We study static electrical conductivity of water-in-oil microemulsions in the single-phase region. Below the percolation threshold, the data can be interpreted in terms of a fluctuating-charge model. Above the percolation threshold, in the lamellar region, the conductivity is consistent with randomly oriented water layers separated by surfactant sheets. The loci of the percolation thresholds are measured for different values of water to surfactant molar ratio and explained in terms of a continuum percolation model.

The static dielectric permittivity of the smectic-${\mathit{B}}^{\mathrm{*}}$ phase is studied as a function of temperature. The field-induced tilt angle, which is due to the electroclinic response, is measured as a function of temperature. The investigated phase precedes the chiral smectic-${\mathit{A}}^{\mathrm{*}}$ phase upon heating. In the ${\mathit{A}}^{\mathrm{*}}$ phase, the soft-mode dielectric contribution increases with decreasing temperature but does not diverge at the transition, a behavior similar to that of a first-order phase transition. Below the ${\mathit{A}}^{\mathrm{*}\mathrm{-}}$${\mathit{B}}^{\mathrm{*}}$ transition temperature ${\mathit{T}}_{\mathit{C}}$, the dielectric permittivity shows a sharp drop to a value considerably lower than that of the adjacent ${\mathit{A}}^{\mathrm{*}}$ phase. On further cooling one would expect a monotonic decrease of the soft-mode contribution. However, in this compound, at a certain temperature ${\mathit{T}}_{\mathrm{rev}}$, in the ${\mathit{B}}^{\mathrm{*}}$ phase, the dielectric permittivity starts to increase again with decreasing temperature. This anomaly in the soft-mode dielectric response is attributed to a change of sign in the electroclinic coefficient, which has been observed by an electro-optic experiment. An attempt to fit the measured dielectric permittivity to a modified expression for the dielectric function that contains a temperature-dependent coupling coefficient is presented.

We present here a nonlinear treatment of the acoustoelectric instability in piezoelectric semiconductors subjected to an external dc electric potential used as a control parameter. This analysis was motivated by a need to get a better understanding of the chaotic behavior recently observed in InSb. The approach is based on a two-mode coupling approximation, whereby only two linearly unstable modes are coupled and the motion reduced on their central manifold. It is found that the system may exhibit bistability between two limit-cycle solutions as well as between a limit cycle and a quasiperiodic solution.

A spatially periodic perturbation can lead to a breakup of large-amplitude sine-Gordon breathers into kink and antikink solutions, each oscillating around a minimum of the perturbing potential. This behavior can be understood by studying the effective potential experienced by the breather (bound kink-antikink) or the (free) kink-antikink solution as long as kink and antikink are sufficiently far apart. The resulting kinks and antikinks move independently and nearly radiationlessly in the presence of the perturbation and can travel arbitrarily far for sufficiently large initial kinetic energy. Upon interacting with each other they are strongly affected by the perturbation, lose energy by radiating, and can end in a bound state having the character of a distorted breather.

A method is proposed for combining quantum and classical perturbation theories into a single formalism. The method is applied to a model consisting of a periodically kicked particle in one dimension. The small-denominator problem and the transition, as ħ→0, from quantum to classical dynamics are discussed. It is found that the quantum to classical transition is characterized by two times, one scaling as ${\mathrm{ħ}}^{\mathrm{-}2/3}$ and one scaling as ${\mathrm{ħ}}^{\mathrm{-}1}$.

A method of integration of the Heisenberg equation of motion is proposed in which the time evolution of the basis set {${\mathit{T}}_{\mathit{m},}$n(t)} of the Weyl-ordered operators introduced by Bender and Dunne [Phys. Rev. D 40, 3504 (1989)] is obtained from the Taylor expansion and is expressible in terms of the initial {${\mathit{T}}_{\mathit{m},}$n(0)}’s. In the absence of damping forces, the constant values of the energy and the position-momentum commutation relation are used to check the accuracy of the integration. This method is applied to obtain the mean position and velocity of the particle as a function of time as well as the dwell time of the particle inside the barrier. In the example that is considered here, the potential is assumed to be the sum of a harmonic and a cubic term, and the calculation is done with and without dissipative coupling.

