Intensities of x-ray lines emitted from highly dense plasmas in the recombining phase are studied computationally. Transient characteristics associated with picosecond x-ray generation are clearly revealed. It is also shown that intensity ratios of x-ray lines are apt to offer unreliable values in the estimation of electron densities and temperatures after satellite lines are decayed down to negligible levels. Based on our computed results, a new correct interpretation for experimental ones obtained by Key et al. [Phys. Rev. Lett. 49, 1669 (1980)] is suggested.

The $R_1$ dephasing time in ruby (0.05 wt.% ${\mathrm{Cr}}_2$${\mathrm{O}}_3$) is observed to increase by an order of magnitude when selected transitions of the $R_2$ line are pumped. Spin flip-flop dephasing in the ground state is suppressed by optically induced depopulation of the ${}_{}{}^4{}_{}{}^{}A_2^{}{}_{}{}^{}(\pm \frac{1}{2})$ levels.

Self-induced transparency has been observed on a $Q\left(2\right)\mathrm{}$-degenerate transition for the first time. Coherent interaction occurs as a short pulse from the ${}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}F=2\mathrm{}\to {}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}{F}^{\prime }=2\mathrm{}$, magnetic dipole transition of the atomic-iodine laser passes through a self-resonant iodine vapor. High transparency and considerable pulse delay at input pulse areas $\theta >\pi$, and small-pulse splitting at $\theta \simeq \pi$ characterized the phenomena.

When the Reynolds number for a Taylor-Couette flow with a radius ratio $\eta =0.782\mathrm{}$ is ramped quasistatically, a wavy vortex flow with an azimuthal $m$ number $m=2\mathrm{}$ is excited at a transition Reynolds number of $R=137\mathrm{}$. This mode disappears at $R=161\mathrm{}$, and the flow returns to the Taylor vortex state and remains in this state until a new wavy state with $m=3\mathrm{}$ is excited at $R=322\mathrm{}$. This unusual sequence of flow evolution seems to be consistent with the stability boundaries calculated by Jones.

The ratio of the intensities of the Balmer $\alpha$ fine-structure components of hydrogenlike ions emitted from plasmas of various atomic number $Z$ is examined. It is shown that the fine-structure intensities can only be deduced assuming statistical equilibrium between the fine-structure sublevels for electron densities $N_e\gtrsim Z^9{10}^{12}$ ${\mathrm{cm}}^{-3\mathrm{}}$. At lower electron densities, the Balmer $\alpha$ fine-structure ratios vary rapidly with $N_e$ and should be useful as an electron density diagnostic.

The transition from quasiperiodicity to chaos is studied by a "momentum space" renormalization-group method similar to that employed in phase-transition studies. A perturbative expansion in a universality class parameter is developed, and approximate analytic expressions for the spectra as well as for one of the critical exponents are obtained and are in excellent agreement with previous numerical evaluations.

Doubly-excited-state basis (DESB) functions of Herrick and Sinanoǧlu are compared with the large-scale configuration-interaction (CI) wave functions of Lipsky et al., and with the adiabatic channel functions in hyperspherical coordinates. It is shown that DESB functions will represent those states where the mean value of ${\theta }_{12}$ is large. Owing to the absence of intershell correlations, and a consequent underestimation of radial correlations, the DESB functions give excessive concentrations near ${\theta }_{12}=0\mathrm{}$ for other, less sharply correlated in angle, states.

Using accurate correlated wave functions calculated earlier by Bunge and by Larsson, we have constructed the Hohenberg-Kohn-Sham density functionals and exchange-correlation (ground-state) potentials and have obtained orbital energy eigenvalues for a number of light atoms by in principle exact numerical algorithms. While the uppermost occupied density-functional eigenvalue always gives an exact excitation energy as has been shown earlier, we find that eigenvalues for deeper shells lie above the corresponding excitation energy. We have compared our essentially exact density-functional (DF) results with those obtained in the local-density (LD) approximation. We find that the LD theory approximates the exchange-correlation energy rather well, but that it gives larger errors in the exchange-correlation potential and in the DF orbital eigenvalues. In all cases we have found that the LD error in the orbital eigenvalue is larger than the difference between the true DF eigenvalue and the corresponding exact excitation energy. Possible implications of these results for solid-state work are briefly discussed.

We show how the corrections for strongly bound electrons are incorporated into the Thomas-Fermi energy functional, and derive for the density the analog of what is known as Scott's correction to the energy. The scaling properties of this energy functional supply a new, consistent derivation of the Scott term.

The Thomas-Fermi model is improved by simultaneously introducing three different quantum corrections. The first concerns the nonlocality of quantum mechanics; we go beyond the von Weizsäcker approach by including arbitrary powers of the gradient of the single-particle potential. The second is a special treatment of the strongly bound electrons, which removes the incorrect statistical description of the vicinity of the nucleus. In the third we generalize Dirac's way of handling the exchange interaction by, again, including gradient effects to arbitrary order. All this is done in the framework of a "potential-functional method" and results in a new differential equation for the potential. The comparison of numerical results with both experimental and Hartree-Fock data for the mean-squared distance indicates a superiority of the new statistical theory over the Hartree-Fock theory, at least for the description of the outer reaches of the atom.

The new differential equation for the statistical atom is derived and discussed in detail. Numerical results are presented which provide evidence for the validity of all approximations that have entered the formalism. A comparison of experimental data for diamagnetic susceptibilities with theoretical predictions shows that the new statistical atom significantly surpasses its Hartree-Fock competitor.

