We have calculated the frequency-dependent nonlinear susceptibilities of hydrogenic ions up to the 70th order of nonlinearity, in the framework of lowest-order perturbation theory. In this approximataion, the critical driving intensity, at which the radiated harmonic intensity of the (n+2)th order exceeds that of the nth order, is found to decrease rapidly with n. The computed values of critical intensity are comparable to those at which ‘‘plateau’’ behavior is observed in recent experiments.

Cross sections for the production of Ar recoil ions in collisions with 1-MeV/amu ${\mathrm{O}}^{\mathrm{q}+}$ and ${\mathrm{F}}^{\mathrm{q}+}$ (q=2 to bare nuclei) were measured by the time-of-flight technique. The cross sections for the production, by pure ionization, of recoil ions having charges greater than 6 display an unexpected behavior as a function of q. They rise at low q, reach a maximum in the vicinity of q=5–7, and then decrease at high q. Cross sections calculated using the independent-electron approximation rise continuously in this region and are lower than the experimental cross sections by as much as 4 orders of magnitude for high recoilion charge and low q. The observed turnover in the cross sections, as well as the large discrepancies in absolute magnitude between experiment and calculation, are accounted for by vacancy multiplication resulting from L-shell ionization followed by Auger decay.

The technique of 0° Auger-electron spectroscopy has been used to study Na-like ${\mathrm{Ar}}^{7+}$ excited states populated in double- and single-capture collisions by 90-keV ${\mathrm{Ar}}^{9+}$ and 80-keV ${\mathrm{Ar}}^{8+}$ projectiles from He target atoms. Metastable Ne-like ${\mathrm{Ar}}^{8+}$ 2$p^5$3s ${}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}$,2 states play an important role in populating several ${\mathrm{Ar}}^{7+}$ final states. Careful He-target pressure dependence studies were performed to establish the excitation and/or capture mechanism for the Na-like core-excited levels. Highly nonequivalent 2$p^5$3lnl’ configurations, with n values peaking at n=8 but extending to near the series limits, were produced in double-electron capture onto ${\mathrm{Ar}}^{9+}$ projectiles. The spectra have been identified and compared with calculated multiconfiguration Dirac-Fock (MCDF) Auger energies and previous measurements. The Auger decay of the ${\mathrm{Ar}}^{7+}$ 2$p^5$3s3p ${}_{}{}^4{}_{}{}^{}\mathrm{D}_{7/2\mathrm{}}^{}{}_{}{}^{}$ metastable level has been observed and the energy of the line from the Breit induced decay has been measured. Allowed doublet lines from the 2$p^5$3$s^2$ ${}_{}{}^2{}_{}{}^{}\mathrm{P}_{1/2}^{}{}_{}{}^{}$,3/2 states were also measured. The experimental values are in strong agreement with the results of the MCDF calculations.

Rydberg←Rydberg state transitions of ${\mathrm{Ne}}_2$ have been observed for the first time by laser-excitation spectroscopy. Molecular Rydberg states having principal quantum numbers as large as 17 have been detected despite the predissociative nature of the high-lying ${\mathrm{Ne}}_2$ excited states. Several bands have been rotationally resolved and the rotational constant measured for the metastable 3sσ ${}_{}{}^3{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$ state of the excimer agrees with theoretical (ab initio) predictions to within 4%.

Kinetic sound is predicted in dilute disparate-mass binary gas mixtures, propagating exclusively in the light compound and much faster than ordinary sound. It should be detectable by light-scattering experiments, as an extended shoulder in the scattering cross section for large frequencies. As an example, ${\mathrm{H}}_2$-Ar mixtures are discussed.

We have studied the numerical model of a two-dimensional gel exhibiting the volumetric phase separation between the swollen and shrunken phases. We have found a peculiar percolating (spongelike) structure of the shrunken phase domain. A qualitative explanation for the appearance of such a structure is given and its relevence to the real gel system is discussed.

We develop a singular perturbation approach to the problem of the calculation of a characteristic time (the nonlinear relaxation time) for non-Markovian processes driven by Gaussian colored noise with small correlation time. Transient and initial preparation effects are discussed and explicit results for prototype situations are obtained. New effects on the relaxation of unstable states are predicted. The approach is compared with previous techniques.

High-resolution ac calorimetric data are reported for three polar liquid-crystal systems: octyloxyphenylcyanobenzoxybenzoate (80PCBOB), a mixture of pentylphenylcyanobenzoyloxybenzoate (${\mathrm{DB}}_5$CN)+cyanobenzoyloxypentylstilbene (${\mathrm{C}}_5$ stilbene), and a mixture of ${\mathrm{DB}}_6$CN+${\mathrm{C}}_5$ stilbene. All three exhibit nematic–smectic-$A_1$ one liquid-crystal transition heat-capacity peaks well described by the XY critical exponent ${\alpha }_{\mathrm{XY}}$=-0.007. The critical amplitude ratio $A^{\mathrm{-}}$/$A^{+}$ (=0.99) agrees fairly well with the XY value and is inconsistent with the theoretically expected inverted-XY value. Correction terms also play an important role.