We present a state-specific approach to the calculation of correlated wave-functions and potential-energy surfaces (PES’s) of ground and excited states of diatomic molecules. Its emphasis is on the optimal choice of zeroth-order and of correlation-function spaces, which are computed separately. The zeroth-order Fermi-sea multiconfigurational wave function is obtained numerically, using McCullough’s partial-wave multiconfiguration self-consistent field [Comput. Phys. Rep. 4, 265 (1986)] program pwmcscf and numerical one-electron two-center orbitals as input. The correlation functions are obtained from partial and total configuration interaction (CI), using two-center virtual molecular orbitals, optimized by minimizing the energy. The method is demonstrated on the prototype ${\mathrm{He}}_2^{2+}$ ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathit{g}}^{+}{}_{}{}^{}$. A number of wave functions of acsending accuracy have been calculated. The most accurate one is composed of 116 configurations (multiconfiguration Hartree-Fock plus higher-order correlations), arising from 43 orbitals. It yields results which are lower over the entire PES than those obtained from the conventional linear combination of atomic orbitals including full CI with 158 basis functions and 2282 configurations. Compared with a published large CI calculation with ${\mathit{r}}_{\mathit{i}\mathit{j}}$-dependent basis sets, only at the equilibrium position, where the influence of the Coulomb cusp increases, does the present approach yield a slightly (4×${10}^{\mathrm{-}4}$ a.u.) higher energy. For the rest of the PES, our calculation yields the lowest energies yet.

Radiative lifetimes were determined for three quartet states of neutral nitrogen, and sequences of Rydberg states were studied using depletion spectroscopy. Free nitrogen atoms were generated by photodissociation of ${\mathrm{N}}_2$O using frequency-tripled dye-laser radiation that was two-photon resonant with the 2${\mathit{p}}^2$3p ${}_{}{}^4{}_{}{}^{}$S or ${}_{}{}^4{}_{}{}^{}$D states. Further quartet states were reached by a subsequent single-photon absorption. We obtain τ(2${\mathit{p}}^2$3p ${}_{}{}^4{}_{}{}^{}$${\mathit{D}}_{7/2}$)=44(2) ns, τ(2${\mathit{p}}^2$3p ${}_{}{}^4{}_{}{}^{}$${\mathit{S}}_{3/2}$)=26.0(1.5) ns, and τ(2${\mathit{p}}^2$6${\mathit{s}}^4$${\mathit{P}}_{5/2}$)=41(7) ns.

The radiative lifetime of the 3s3${\mathit{p}}^3$${(}^5$${\mathit{S}}_2^{\mathit{o}}$) metastable level of ${\mathrm{P}}^{+}$ has been measured by counting, for equal time intervals, the ∼221-nm photons emitted when the metastable ions decay to the 3${\mathit{s}}^2$3${\mathit{p}}^2$${(}^3$${\mathit{P}}_{2,1}$) levels of ${\mathrm{P}}^{+}$. This is the first lifetime measurement of the 3s3${\mathit{p}}^3$${(}^5$${\mathit{S}}_2^{\mathit{o}}$) level belonging to a low-charge-state ion in the Si i isoelectronic sequence. Although forbidden to decay by the LS selection rule ΔS=0, the ${}_{}{}^5{}_{}{}^{}$${\mathit{S}}_2^{\mathit{o}}$ level decays via intercombination electric dipole transitions by spin-orbit mixing with other levels of the 3s3${\mathit{p}}^3$ configuration. A metastable ${\mathrm{P}}^{+}$ ion population was produced inside a cylindrical radio-frequency ion trap by electron bombardment of ${\mathrm{PH}}_3$ vapor at pressures ranging from 5×${10}^{\mathrm{-}8}$ to 40×${10}^{\mathrm{-}8}$ Torr. The trap, operated with potential-well depths ranging from 12 to 20 eV, consists of two circular, wire-mesh end caps and a cylindrical, wire-mesh ring electrode with physical dimensions ${\mathit{r}}_0$=${\mathit{z}}_0$=1.67 cm. Some of the light emitted by the decaying ${}_{}{}^5{}_{}{}^{}$${\mathit{S}}_2^{\mathit{o}}$ population was focused onto a 19-nm-bandwidth interference filter in front of a photomultiplier tube operated in single-photon counting mode. The mean lifetime was obtained from the decay-rate parameter of a nonlinear least-squares fit of a single exponential plus a constant background to the decay counts. Our result for the radiative lifetime of the 3s3${\mathit{p}}^3$${(}^5$${\mathit{S}}_2^{\mathit{o}}$) metastable level of ${\mathrm{P}}^{+}$ is 167±12 μs.

