitation scheme for ${\mathrm{H}}_2$ is combined with time-of-flight ion detection and is used for high-resolution spectroscopy of autoionizing and field-ionizing Rydberg states. Using modest laser powers, we have achieved a Doppler-limited resolution of 0.15 ${\mathrm{cm}}^{\mathrm{-}1}$.

New resonances have been observed in the fluorescence spectrum of atomic sodium, near the D lines, for both resonant and nonresonant laser excitation. The resonances are interpreted as arising from the interaction of the strong driving laser field and the three-level atom. Specifically, two simultaneously acting mechanisms are identified: resonantly enhanced three-photon scattering and excited-state Raman scattering.

A perturbative solution to the difference-differential equation describing the time evolution of a free-electron laser based on the Bambini-Renieri Hamiltonian is obtained. This solution indicates that the photon number distribution is always sub-Poissonian as long as the perturbation approximation is valid. This photon antibunching becomes much more prominent as more photons are emitted; so it can enhance the coherent properties of the free-electron-laser radiation in a way that is very welcome.

The onset of time dependence in Taylor-Couette flow has been studied experimentally for a range of the radius-ratio parameter η. The results indicate that there are two types of sensitivity to aspect ratio in agreement with recent numerical and experimental work. As η is varied, a continuous transition between the two types of sensitivity is uncovered instead of a critical value of η as indicated by the numerical model.

Results of the application of flux-corrected transport techniques to a two-dimensional numerical simulation of streamer propagation are presented. Characteristics such as diameter, velocity, shape, and density gradient of the head, and ionization in the body of the propagating streamer are determined. These results provide new insight into streamer propagation.

While the cluster statistics exponents for three-dimensional continuum systems have been shown to be the same as those of lattices, the cluster structure and the conductivity exponents of such continuum systems have not been reported before. Here we present the first determination of both the fractal dimension of clusters, D, and the conductivity exponent, t, for these systems. We further describe the ‘‘porcupine’’-like morphology of the clusters and the conductivity behavior in continuum anisotropic systems.

The energies and wave functions for the lowest six electronic ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$ states of the ${\mathrm{HeT}}^{+}$ molecule have been obtained for 0.6≤R≤4.0 bohr. The overlap integrals between these wave functions and those for the ground state of the ${\mathrm{T}}_2$ molecule have been calculated. The results show that the probability of ${\mathrm{T}}_2$ decaying into ${\mathrm{HeT}}^{+}$ discrete electronic states amounts to 0.852, with the lowest six states accounting for 0.8422.

Relativistic calculations of atomic-electron binding energies have been refined by using the relativistic LS-average scheme to treat open outer shells, by including self-energy corrections for shells up to 3p as well as 4s, and accounting for energy shifts caused by interaction with Coster-Kronig continua. The contributions of ground-state correlation were estimated from the pair energy calculated through nonrelativistic many-body theory. The need for a relativistic theory of correlations is noted. As in our previous work, the calculations include relaxation, the effect of finite nuclear size, Breit interaction, and quantum-electrodynamic (QED) corrections. Results are compared with binding energies measured on free atoms and with solid-phase measurements on metals that have been corrected for solid-state shifts; these shifts were calculated under the assumption of complete screening with the core-ionized site treated as a neutralized metallic impurity atom in the original metallic host. Discrepancies between experimental energies and relativistic independent-particle calculations including relaxation, QED, and finite-nuclear-size corrections are traced to correlation corrections, uncertainties in the self-energy, and neglect of the effect of (super-)Coster-Kronig fluctuations.

We show that the motion of a particle of mass m in a high-frequency time-dependent potential V(x→)=v(x→)cos(Ωt) is governed by a Schrödinger equation with time-independent effective potential $V_{\mathrm{eff}}$(x→)=∇→v(x→)⋅∇→v(x→) /4m${\Omega }^2$. The validity of this approximation and an exact formal solution based on the Wigner function are discussed for the case in which v(x→) is quadratic.