Detailed close-coupling calculations are reported for the photoionization of the ${}_{}{}^2{}_{}{}^{}S$ ground state of CIV, NV, and OVI. The frozen-core approximation is employed and the eigenfunction expansion includes the ground state and the $n=2\mathrm{}$ excited states of the residual heliumlike ions CV, NVI, and OVII. Autoionizing resonances lying below the $n=2\mathrm{}$ thresholds are taken into account.

We obtain asymptotic approximations to the collision-broadened line shape by the method of steepest descent. Exponentially decreasing line shapes result when the phase at the saddle point has an imaginary part. Averaging over a thermal distribution of velocities is shown to substantially affect the line shape.

A time delay of recombination luminescence has been observed in xenon gas and xenon-nitrogen gas mixtures excited by ${}_{}{}^{252}{}_{}{}^{}\mathrm{Cf}$ fission fragments. The measured delay times are in good agreement with the calculated electron thermalization time in the gases. The effect of nitrogen in xenon on the thermalization process is found to be appreciable for [${\mathrm{N}}_2$]/[Xe] > ${10}^{-3\mathrm{}}$, as a result of inelastic collisions by a rotational energy-transfer process for the electron energy of less than 1 eV.

The relative effects of electronic and nuclear collisions on the shape of the longitudinal ion-range distribution have been examined for incident ion energies well above the stopping-power maximum. At these higher energies the parameter ${\left({\sigma }_{\parallel }\right)}_n$ calculated by Littmark and Ziegler is shown to be of little practical significance. Agreement between the calculated value of ${\left({\sigma }_{\parallel }\right)}_n$ and an experimental measurement quoted by Littmark and Ziegler is shown to be fortuitous.

The analytic self-consistent-field wave functions for ${\mathrm{Cs}}^{+}$ and Cs reported by Sachdeva and Puri are incorrect; so also are their total energies of both the ion and the neutral form.

A new Ritz variational ansatz for bound states of four identical particles is proposed which may be used as the starting point for more detailed calculations. The ansatz is tested for the case of four inert gas atoms bound by Lennard-Jones potentials.

An equation governing the friction pressure tensor is derived from the Kirkwood-Smoluchowski equation where terms, nonlinear in the shear rate, are taken into account. The ensuing non-Newtonian viscosity and normal pressure differences are presented for a (stationary) plane Couette flow.

We first discuss convergence problems of single-center expansions of molecular wave functions in terms of exponential-type orbitals (ETO's). In a test calculation of $\mathrm{H}_2^{}{}_{}{}^{+}$ we find that the expansion coefficients diverge quite rapidly when nonorthogonal basis functions are used. This behavior can cause serious numerical instabilities when the wave function is used in a configuration-interaction calculation. This problem does not occur when the ETO's are orthogonal. We then obtain an energy of -1.1022 a.u. (exact: -1.1026 a.u.) for $\mathrm{H}_2^{}{}_{}{}^{+}$. Secondly, we present a contraction scheme that incorporates the information about the positions of the nuclei of the molecule similar to the information included in the LCAO scheme. It is therefore very efficient in reducing the dimension of the energy eigenvalue problem.

Linear-combination-of-Gaussian-type-orbital $X\alpha$ calculations on NiCO are described. The electronic structure and equilibrium bond distances $R_{\mathrm{Ni}-\mathrm{CO}}=3.11\mathrm{}{a}_0$ and $R_{\mathrm{NiC}-\mathrm{O}}=2.18\mathrm{}{a}_0$ are consistent with recent configuration-interaction calculations employing core pseudopotentials. The computed Ni—CO and NiC—O harmonic vibrational frequencies are 656 and 1933 ${\mathrm{cm}}^{-1\mathrm{}}$. The CO stretch vibration is within 100 ${\mathrm{cm}}^{-1\mathrm{}}$ of experiment and the ratio of intensities for those two modes, 640, is consistent with the fact that the Ni—C stretch has not been seen in matrix isolation experiments. The relevance of NiCO as a model for CO adsorbed on solid nickel is discussed and found to be marginal.