The method of orthogonal collocation using triquintic Hermite-polynomial splines is developed to solve the Faddeev equations in the total-angular-momentum representation for three-body Coulomb bound-state problems. The wave function and the binding energy of the ${\mathit{e}}^{\mathrm{-}}$${\mathit{e}}^{\mathrm{-}}$${\mathit{e}}^{+}$ system are calculated.

Results are given of a calculation of the self-energy radiative correction for electrons bound in a strong Coulomb field. The calculation has been done for the states with principal quantum number n=3, 4, and 5, with angular momentum j=1/2 and 3/2, and for nuclear charge Z in the range 10–110.

The combined configuration-interaction–Hylleraas method has been used to calculate the energies for the ground 2 ${}_{}{}^2{}_{}{}^{}$S and the excited 2${\mathrm{}}^2$P and 3 ${}_{}{}^2{}_{}{}^{}$D states of the lithium atom. The energies obtained, -7.478 060 1 a.u. for the 2 ${}_{}{}^2{}_{}{}^{}$S state, -7.410 155 4 a.u. and -7.335 523 1 a.u. for the 2 ${}_{}{}^2{}_{}{}^{}$P and 3 ${}_{}{}^2{}_{}{}^{}$D states, respectively, are the lowest nonrelativistic variational upper bounds found so far. Ionization potentials, lifetimes, dipole oscillator strengths and their sums, dynamic dipole, quadrupole and dipole-quadrupole polarizabilities, and the static second hyperpolarizability are also reported and compared with experimental and other theoretical results.

The formation of n=2 positronium is investigated using a positron beam incident on a variety of untreated metal foils and crystals. The maximum measured formation fraction is much higher than any previously reported for such targets. Fully 2% of the incident positrons are observed to form n=2 positronium at low input energy with little dependence upon the metal substrate of the formation surface. The n=2 positronium spectra exhibit lifetime components characteristic of two distinct populations with different kinetic energies. The dependence of each of these components on the incident positron energy is studied and interpreted as being consistent with existing theories of positron interactions with metals. The production of n=2 positronium using positrons transmitted through metal meshes and thin foils is also observed and discussed briefly.

Radiative lifetimes of five levels belonging to the 3${\mathit{p}}^5$6p configuration of Ar i have been measured by means of electron-impact excitation followed by selective pulsed-laser excitation. The present experimental values have been compared with calculations performed in an intermediate-coupling scheme employing for the radial part of the transitions the Coulomb approximation as well as with theoretical results from other authors obtained with Hartree-Fock wave functions. The agreement between the experimental values and the Hartree-Fock calculations is within 4%.

The Schrödinger equation for two-electron atoms is replaced by another equation depending on a free dimensionless parameter β. Solution of the latter equation amounts to the diagonalization of a (β-dependent) infinite symmetric sparse matrix. The nonzero elements of this matrix are very simple and directly related to a representation of the o(4,2) algebra. Numerical results are in agreement with energy levels of the helium atom when β goes to infinity.

Using a split-valence Gaussian 4-31G basis function augmented with diffuse p and d function and multiconfiguration self-consistent-field optimized geometries, the frequency-dependent polarizability α and second hyperpolarizability γ of ethylene, trans-butadiene, trans-hexatriene, and trans-octatetraene molecules have been calculated by the time-dependent coupled perturbed Hartree-Fock ab initio method. The calculated values of α and γ are in good agreement with the corresponding gas-phase experimental values at the same fundamental wavelength. The various γ values corresponding to different third-order processes exhibit marked difference in their dependence on the conjugation length. For a specific fundamental frequency, the calculated γ value exhibits the following order: γ(-3ω;ω,ω,ω)>γ(-2ω;0,ω,ω)>γ(-ω;ω,ω,-ω) >γ(-ω;0,0,ω)≊γ(0;0,ω,-ω).

