The optical transmission properties of a quasiperiodic sequence of two types of directional ($\Delta \beta$) couplers are studied. Under certain resonant conditions, the spatial evolution of the field amplitude is found to be fractal. We also show that the transmission coefficient as a function of phase mismatch $\Delta \beta$ displays scaling with respect to the number of directional couplers in the sequence.

We investigate the transition from weakly nonlinear to nonlinear traveling-wave states. Pattern selection due to a transition from convective to absolute instability conditions is found, in good agreement with theory. While the linear properties depend on the (boundary-dependent) threshold of convection, the weakly nonlinear properties refer back to the threshold of an infinite system.

We report extensive simulations of a model for tethered self-avoiding membranes with bending rigidity. These simulations have been performed at finite and infinite temperature for membranes whose stretched configurations are hexagonal with linear dimensions $L$ in the range 5-19. We have analyzed the shape of the clusters by calculating the eigenvalues ${\lambda }_i$, $i=1-3\mathrm{}$ of the inertia tensor and the structure factor for wave vectors in the direction of the eigenvectors of this matrix. We find that the smallest eigenvalue scales, for all temperatures investigated, as ${\lambda }_1\sim L^{v_1}$ with $v_1\approx 0.65$; the two larger eigenvalues scale as $L$. Thus, in the thermodynamic limit $L\to \infty$, the tethered self-avoiding membrane is flat but rough, in contrast to previous conclusions [Y. Kantor and D. R. Nelson, Phys. Rev. Lett. 58, 2774 (1987); Phys. Rev. A 36, 4020 (1987)], and in contrast to the behavior of membranes without self-avoidance which display a thermodynamic phase transition between a crumpled high-temperature phase and a low-temperature flat phase [Y. Kantor, M. Kardar, and D. R. Nelson, Phys. Rev. Lett. 57, 791 (1986); Phys. Rev. A 35, 3056 (1987)].

Two complementary variational principles are derived for the one-electron Schrödinger or local-density-functional equation in a closed cell of arbitrary shape, for external Neumann and Dirichlet boundary conditions, respectively. The surface operators scrR and ${\mathrm{scrR}}^{\mathrm{-}1}$, respectively, are stationary in these two variational principles. Subject to a condition of compatibility of the boundary conditions, these results are combined to give variational equations that are valid for an arbitrary cluster of atomic cells, assumed to fill space within an outer boundary. Cell interface terms agree with prior variational derivations for discontinuous functions. It is shown that structure constants of multiple scattering theory can be used within the variational formalism, giving contracted Hermitian matrix equations linearized in energy. New variational prescriptions are given for two broad classes of applications: (i) electron scattering by a cluster, or bound states using scattering theory; (ii) embedding a cluster in a substrate.

The question of which contributions to the energy levels of cesium must be included in many-body perturbation theory to achieve accuracies of parts per thousand is addressed. To this end, we evaluate second- and third-order correlation corrections to the energy levels of several states. When these corrections are supplemented with two dominant classes of corrections from fourth and higher order, the calculated energy of each of the states considered is brought to within a few parts per thousand of the measured energy. Implications for calculations of transition amplitudes, in particular, amplitudes of parity-nonconserving transitions, are discussed.

Using a rotational-invariant Faddeev Ansatz for the electronic two-center wave function that is written as a sum of terms involving hydrogenic Sturmians and appropriate spherical harmonics coupled to total angular momentum J and parity P, we are able to diagonalize the two-center Hamiltonian to obtain the 1s${\sigma }_g$, 2s${\sigma }_g$, 2p${\sigma }_u$, 2p${\pi }_u$, and 3d${\sigma }_g$ electronic energy curves. For 36 Sturmians in the wave function we get energy states that are accurate to six to nine digits for 0$a_0$. All adiabatic corrections are calculated for the 1s${\sigma }_g$ state and the results compared with previous work by W. Kolos [Acta Phys. Acad. Sci. Hung. 27, 241 (1969)] and C. L. Beckel, B. D. Hausen, and J. M. Peek [J. Chem. Phys. 53, 3681 (1970)]. Using the ideas of R. T. Pack and J. O. Hirschfelder [J. Chem. Phys. 49, 4009 (1968); 52, 521 (1970); 52, 4198 (1970)] we calculate the avoided crossing energy gap Δɛ between 2s${\sigma }_g$ and 3d${\sigma }_g$ curves. For a 36-term Sturmian basis set we get Δɛ=3.27 ${\mathrm{cm}}^{\mathrm{-}1}$ at R=4.053 52$a_0$. Our work allows for a general approach to the solution of any molecular three-body problem that is applicable independently of the light-particle–heavy-particle interaction and the masses of the two heavier particles.

