We show that a flow field, which can be either externally imposed or caused by the geometrical configuration, gives rise to a convective term or a material derivative in the resulting phase equation. The stationary solutions of this equation are in agreement with recent experimental results on convection with a through flux and on the flow between two rotating concentric cones (a modified Taylor configuration). We also discuss the fact that there is no additional independent dynamic degree of freedom associated with these flow fields.

By use of an adiabatic elimination procedure and a time scaling t^=${\tau }^{\mathrm{-}1/2}$t, where τ denotes the correlation time of colored noise ɛ(t), one arrives at a novel colored-noise approximation which is exact both for τ=0 and τ=∞. The theory is implemented for one-dimensional flows of the type ẋ=f(x)+g(x)ɛ(t). The approximation has the form of a Smoluchowski dynamics which is valid in regions of state space for which the damping γ(x,τ)=${\tau }^{-1/2}$-${\tau }^{1/2}$[f’1(g’/g)f] is positive and large; and times t≫${\tau }^{1/2}$/γ(x,τ). This novel Smoluchowski dynamics combines the advantageous features of a recent decoupling theory that does not restrict the value of τ, together with those occurring in the small-correlation-time theory due to Fox. The approximative theory is applied to a nonlinear model for a dye laser driven by multiplicative noise. Excellent agreement for the stationary probability is obtained between numerical exact solution and the novel approximative theory.

The fine-structure levels of helium from microwave data are coalesced into a single-term-value table by means of theories. It is found to yield transition frequencies in excellent agreement with some diode laser measurements and a consistent ionization energy of 198‖310.772‖2(5) cmsup-1. This value is 1 order of magnitude higher in precision and in accord with Martin’s value [Phys. Rev. A 29, 1883 (1984)], subject to the same assumption on the 2 ${}_{}{}^1{}_{}{}^{}P$ level. A semiempirical theory is developed and fitted to all levels (L≥2). The result suggests a modification in the usual usage of the polarization formula for the direct energy and extends its utility to the exchange energy.

We investigate the effects of quantized radiation reaction fields on the motion of a charged particle using the gauge-independent Wigner operator (GIWO) and gauge-independent Wigner function (GIWF) introduced earlier [Phys. Rev. A 33, 2913 (1986)]. To complement the equation of motion of the GIWO, the Heisenberg equations of motion of the quantized electromagnetic fields are solved within the Markov approximation. After considering the operator orderings and orders of magnitude of the radiation reaction terms, we eliminate the quantum fields from the evolution equation of the GIWO, and obtain for the GIWF a closed equation containing relaxation terms. As an example of the formalism we derive a Fokker-Planck equation (FPE) for the GIWF of a particle in a constant magnetic field. To the order ħ ${}_{}{}^0{}_{}{}^{}$ the classical radiation damping ensues, and the first quantum correction proportional to ħ emerges as diffusion. The diffusion operator turns out to be indefinite and the FPE consequently defies our attempts at a complete analysis, but we demonstrate that at least the coherent states constructed from the Landau levels exhibit a manifestly physical time evolution under the FPE. We point out that the GIWF calculated with quantized electromagnetic fields is divergent even if the fields are in the vacuum state, and suggest that the GIWF should be associated with the particle state by ignoring the quantized fields altogether.

Calculations are presented that show the behavior of a wave packet composed of alkali-metal-atom Rydberg states. We demonstrate that it is possible to localize such a wave packet in the polar and azimuthal angles. The evolution of this wave packet is equivalent to the precession of a classical Kepler orbit under the influence of a perturbing potential. In this case, the perturbation is the quantum defect of the alkali-metal atoms. An excitation scheme is proposed for producing these states and the results of a numerical model based on this scheme are presented. Finally, the interaction of these angularly localized wave packets with external fields is discussed and a method of detection is suggested.

With use of the neutron interferometric technique, the real parts of the bound-coherent scattering length, b, of ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$ have been precisely measured for five different incident neutron energies in the range of 30 to 92 meV. The value of b at each incident neutron energy was obtained from the average of two independent measurements using two samples of different thicknesses. The results are b=10.47±0.04 fm (E=30.34 meV), b=10.47±0.03 fm (E=41.02 meV), b=10.51±0.03 fm (E=51.43 meV), b=10.39±0.03 fm (E=74.90 meV), b=10.41±0.03 fm (E=91.39 meV). The uncertainty in these results is about an order of magnitude smaller than the present literature value. The small energy dependence of the observed scattering lengths has been used to establish the parameters of the negative energy resonance level (-1.4 eV) using the Breit-Wigner formalism.

In the distorted-wave formalism we have proposed a modification in the peaking-impulse approximation suitable for asymmetric collisions. Using this method we have calculated the charge-transfer cross section for K-K capture in collisions of protons with carbon, nitrogen, oxygen, neon, and argon in the energy range of 0.15–20.0 MeV. The present modified peaking-impulse approximation, amenable to exact calculations for the transition amplitude, reproduces results in favorable agreement with observed data and existing theoretical results.

