Collisional $J$-mixing rates between the $J=0, 1, 2$ states of the $\mathrm{Sr}\left(5\mathrm{}{}_{}{}^3{}_{}{}^{}P_J^{}{}_{}{}^{}\right)$ multiplet have been measured in the presence of rare-gas perturbers. For Kr and Xe pressures above 100 Torr, the rates are dominated by a component which is quadratic in pressure. We believe this very unusual behavior is brought about by the simultaneous interaction of a Sr atom with two perturbers and not by excimer formation.

The $n=2\mathrm{}$ to $n=4\mathrm{}$ Balmer-$\beta$ transitions in hydrogenic ${\mathrm{Fe}}^{25+}$ have been observed in the first order of Bragg diffraction in a beam-foil light source. Simultaneous observation of the $1s-2p$ Lyman-$\alpha$ transitions from the same source in the fourth diffraction order leads to a new method for the measurement of the $1s$ ground-state Lamb shift which is less sensitive to uncertainties arising from Doppler shifts than previous work. With the use of the Balmer-$\beta$ transitions for calibration, the Lyman-$\alpha$ wavelengths are, for the $1s{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}-2p{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ transition, 1.778 15±0.000 19 Å, and for the $1s{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}-2p{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ transition, 1.783 64±0.000 19 Å. Values of the Lamb-shift contributions to the $1s-2p$ transitions, and the $2p_{\frac{1}{2},\frac{3}{2}}$ fine structure, are extracted.

Classical trajectory Monte Carlo calculations have been used to elucidate the collision mechanisms responsible for the differences in the single- and double-ionization cross sections of He atoms by protons and antiprotons in the energy range from 250 to 1000 keV. The calculations employed the Bohr helium-atom model which includes the $\frac{1}{r_{12}}$ electron-electron interaction. The unexpected large observed difference [Andersen et al., Phys. Rev. Lett. 57, 2149 (1986)] in the ratio $R$ of double to single ionization for proton and antiproton collisions is reproduced by the calculations. The calculations indicate that the antiproton double-ionization cross section is larger than that for protons because of two effects. The first effect is that the antiproton can push one electron into the other from larger impact parameters than for protons which must be between the nucleus and the first electron in order to pull it into a trajectory which collides with the second electron. The most important effect, however, is that at small impact parameters the antiproton screens the helium nucleus causing a Coulomb explosion while the proton increases the binding of the two electrons. The calculations also show a component of the difference in the ratio $R$ at low energies ($E<~500$ keV) is due to the single-ionization cross sections with protons predicted to have a larger cross section than antiprotons (36% difference at 250 keV).

The predicted transition from a traveling wave to a modulated traveling wave with increasing Rayleigh number was recently observed in an experiment on a water-ethanol mixture heated from below. Close to the codimension-two bifurcation the particle trajectories in such a modulated wave are predicted to be chaotic.

The absolute half-cell entropy is defined here as the entropy of the cell process $M\to M^{+}\left(\mathrm{solution}\right)+e^{-}\left(\mathrm{gas}\right)$. A method of determining absolute half-cell entropies is described. The relationship is discussed for single-ion entropies in solution. $\Delta S^0$ for the hydrogen electrode is provisionally recommended to be -66.6±1.4 J/K mole at 298 K, based on a previously recommended value for the absolute entropy of ${\mathrm{H}}^{+}$ in water. More accurate measurements should be attempted.

We present experimental data of viscous fingering patterns in a radial Hele-Shaw cell filled with the liquid crystal 4,4′-$n$-octylcyanobiphenyl (8CB). We observe a dense-branching-dendritic-dense-branching morphological phase sequence as a function of temperature. The wave number of the fastest growing mode can be selected by varying experimental parameters, and the number of initially growing fingers on a circular interface is in good agreement with linear-stability analysis which includes the full kinetic term. A mechanism is proposed for tip stabilization by anisotropic viscosity; the critical viscosity ratio for circular tips is ≃2.

Quantum defects are determined for the beryllium ${}_{}{}^3{}_{}{}^{}\mathrm{S}$, ${}_{}{}^3{}_{}{}^{}\mathrm{P}$ °, and ${}_{}{}^1{}_{}{}^{}\mathrm{P}$ ° Rydberg series below the first ionization threshold by searching for the poles of the multichannel Schwinger T matrix along the negative real-energy axis. The ab initio calculations are performed using static-exchange target functions for the ion cores. The results show increasing accuracy as the principal quantum number increases reflecting the fact that this method essentially treats bound states as negative-energy states scattering off an ion core. Small fixed grids and small fixed basis sets are sufficient to describe each Rydberg series of a particular symmetry. The long-range behavior is enforced by using a closed-channel (i.e., negative-energy) Coulomb Green’s function. Channel wave functions with the correct asymptotic form can be easily determined using this method.