Microwave resonances in Na Rydberg states n=22–30 between d, f, g, and h states have been detected by field ionization. The 39 new transition frequencies have been combined with previously measured frequencies in the same Rydberg series, n=9–17, in order to test the internal consistency and reliability of the data by using series formulas. A new analysis of the effective dipole and quadrupole core polarizabilities in ${\mathrm{Na}}^{+}$, based on the enlarged data set, has been carried out, and the sensitivity of the results to several model assumptions has been examined. The results are ${\alpha }_d^{\mathcal{’}}$=0.9980±0.0033 a.u. and ${\alpha }_Q^{\mathcal{’}}$=0.351±0.081 a.u.

We present the finite-element method in its application to solving quantum-mechanical problems for diatomic molecules. Results for Hartree-Fock calculations of ${\mathrm{H}}_2$ and Hartree-Fock-Slater calculations for molecules like ${\mathrm{N}}_2$ and CO are presented. The accuracy achieved with fewer than 5000 grid points for the total energies of these systems is ${10}^{\mathrm{-}8}$ a.u., which is about two orders of magnitude better than the accuracy of any other available method.

The explicit form of the first-order density matrix ρ${(\mathrm{r}}_1$,${\mathrm{r}}_2$) for independent electrons moving in a bare Coulomb field is first set up for the case of K plus L closed shells. The density matrix has a simple separable form in terms of the variables $r_1$+$r_2$ and ‖${\mathrm{r}}_1$${\mathrm{-}\mathrm{r}}_2$‖, a property exclusive to the Coulomb potential. Also, the off-diagonal dependence is simply quadratic in ‖${\mathrm{r}}_1$${\mathrm{-}\mathrm{r}}_2$‖. These two properties allow ρ${(\mathrm{r}}_1$,${\mathrm{r}}_2$) to be written solely in terms of electron and kinetic energy densities. Other implications for density-functional theory are briefly referred to.

It is shown that an analytic effective potential given by a sum of Yukawa terms plus a long-ranged Coulomb tail can provide atomic data (energy levels, oscillator strengths, photoionization cross sections) of accuracy comparable to single-configuration, relativistic, self-consistent-field calculations. The Yukawa terms are weighted by shell occupancy. The screening parameters in the exponentials account for electron shielding of the nuclear charge. Parameter values are obtained by an iterative solution for the eigenvalues of a spin-averaged Dirac equation to match experimental ground-state configuration-averaged ionization energies. The configuration term structure is included by use of Condon-Slater theory. Scaling laws to adjust the screening parameters are given in order to account for multiply excited configurations, inner-core excitations, and the orbital-angular-momentum dependence of excited valence electrons. The method is used to generate prefitted effective potentials for all isoelectronic sequences up to zinc. Comparisons to experimental and self-consistent-field calculations are presented.

Within the Trotter-Suzuki approximations on $e^{\mathrm{-}\beta H}$, the extended projector method [Phys. Rev. A 36, 4612 (1987)] previously introduced by us is shown to be a valuable technique in investigating the general class of few-level systems coupled both linearly and quadratically to a selected number of harmonic oscillators. As an illustration we compare eigenvalues and Ham-reduction factors with the literature for the cubic linear Jahn-Teller systems T⊗ε and T⊗${\tau }_2$ as well as for the system E⊗ε for which a quadratic warping interaction is included. For the latter system a symmetry projector is additionally developed, dealing with the transformation properties of nonlinear combinations of representational basis functions. As another illustration, the low-energy eigenstates of a two-level system quadratically coupled to a single harmonic oscillator are investigated. Within the ground state, the system becomes unstable at high coupling strengths and through the evaluation of time- and frequency-dependent correlation functions we found substantially different ground-state dynamic properties compared with those of a linearly coupled system.