We have previously developed a basic $U$-matrix formalism and have been able to obtain explicit expressions for the $U$ matrix and the wave function of a quantum-mechanical system by solving the operator Schrödinger equation directly within the regime of the interaction picture [Phys. Rev. A 27, 1760 (1983)]. In our approach, we introduce the switching function $S_w$ which describes how the interaction Hamiltonian is introduced to the system. In the present investigation, we list the corresponding $U$ matrix and wave function pertaining to the Schrödinger picture. Under the special case where the unperturbed Hamiltonian and the Lagrangian commute, our wave function can be reduced to the form identical to that obtained from the path-integral method. A comparison of the path-integral theory and our $U$-matrix theory is presented. The difference in the wave functions of the two theories lies in the fact that in the $U$-matrix approach the Schrödinger equation is treated as an operator equation, whereas the key equation in the path-integral theory is taken as algebraic.

Previously the inverse scattering method has been applied by various authors (Gardner, Greene, Kruskal and Miura, and Lax) to obtain solutions $u(x,t)\mathrm{}$ of certain nonlinear equations [e.g., the Korteweg—de Vries (KdV) equation] under the boundary condition $u(x,t)\mathrm{}\to 0 \mathrm{as} x\to \pm \infty$. Recently via Bäcklund transformation, Au and Fung have obtained the KdV one-soliton solution which contains the vacuum parameter $b\ne 0$, and $b$ has been shown to be of physical significance. In fact, $b$ is the boundary value of $u(x,t):u(x,t)\mathrm{}\to b \mathrm{as} x\to \pm \infty$. In this investigation we provide the generalized inverse scattering theory under the more general boundary condition $u(x,t)\mathrm{}\to b\ne 0 \mathrm{as} x\to \pm \infty$. The one-soliton solution obtainable from this inverse scattering method is identical to the new solution just found by Au and Fung [Phys Rev. B 25, 6460 (1982)]. The solution containing nonzero $b$ is outside the square-integrable class. This extension of the class of functions has a crucial feature in attempting to understand physical observables.

Space-curvature theoretical modifications of the fine- and hyperfine-structure energy levels have been investigated in the framework of a curved-Dirac-orbital model. Fairly accurate approximate solutions of the Dirac equation in a geometrically simple, curved space, i.e., the spherical three-space of radius $R$ have been obtained. An efficient ladder-operator technique has been devised in order to obtain closed-form expressions of the "curved" fine- and hyperfine-structure parameters in terms of the quantum numbers. Particularly, it has been found that the degenerate one-electron fine-structure energy levels are split by an additional space-curvature contribution ${\Delta }_c={\mathrm{}(-1\mathrm{})\mathrm{}}^{l+j+\frac{1}{2}}\times \frac{(j+\frac{1}{2})}{\left(4\mathrm{}{R}^2\right)}$ which vanishes at the traditional flat-space limit ($R\to \infty$). Space-curvature modifications of both fine and hyperfine parameters, increasing with $n$ as $\frac{n^4}{Z^2{R}^2}$, have been put in evidence. Besides the interest of a theoretical nature concerning specific information about the local curvature at the position of an highly excited astrophysical ion, some other practical interests of formulating quantum mechanics in a spherical three-space of parametric curvature $\frac{1}{R}$ are pointed out.

A classical spinning magnetic dipole is considered within classical electrodynamics with classical electromagnetic zero-point radiation. The stationary probability distribution for the angle of alignment between the spinning magnetic dipole and an external magnetic field is calculated when the system is located in an arbitrary spectrum of random classical radiation. It is found that for the Rayleigh-Jeans spectrum the probability distribution for alignment is just the Boltzmann distribution. However, in classical zero-point radiation the alignment probability distribution is independent of the magnetic field causing alignment. Moreover, for large classical spin angular momentum $S>>\hslash$, the average component of the spin in the direction of alignment is given by $〈S_z〉=S-\frac{1}{2}\hslash$, where $\hslash$ is Planck's constant (divided by $2\pi$) used to set the scale of the classical zero-point radiation spectrum. The results seem suggestive of the idea of space quantization in quantum theory. The model discussed here was first considered by S. Sachidanandam (unpublished).

A time-dependent imaginary optical potential is used to approximate the Schrödinger time evolution in a necessarily truncated subspace. The flux of probability into the neglected space, for which the ordinary unitary subspace Schrödinger solution does not account, can generally be well reproduced by an optical potential that is diagonal in energy and linear in time. This is demonstrated in a number of examples including the Lipkin model, Gaussian Hamiltonians, and a schematic heavy-ion collision model.

The tensor-operator form of the effective electrostatic—spin-orbit (effective EL-SO) interaction for ${\mathrm{}\left(\mathrm{nl}\right)\mathrm{}}^N{n}^{\prime }{l}^{\prime }$ configurations is obtained by considering all possible types of perturbing configurations. It is shown that for $l^{\prime }\ne l$ this interaction is represented by a two-electron operator. Therefore, it comprises, in analogy with the electrostatic interaction, both direct and exchange parts. However, unlike the electrostatic interaction, it is, of course, spin dependent. It is proved that for $l^N{l}^{\prime }$ configurations, the pure effective spin-orbit interaction is, as for $l^N$ configurations, fully absorbed in the first-order spin-orbit parameters.

The total cross section (inclusive of all scattering) is calculated as a function of energy for a simplified model of electron-hydrogen scattering in which all terms involving nonzero angular momenta are neglected. Only the ${}_{}{}^1{}_{}{}^{}S$ state is considered. The two-body Schrödinger equation is integrated numerically, and the optical theorem is used to determine the total cross section. The results agree rather well with those obtained from a pseudostate expansion. High and low bounds are given for the ionization cross section, and these are compared with estimates of ionization obtained from a pseudostate expansion.