Equations are presented for the first-order property using our recently developed bivariational coupled-cluster approach for calculation of static property in a two-body approximation of the cluster parameters.

The Born-Oppenheimer (BO) and Born-Huang (BH) treatments of molecular eigenstates are reexamined. It is argued that in application of the BO approximation to nonrigid molecules and chemical dynamics involving single potential-energy surfaces (PES’s), errors on the order of tens of percents can easily occur in many computed properties. Introduction of a BH expansion (in BO states) will always lead to poor convergence when the BO approximation fails; its diagonal (or adiabatic) approximation will not change this situation. The main problem in the above applications is the absence of well-developed, well-separated minima in the PES (or no minima at all). Inspired by a non-BO view of a molecule by Essén [Int. J. Quantum Chem. 12, 721 (1977)], a molecular coupled-cluster (MCC) method is formulated. An Essén molecule consists of neutral subunits (‘‘atoms’’), weakly interacting (‘‘bonds’’) in some spatial arrangement (‘‘structure’’). The quasiseparation in collective and individual motions within the molecule comes about by virtue of the virial theorem, not the smallness of the electron-to-nuclear mass ratio. The MCC method not only should converge well in the cluster sizes, but it also is capable of describing electronic shell and molecular geometric structures. It can be viewed as the workable formalism for Essén’s physical picture of a molecule. The time-independent and time-dependent versions are described. The latter one is useful for scattering, chemical dynamics, laser chemistry, half-collisions, and any other phenomena that can be described as the time evolution of many-particle wave packets. Close relationship to time-dependent Hartree-Fock theory exists. A few implementational aspects are discussed, such as symmetry, conservation laws, approximations, numerical techniques, as well as a possible relation with a non-BO PES. Appendixes contain mathematical details.

For a given one-dimensional Hamiltonian we construct a family of Hamiltonians whose Hilbert spaces are related by shifting operators such that each level of the original Hilbert space corresponds to the ground state of another one of the family. This allows us to establish the equivalence between the Schrödinger equation and a sequence of Ricatti equations.

We present Kummer-function representation of an infinite set of local solutions for describing the double continua of two atomic electrons. Specific connection between the rate of flux loss from the ridge region and the double-excitation mechanism is discussed. Analysis based strictly on the local behavior of the solution leaves some ambiguity in threshold law for ${}_{}{}^3{}_{}{}^{}\mathrm{S}_{}^{\mathrm{e}}{}_{}{}^{}$ and ${}_{}{}^1{}_{}{}^{}\mathrm{P}_{}^{\mathrm{e}}{}_{}{}^{}$; otherwise Wannier’s threshold law holds beyond reasonable doubt. The quantum-mechanical treatment is complemented and elucidated by classical trajectories.

As an approach to the electronic structure of the doubly excited and other highly correlated states of atoms, we consider the angular correlation of two electrons on a sphere of radius R. The Hamiltonian is scaled by a factor $R^2$ and the parameter R is reinterpreted as the strength of electronic repulsion. The scaled Hamiltonian $H_S$ is the sum of an analytically solvable Hamiltonian $H_0$+$V_M$ and a perturbation Δ$H_1$+Δ$H_2$ which becomes negligible as R→∞. The spectrum of $H_0$+$V_M$ therefore approaches the spectrum of $H_S$ in the asymptotic limit. The eigenfunctions of $H_0$+$V_M$ show a transition from weak correlation at small R to strong correlation and ‘‘molecular’’ motion at large R.

Charge-state distributions were measured for incident 105-, 220-, 430-, and 955-MeV/amu U ions on thin and thick solid targets. Initial bare, one-, two-, three-, nine-, and 24-electron ions were used, so that single and multiple ionization of K-, L-, and M-shell electrons and electron capture into bare ions and into ions having initially full or partially full K and L shells could be observed. Multiple-ionization effects in two-electron U ions and in ions having many electrons in the K, L, and M shells are calculated by using the semiclassical approximation and assuming binomial statistics. Binding effects on K-shell ionization are compared with previous measurements using relativistic Xe ions, and with the Glauber theory. For 430- and 955-MeV/amu U ions, good agreement is obtained between measured capture cross sections and calculated radiative and nonradiative (eikonal-approximation) cross sections. Some disagreement is found at lower energies. An approximate model is proposed for multiple-capture cross sections. Finally, the measured equilibrium charge states are compared to ground-state models and to models including excited-state effects. Excited-state effects are less important for relativistic U ions than for any other ion in matter. Differences between the excited- and ground-state models are found to be too small to be observed.