The nature of electron correlations between two excited electrons is examined in terms of surface plots of charge-density distributions on suitably chosen planes. Initially the angular correlation is neglected such that charge distributions for singly and doubly excited states are displayed on the conventional ($r_1,r_2$) plane. It is shown that all singly excited states exhibit circular nodal lines on the ($r_1,r_2$) plane along $R={(r_1^2+r_2^2)}^{\frac{1}{2}}=\mathrm{const}$ and no radial nodal structure in the $\alpha =arctan\left(\frac{r_1}{r_2}\right)$ coordinate, while doubly excited states are characterized by additional radial nodal structure. The interplay between angular and radial correlations is examined in terms of plots of surface charge density at each $R$ on the ($\alpha ,{\theta }_{12}$) plane for each channel. It is shown that channels which have attractive potential curves are characterized by large charge concentration for large ${\theta }_{12}$, while other channels which have less attractive or repulsive potentials are characterized by large charge concentration in the small-${\theta }_{12}$ region.

A previously developed method for self-consistent-field density-functional calculations involving a variational fit to the charge density is generalized to the case in which the total (electronic plus nuclear) Coulomb potential is fit. Previously the total energy $E(\rho ,\tilde{\rho })$ was viewed as a functional of the exact $\rho$ and fitted $\tilde{\rho }$ charge density. The energy expression was modified to be correct when $\tilde{\rho }=\rho$ while at the same time allowing $\tilde{\rho }$ to be obtained variationally through $\frac{\partial E(\rho ,\tilde{\rho })}{\partial \tilde{\rho }}=0\mathrm{}$. Herein an expression for $E(\rho ,\tilde{V})$, where $\tilde{V}$ is the fit to the Coulomb potential, is derived with similar properties. In particular, $\tilde{V}$ can be determined variationally through $\frac{\partial E(\rho ,\tilde{V})}{\partial \tilde{V}}=0\mathrm{}$. In various linear-combination-of-atomic-orbitals calculations on atomic neon, the superiority of variational over conventional least-squares-fitting methods is demonstrated.

The results of a recent calculation of the correlation energy in the relativistic electron gas are used to calculate the correlation contributions to the total energy and $1s$ binding energy in several heavy atomic systems. To assess the effects of a self-consistent calculation, a lowest-order perturbation scheme was also employed. The correlation contribution to the $K\alpha$ lines are compared to the differences between theoretical calculations without correlation of Huang et al. and the accurate experimental values of Deslattes et al. The contributions of Breit and transverse interactions to heavy atoms are calculated within a local-density scheme and comparisons are made to the nonlocal Dirac-Fock results of Mann and Johnson. It is found that nonlocal effects may be important.

Ermakov systems are pairs of coupled, time-dependent, nonlinear dynamical equations possessing a joint constant of the motion called an Ermakov invariant. The invariant provides a link between the two equations and leads to a superposition law between solutions to the Ermakov pair. Extensive studies of Ermakov systems in classical mechanics have been carried out. Here we present a detailed study of Ermakov systems from a quantum point of view, and prove that the solution to the Schrödinger equation for a general Ermakov system can be reduced to the solution of a time-independent Schrödinger equation involving the Ermakov invariant. We thereby arrive at a quantum-mechanical superposition law analogous to the classical superposition law.

The relationship between the density operator and operator solutions of Schrödinger's equation is discussed. We designate operator solutions of Schrödinger's equation as "operator wave functions" and show how they can be constructed from ordinary wave functions.

A method derived earlier to analyze one-dimensional systems is applied to the study of multidimensional isotropic bounded oscillators. The problem is reduced to a one-dimensional one in order to take advantage of several earlier results. The application of the method to the harmonic-oscillator model shows that the results so obtained are excellent.

The relationship between the atomic coherent-state representation of Arecchi et al. [Phys. Rev. A 6, 2211 (1972)] and the state multipoles is established. The state multipoles are used to develop a theory of generalized phase-space distributions for angular momentum (collective atomic) systems. The general theory for angular momentum systems is shown to have many features in common with the general theory for boson systems [Phys. Rev. D 2, 2161 (1970)]. These generalized phase-space distributions contain as a special case the coherent-state representation of Arecchi et al. The applications of the generalized phase-space distributions and state multipoles to the dynamical problems and to the calculation of multitime correlations are given. State-multipole techniques are used to give a brief discussion of the master equation describing cooperative resonance fluorescence.