The $2^{1,3}$${\mathit{P}}_{1–}$2 ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$ transitions in berylliumlike molybdenum and berylliumlike iron have been calculated including all-order relativistic correlations due to the Coulomb as well as the Breit interaction. Important correlation corrections to the radiative contributions to the ground state were found due to the large admixture of ${\mathit{p}}^2$ character in the 2 ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$ wave function. Comparison with experiment is done after the addition of the Lamb shift for the corresponding hydrogenlike systems and an estimate of the screening caused by the 1${\mathit{s}}^2$ electrons. The results of ${\mathrm{Mo}}^{38+}$ are 725 751±300 and 2 004 464±300 ${\mathrm{cm}}^{\mathrm{-}1}$ for the 2 ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_{0–}$2 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$ and 2 ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_{0–}$2 ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$ transitions, respectively, which agree well with the experimental results 725 758±158 and 2 003 847±1200 ${\mathrm{cm}}^{\mathrm{-}1}$. The corresponding results for ${\mathrm{Fe}}^{22+}$ are 379 118±90 and 752 459±90 ${\mathrm{cm}}^{\mathrm{-}1}$, which can be compared to the experimental values 379 140±20 and 752 372±57 ${\mathrm{cm}}^{\mathrm{-}1}$. The uncertainty in the theoretical value is completely dominated by the uncertainty in the evaluation of the radiative effects in the electronic field.

Total cross sections for electron scattering have been measured in the 75–4000-eV energy range for ${\mathrm{NH}}_3$, ${\mathrm{SiH}}_4$, and ${\mathrm{H}}_2$S. For these gases, as well as for ${\mathrm{CH}}_4$ and ${\mathrm{H}}_2$O, cross sections have been fitted with a Born-like formula containing two parameters for each gas. The high-energy parameter of the fit to the cross sections has been related to the bond length of molecules. Partitioning of total cross sections into inelastic and elastic cross sections for these gases is discussed on the basis of available experimental data.

Ab initio calculations using the Born-Oppenheimer approximation are described of the dipole moments of the ${\mathit{i}}^3$${\mathrm{\Pi }}_{\mathit{g}–}$b ${}_{}{}^3{}_{}{}^{}\mathrm{\Sigma }_{\mathit{u}}^{+}{}_{}{}^{}$, ${\mathit{c}}^3$${\mathrm{\Pi }}_{\mathit{u}–}$a ${}_{}{}^3{}_{}{}^{}\mathrm{\Sigma }_{\mathit{g}}^{+}{}_{}{}^{}$, and ${\mathit{i}}^3$${\mathrm{\Pi }}_{\mathit{g}–}$c ${}_{}{}^3{}_{}{}^{}\mathrm{\Pi }_{\mathit{u}}^{}{}_{}{}^{}$ transitions of molecular hydrogen. Tables are provided of the dipole transition probabilities and Franck-Condon factors. Franck-Condon factors are presented for transitions originating in the lowest vibrational level of the ground ${\mathit{X}}^1$${\mathrm{\Sigma }}_{\mathit{g}}^{+}$ state.

The Dyson equation represents a well-defined connection between the one-particle Green’s function and the self-energy. By means of the Dyson equation, the evaluation of the one-particle Green’s function can be reduced to the evaluation of the self-energy. As it is well known, the one-particle Green’s function is composed of an advanced and a retarded part, which can be represented in the (N+1)- and (N-1)-particle configuration spaces, respectively. The Dyson equation combines these two spaces into a matrix in the union space. This is difficult to understand in configuration-interaction language, where the Hamiltonian matrices for systems containing different numbers of particles are naturally separated. Starting with the usual matrix representations of the Hamiltonian in the (N+1)- and (N-1)-particle spaces, it is shown that it is possible to define a class of unitary transformations that mixes the two parts and gives rise to an effective Hamiltonian matrix in the union space. This effective Hamiltonian leads to all possible representations of the Dyson equation. The transformations used arise from suitable combinations of the matrices of residues of the advanced and retarded Green’s functions. Several specific members of the above class of unitary transformations are discussed in some detail also in connection with possible approximation schemes for the Green’s function. Special attention is paid to those unitary transformations that depend on the ground state of the N-particle system as the only unknown quantity. This investigation has given rise to some general conclusions and to an alternative approach to the one-particle Green’s function.