We have thoroughly investigated electron capture from a hydrogen atom by bare nuclei at intermediate and high energies. The first Born approximation with and without correct boundary conditions is used to compute total cross sections. Both methods possess the same perturbation potential for the reaction under study. The only difference is in the logarithmic phase distortion of the exit channel state due to the long-range Coulomb interaction between the two aggregates. Evidence is presented which substantiates that these Coulomb phases for the relative motion of heavy particles are of paramount importance for an adequate description of charge exchange. The standard Jackson-Schiff approximation which does not consider the boundary condition problem fails completely in comparison with the measurement. In contrast, the first Born approximation with the correct boundary conditions, which takes the asymptotic Coulomb effect into full account, is found to be systematically in excellent agreement with the experimental data for values of the projectile charge ranging from 1 to 6.

A semiclassical theory for inelastic scattering of a particle by a two-state system in the near-adiabatic limit is developed. The exponentially small transition amplitude is calculated. The theory is an extension of Pokrovskii and Khalatnikov’s theory for above-barrier reflection (Zh. Eksp. Teor. Fiz. 40, 1713 (1961) [Sov. Phys.—JETP 13, 1207 (1961)]). The analysis involves studies of the WKB solutions in the complex coordinate plane along certain contours. The region of validity of the theory is established. Our result has the same form as the Landau-Zener-Stueckelberg formula; however, our theory is applicable to more general systems. Numerical comparisons with exact solutions are presented; the differences between our results and exact solutions become negligible as the adiabatic limit is approached.

We report the results of a study on electron-target correlations in the ${}_{}{}^2{}_{}{}^{}\mathrm{\Pi }_{\mathrm{g}}^{}{}_{}{}^{}$ shape resonance of elastic e-${\mathrm{N}}_2$ scattering, using the Schwinger multichannel formulation. The effects of basis set, orbital representation, and closed-channel configurations are delineated. The different roles of radial and angular correlations are compared. Our results are in good agreement with a recent calculation by Schneider and Collins [Phys. Rev. A 30, 95 (1984)] using the linear algebraic-optical potential method whereas calculations using radial correlations alone agree well with previous calculations based on a variety of different approaches.

The Schwinger multichannel formulation has been applied to study the role of electron correlation in low-energy e-${\mathrm{N}}_2$ scattering. For the five nonresonant partial-wave channels studied here, ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$, ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$, ${}_{}{}^2{}_{}{}^{}\mathrm{\Pi }_{\mathrm{u}}^{}{}_{}{}^{}$, ${}_{}{}^2{}_{}{}^{}\mathrm{\Delta }_{\mathrm{g}}^{}{}_{}{}^{}$, and ${}_{}{}^2{}_{}{}^{}\mathrm{\Delta }_{\mathrm{u}}^{}{}_{}{}^{}$, we find angular correlation to be much more important than radial correlation. Our results for the ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$ channel are in agreement with those of Schneider and Collins [Phys. Rev. A 30, 95 (1984)]. Our calculated total and differential cross sections agree with experiment except for the differential cross sections at 1.5 eV. Our results are also compared with those obtained using model polarization potentials.

The first measurements of the mean energies $E_r$ of highly charged recoil ions detected in coincidence with multiply ionized swift projectiles are reported. Beams of 23-, 27.6-, and 33-MeV ${\mathrm{Cl}}^{5+}$ produced Ar recoil ions whose mean energies exhibited a strong dependence on the product (qr) of final projectile and recoil charge states. For large qr values, $E_r$ is substantially larger than earlier estimates, and allows inference of characteristic impact parameters without requiring measurements of projectile scattering angle.

We have measured the energy spectrum of detached electrons at ${\theta }_L$=0° in coincidence with Lyman-α photons from the excitation and subsequent decay of H(2p) produced during the process ${\mathrm{H}}^{\mathrm{-}}$+He→H(2p)+$e^{\mathrm{-}}$+${\mathrm{He}}^{\mathrm{*}}$ at 0.5-MeV incident ion energy. We find that this electron energy distribution mimics the so-called very sharp peak feature of the doubly differential cross section previously measured under $e^{\mathrm{-}}$-H coincidence conditions. This result shows that excitation of H is responsible for the very sharp peak and that the detached electron energy distribution associated with H(2p) is significantly different from the distribution associated with the production of H(1s).