Utilizing the magnetic field-dependent spin-orbit interaction, the relativistic correction to the Zeeman energy, and the usual diamagnetic interaction, we have calculated spin-dependent electrical polarizabilities of hydrogenic atoms using the Hassé variational approach. The polarizabilities $\alpha \left(\uparrow \right)$ and $\alpha \left(\downarrow \right)$ for the two spin directions have been obtained for the electric field both parallel and perpendicular to the magnetic field $H_z$ in the weak-field ($\gamma \ll 1$), intermediate-field ($\gamma \sim 1$), and strong-field ($\gamma \gg 1$) limits, where $\gamma =\left(\frac{{\epsilon }^2{\hslash }^3{H}_z}{m{}_{}{}^{*2\mathrm{}}{}_{}{}^{}e{}_{}{}^3{}_{}{}^{}c}\right)$, with $\epsilon$ a static dielectric constant and $m^{*}$ an isotropic effective mass. The results for hydrogen atoms ($\epsilon =1\mathrm{} \mathrm{and} m^{*}=m$) in the weak-field limit yield $\frac{\left[\alpha \right(\downarrow )-\alpha (\uparrow \left)\right]}{\alpha \mathrm{}\left(0\right)\mathrm{}\approx 2.31{\alpha }_{\mathrm{f}}^2{}_{\mathrm{s}}{}^{}{}_{}{}^{}\gamma } ({\alpha }_{\mathrm{fs}}=\frac{1}{137})$ with a negligible anisotropy. In the strong-field limit [${\alpha }_{\perp }\left(\downarrow \right)-{\alpha }_{\perp }\left(\uparrow \right)$] falls precipitously while $\left[{\alpha }_{\parallel }\right(\downarrow )-{\alpha }_{\parallel }(\uparrow \left)\right]$ continues to increase up to at least $\gamma ={10}^4$, but more slowly than linearly with $\gamma$. The spin-independent quantities [${\alpha }_{\parallel }\left(\downarrow \right)+{\alpha }_{\parallel }\left(\uparrow \right)$] and [${\alpha }_{\perp }\left(\downarrow \right)+{\alpha }_{\perp }\left(\uparrow \right)$] are discussed in the intermediate- and high-field limits and represent an extension of the earlier low-field results obtained by Dexter. The implications of these results for shallow-donor impurity atoms in semiconductors and for hydrogen-atom atmospheres of magnetic white dwarfs and neutron stars are briefly considered. The effects of the dramatic shrinkage of the electron's wave function on the spin Zeeman energy and the electron-proton hyperfine interaction are also discussed.

Electron momentum distributions have been obtained from electron densities derived from the Thomas-Fermi, local-density-functional, and general-density-functional theories by the application of the procedure of Burkhardt, Kónya, and Coulson and March (the BKCM procedure). The BKCM procedure has been modified so as to simulate the correct asymptotic behavior of the electron momentum distributions. It has been shown that, by means of reciprocal relationships to those in the direct BKCM procedure for estimating electron momentum density from a given electron density, a reverse transformation from electron momentum density to electron density can be effected. This reverse transformation enables one to obtain reasonable estimates of $〈r^n〉$ expectation values and form factors from a given electron momentum distribution. It is also noted that the shell structure, i.e., the maxima in the original radial electron density $4\pi r^2\rho \mathrm{}\left(r\right)\mathrm{}$, are reproduced upon reconstructing the radial electron density from an application of the reverse BKCM procedure. It is also shown that, with the use of extremely accurate experimental Compton profiles, the electron density along with its shell-structure characteristics can be estimated reasonably accurately.

For a special class of truncated and screened Coulomb potentials, some analyticity properties of the phase shifts are deduced as functions of $\beta$, the truncation and screening parameter. Use of these properties and scale transformations leads to analytic expressions for the phase shifts, which are valid in the region of small $\beta$.