Dielectronic recombination of the iron ions ${\mathrm{Fe}}^{15+}$, ${\mathrm{Fe}}^{23+}$, and ${\mathrm{Fe}}^{25+}$ has been studied in the isolated-resonance, distorted-wave approximation. The cross-section calculations include the dielec- tronic transitions associated with the 3s→3l and 3s→4l excitations in ${\mathrm{Fe}}^{15+}$, the 2s→2p and 2s→3l excitations in ${\mathrm{Fe}}^{23+}$, and the 1s→2l excitations in ${\mathrm{Fe}}^{25+}$. The effects of external electric fields have been included by employing intermediate-coupled, field-mixed eigenvectors for the doubly excited Rydberg states, determined by diagonalizing a Hamiltonian matrix which includes the internal electrostatic and spin-orbit terms, as well as the Stark matrix elements. The field effects are found to be quite large in ${\mathrm{Fe}}^{15+}$, relatively small in ${\mathrm{Fe}}^{23+}$, and negligible in ${\mathrm{Fe}}^{25+}$. The calculations indicate that there are large resonances near threshold in ${\mathrm{Fe}}^{23+}$ that are unaffected by external fields and may be measurable in new experiments currently being designed. In addition, the contributions of radiative recombination and the possible interference between radiative and dielectronic recombination in low-lying resonances are considered. Even though the radiative recombination cross sections may be appreciable near threshold in ${\mathrm{Fe}}^{15+}$ and ${\mathrm{Fe}}^{23+}$, the interference between these processes appears to be completely negligible.

Differential and integral cross sections for electron-impact excitation of the b ${\mathrm{}}^3$${\Sigma }_u^{+}$ state of ${\mathrm{H}}_2$ have been determined in the 20–100-eV impact energy region. The calibration of the cross sections was achieved through the ${\mathrm{H}}_2$ elastic scattering cross sections, which in turn were normalized to absolute He elastic scattering cross sections. Comparison is made with available experimental data and with theoretical results applying Born-Ochkur-Rudge, distorted-wave, and close-coupling approximations.

A model based on the Hartree-Fock-Slater theory is proposed for the charge transfer in ionic materials. Application of this model to some diatomic molecules is demonstrated. Most available experimental data are well reproduced.

The origin of giant resonance effects in the electron-impact ionization of heavy (Z>50) atoms and ions is discussed in terms of the potentials governing the scattering states. Calculations are presented for electron-impact ionization of the 4d subshell in Xe, ${\mathrm{Cs}}^{+}$, ${\mathrm{Ba}}^{2+}$, ${\mathrm{Xe}}^{+}$, and ${\mathrm{I}}^{+}$, and for ionization of the 4f subshell in ${\mathrm{Eu}}^{+}$, ${\mathrm{Tm}}^{+}$, ${\mathrm{Yb}}^{2+}$, ${\mathrm{Lu}}^{3+}$, and ${\mathrm{W}}^{+}$. .AE

Molecular ionization by electron impact is examined in the Born-Oppenheimer approximation where the rotational and vibrational motions of the nuclei are considered separable. Expressions for the differential cross section, applicable to an exact treatment of the adiabatic electronic wave functions, are derived in terms of a momentum-transferred summation for three levels of experimental resolution, spatially unpolarized, spatially unpolarized and rotationally unresolved, and spatially unpolarized and rotationally and vibrationally unresolved. Several possible advantages of a momentum-transferred summation relative to a partial-wave summation are discussed. Most importantly, the expected relatively rapid convergence of the momentum-transferred summation effectively reduces the number of transition matrix elements which must be calculated. Additionally, the momentum-transferred summation involves an ‘‘incoherent’’ summation which, in general, is more easily computed. Lastly, we present explicit expressions for the transition probabilities in the plane-wave and distorted-wave Born approximations.

A Bohr classical model for He is applied to multiply charged ions colliding with He at intermediate energies. Reactions studied are single-electron capture, single and double ionization, and electron-capture ionization for projectile charge states q=1+ to 100+, and the energy range E=1–5 MeV/amu. The dominant electron-removal collision process is single ionization. For the higher-charge-state ions, single-charge exchange is found to be primarily due to transfer ionization, a two-electron process where one electron is ionized and the other is captured by the projectile. For low-charge states, the single- and double-ionization cross sections are close to the expected $q^2$ and $q^4$ scaling. The calculations are in reasonable agreement with available experimental data.

A new formalism is introduced for discussing propagation of electromagnetic waves in space- and time-varying media. The approach taken here is to supplement the velocity-independent solution by a correction factor. This factor involves a four-dimensional line integral and is therefore a WKB-type solution. The formalism is relativistically exact to the first order in v/c. Special cases are discussed, demonstrating how time-harmonic velocity fields modulate the propagating electromagnetic fields. Scattering problems involving time-varying surfaces have been considered in the past. The scatterers were situated in free space (vacuum), or if material media were involved, the mechanical interaction of the moving surfaces with the medium was usually ignored. The new theory presented here facilitates the analysis of electromagnetic scattering problems in the presence of combined surface and medium motion. Consequently, mass continuity at the moving surfaces can be preserved. This makes the modeling of such problems much more realistic. Simplified canonical problems involving interaction of electromagnetic and mechanical waves are discussed to highlight the effects resulting from the new boundary considerations. Surprisingly, for bounded surfaces the time-varying medium effects vanish in the far field. This means that previous results which simply ignored the medium motion are still valid as good approximations.