Electron capture from the K shell by protons is calculated by using the exact on-shell impulse and eikonal wave functions in the final and initial channels, respectively. Both wave functions have the proper normalization and asymptotic conditions. A good agreement with available experiments is found.

It is shown that in classical mechanics for a finite scattering region a spherically symmetric potential can sometimes be determined from the deflection function for particles of a single energy E. Calculations for several examples such as a harmonic oscillator, a repulsive-attractive potential, and a reflection from a spherical mirror have been performed. Nonuniqueness is shown to occur in some cases.

The first Born approximation with boundary conditions which take the asymptotic Coulomb phases into full account is used to calculate the muon charge-transfer cross sections from αμ to protons at intermediate and high collision energies. Our computed cross sections are in good agreement with the experimental data on the equivalent electronic system in the energy range 50 to 180 keV.

Differential scattering of ${\mathrm{Na}}^{+}$ ions from ${\mathrm{N}}_2$ molecules was studied at laboratory energies of 100≤$E_{\mathrm{lab}\mathrm{\le }350}$ eV and scattering angles of 15°≤θ≤45°. The energy-loss spectra were measured with the time-of-flight technique. The experimental results were analyzed by the classical trajectory calculation. The spectra measured at small angles show a typical double-peak structure, while at large angles the spectra are composed of the three peaks. The triple-peak structure can be explained in terms of the rainbow effect on the angular momentum transfer mechanism, by taking into account the direction of the final rotational angular momentum vector. A drastic structural change of the energy-loss spectra was observed around the reduced scattering angle of τ=8 keV deg, independent of the collision energy. This can also be attributed to the rainbow effect arising from vibrational excitation.

Vacuum polarization in the field of a high-Z finite-size nucleus is examined, and the polarization charge density in coordinate space of order α(Zα${)}^n$ with n≥3 is calculated. Energy-level shifts of K- and L-shell electrons in hydrogenlike systems are given.

Dielectronic recombination (DR) cross sections and rate coefficients are calculated for the Ne-like ${\mathrm{Mg}}^{2+}$, ${\mathrm{P}}^{5+}$, and ${\mathrm{Cl}}^{7+}$ in which L-shell excitations are involved during the initial resonance capture. The result on ${\mathrm{P}}^{5+}$ is consistent with the first direct DR experiment of the Δ$n_t$≠0 mode carried out recently by P. F. Dittner et al. Multiple Auger channels complicate the dependence of the cross sections on principal quantum number and nuclear charge. Rapid decrease in the rate coefficient with decreasing atomic number was found, except at very low temperature, where this trend is reversed.

The lifetimes of several atomic levels of Am i that are connected by electric dipole transitions to the ground state have been measured. The Am atoms were excited by light pulses from a cw single-mode dye laser with the aid of an optoacoustic modulator. The decay curve of the delayed emitted photons was measured by counting single photons in the beam-off periods. The lifetimes of 14 levels in the wavelength region between 6405 and 4265 Å were measured using Am-metal vapor. The metallic Am was obtained by reducing ${\mathrm{AmO}}_2$ with La at 1500 °C in a high-vacuum system and collecting Am on a catcher foil. The Am vapor was then produced by controlled reevaporation from the foil at a temperature of about 800 °C. These lifetime measurements, in combination with the line intensities from a hollow-cathode discharge, allow the identification of the Am transitions homologous to the strong Eu i transitions from the $y^8$$P_{5/2}$,7/2,9/2 terms to the ground state.

We have extended a recent theory of spin relaxation in gases due to static magnetic field inhomogeneities to include the effects of oscillating magnetic fields. We use this theory to show how magnetic field inhomogeneities cause spin relaxation under magnetic resonance conditions. We have confirmed some of the main theoretical predictions by experimental observations. Spin relaxation in inhomogeneous magnetic fields can be used as a convenient new way to measure diffusion constants in gases.

Calculations of the frequency-dependent electric dipole polarizabilities have been carried out for atomic Cl and ${\mathrm{Cl}}^{\mathrm{-}}$ using many-body perturbation theory. Higher-order diagrams have been evaluated to include the effects of electron correlation. These results are used to interpret a recent experimental observation of shifts in the photodetachment threshold of ${\mathrm{Cl}}^{\mathrm{-}}$ in the presence of a strong laser field.