Energy-resolved photoelectron angular distributions have been measured for the nd ${}^2$D states (n=11–23) in cesium and rubidium atoms for two-photon resonant, three-photon ionization under conditions where the spin-orbit fine structure was not resolved. The photoelectron angular distributions reveal strong fine-structure mixing effects when the time duration of the laser pulse is longer than the time corresponding to the inverse of the fine-structure splitting of the nd states involved. Three-photon ionization photoelectron angular distributions for sodium atoms have been studied both experimentally and theoretically for laser frequencies in which resonance enhancement occurs via the two-photon excited nd ${}^2$D states (n=5–9). The laser pulse duration is ∼6 ns which is comparable to or less than the fine-structure mixing time for the unperturbed fine-structure nd ${}^2$$D_{5/2}$,3/2 levels. In addition, the high laser powers ∼${10}^8$ W/${\mathrm{cm}}^2$ employed result in alterations of the energy separations of the fine-structure levels (and cause corresponding changes in the mixing times) due to the ac Stark effect. A detailed theoretical analysis is presented and good agreement is obtained with the experimental results.

We have studied sodium resonance radiation under conditions of severe radiation trapping in sodium-argon mixtures, and we report measured values of the effective radiative decay rates. The measured values are compared with values calculated from the Holstein theory of radiation trapping in the impact-regime, foreign-gas pressure-broadening limit. The experiment was designed to satisfy all of the validity criteria imposed by the approximations of the Holstein theory, and the experiment and theory are in good agreement. Since the effective radiative decay rate depends upon the collisional line-broadening rate, confirmation of the theory allows such measurements to be used to determine unknown line-broadening constants using only broadband lasers and low resolution monochromaters. We demonstrate this technique for the sodium D lines broadened by xenon and neon perturbers. The values for the broadening constants obtained in this manner are in reasonable agreement with values from several previous studies utilizing more traditional techniques.

A practical method for calculating the Clebsch-Gordan coefficients and the rotational matrices in nested form is described for large arguments. A similar approach can be adopted for the evaluation of 6j and 9j symbols. Sample values of the 3j symbols and rotational matrices are presented.

We present emission measurements on a hollow-cathode discharge containing barium that were taken with the aid of a Fourier-transform spectrometer (FTS). We have determined the branching fractions for ten upper levels of the neutral barium atom. In the case of the resonance level 6s6p ${}^1$P°${}_1$, we had to augment our FTS measures with literature data that had recently been obtained by use of different laser-excitation techniques. Using four published lifetimes and also through combining our emission measurements with relative absorption data from the literature, we could convert the branching fractions of eight upper levels into transition probabilities. The resulting A values (with accuracies ranging from 1% to 60%) give support to the correction of earlier literature data, recommended by Jahreiss and Huber [Phys. Rev. A 31, 692 (1985)].

The n=2 to n=2 transition lines in the Be i ion sequence of moderately-high-Z elements (Cl to Cr) were studied in the emission spectra of the Texas Experimental tokamak plasma when the appropriate elements were injected. A number of lines were identified for the first time. The relative brightnesses of the spectral lines were measured by an instrument with a photoelectric detector which was photometrically calibrated against synchrotron radiation. The brightness ratios of the 2s2p ${}^3$$P_2$–2$p^2$ ${}^3$$P_2$ (R) and the 2$s^2$ ${}^1$$S_0$–2s2p ${}^3$$P_1$ ($R^{\mathrm{*}}$) transitions to the resonance 2$s^2$ ${}^1$$S_0$–2s2p ${}^1$$P_1$ line were determined and compared with theoretical predictions. For R, the ratio of the experimental to the theoretical values was 1.01±0.19 and for $R^{\mathrm{*}}$, 0.84±0.17, indicating a good agreement with the calculations of relative level populations using collision strengths computed by the distorted-wave approximation.

Individually resolved rotational photodetachment thresholds have been observed for ${\mathrm{SeH}}^{\mathrm{-}}$ ions in a magnetic field. The observed photodetachment cross section exhibits structure due to the cyclo- tron levels of the detached electron in the magnetic field. The electron affinity of SeH and the rotational constants of ${\mathrm{SeH}}^{\mathrm{-}}$ are determined from the measured rotational threshold energies. In addition to the high-resolution individual rotational threshold spectra, low-resolution spectra, for which the rotational band structure dominates, are obtained. These low-resolution spectra are used to assign rotational quantum numbers to the individual thresholds. The electron affinity of SeH is found to be 17?5.17(20) ${\mathrm{cm}}^{\mathrm{-}1}$, and the rotational constants of ${\mathrm{SeH}}^{\mathrm{-}}$ are found to be B=7.7289(46) ${\mathrm{cm}}^{\mathrm{-}1}$ and D=3.33(9)×${10}^{\mathrm{-}4}$ ${\mathrm{cm}}^{\mathrm{-}1}$.