Two growing kinetics of self-avoiding walks on dilute lattices are considered for discussion of the crossover scaling behavior of self-avoiding walks near percolation threshold. The crossover properties for each kinetics are exactly calculated on a diluted linear chain and on a Cayley tree. We also consider crossover properties for each kinetics on general lattices. From the results the recent controversies of self-avoiding walks near the threshold are analyzed.

A nonperturbative method using a Monte Carlo algorithm is used to integrate the Bethe-Salpeter equation in momentum space. Solutions for two scalars and two fermions with an arbitrary coupling constant are calculated for bound states in the ladder approximation. The results are compared with other numerical methods.

The problem of atomic dissolution by means of decay to the negative energy continuum is discussed. The derivation of the one-electron central-field Hamiltonian from quantum electrodynamics is made as an example. It is found that the operators that project the Coulomb interaction into positive and negative energy states of the Dirac noninteracting Hamiltonian cause the eigenstates of the atomic Hamiltonian to break up into two sets. One set is expandable in the positive energy noninteracting states, and this set propagates forward in time. The other set is expandable in terms of the negative energy noninteracting states and propagates backward in time. There is, therefore, no danger that transitions will occur from the forward propagating eigenstates into the negative continuum with continued propagation in the forward direction, regardless of the magnitude of the nuclear charge.

The simple configuration-interaction calculational procedure for an alkaline-earth atom is extended to include the continuum contribution to the Hamiltonian matrix evaluated in a basis set constructed from a quasicomplete set of discrete one-particle orbitals expanded in terms of a set of B splines. The procedure is successfully applied to the study of the energy eigenvalues, the excitation energies, and the oscillator strengths for transitions between selected ${}_{}{}^1{}_{}{}^{}$,3S, ${}_{}{}^1{}_{}{}^{}$,3P, and ${}_{}{}^1{}_{}{}^{}$,3D states of the beryllium atom. In addition to the simplicity of this calculational procedure and its effectiveness in generating atomic spectroscopy data for an extended spectral region in a single calculation with a single basis set, our numerical results have shown that the quantitative reliability of this procedure is comparable to or better than many other more elaborate theoretical approaches.

The atomic-beam laser-rf double-resonance method has been used to measure the hyperfine structure (hfs) of the J=2–8 levels of the ${}_{}{}^{11}{}_{}{}^{}\mathrm{F}$ term of 4$f^7$5$d^2$6s in ${}_{}{}^{155}{}_{}{}^{}$,157Gd. Results are also reported for the J=2,5 levels of the ${}_{}{}^7{}_{}{}^{}\mathrm{D}$ term of 4$f^7$5d6$s^2$. Less precise hfs results are given for ten highly excited even-parity levels, and isotope shifts are given for 16 optical lines. L-S limit effective-operator expressions are given for the hfs A and B values of arbitrary states built from three open electron shells. When specialized to the ${}_{}{}^{11}{}_{}{}^{}\mathrm{F}$ term in Gd i, these expressions reveal a marked perturbation between the J=5 levels of 4$f^7$5$d^2$6s ${}_{}{}^{11}{}_{}{}^{}F$ and 4$f^7$5d6$s^2$ ${}_{}{}^7{}_{}{}^{}D$. The perturbation can also be detected from the fine-structure intervals.

The second-order spin-adapted reduced Hamiltonian, usually represented as a matrix, is transformed to the form of a two-body operator in the coordinate representation. The new form of this Hamiltonian deepens our insight into its structure and physical meaning. An analysis of its asymptotic form for complete Hilbert spaces gives a formal proof of an earlier assumption that the spin-adapted reduced Hamiltonian describes independent electron pairs.

It has been found that, when the occupancy of the 3d orbital changes in the iron series (such as in s-d transfer and electron removal), the J-independent relativistic energy contributions (mass-velocity, one- and two-body Darwin, and electron-spin contact terms) to the corresponding energy differences are non-negligible. Thus they should be taken into account when a comparison of the calculated quantities with the experimental values is made for the purpose of testing the accuracy of a given theoretical approximation. In particular, the s-d interconfiguration energies and the removal energies are often used to test various approximations for exchange-correlation and correlation-energy functionals in density-functional theory. One of the conclusions of this study is that density-functional theory with its various approximations for the correlation-energy functional does not reproduce adequately the correlation-energy contributions to these energy differences for the iron-series elements.

We compare the exact solutions for one- and two-electron systems with those given by the Kohn and Sham equations, looking for an exchange-correlation functional with universal use. We conclude that the many local-density approximations now available, all based on the homogeneous electron gas, are probably no improvement over the older exchange-correlation method with parameter α, but with α depending on the number of electrons (and very little on its density) and on symmetry. A surprising result of our search is that exchange correlation can be also described by means of a modification of the electronic mass instead of a local potential.

Using a combination of variational and perturbational techniques, we obtain a shift of +0.20 meV for the energy level of [(td${\mu }_{11}$)e] due to the nonpointlike character of the (j=1, v=1) state of tdμ. We estimate the error to be ${(}_{\mathrm{-}0.1}^{+0.2\mathrm{}}$) meV. Scaling this value for the [(td${\mu }_{11}$)d2e] system gives a shift of +0.29. Earlier perturbational calculations are shown to be affected with an inaccuracy of ∼3 meV resulting from an inadequate choice of the perturbation operator.

An asymptotic analysis of the partial collision strength for quadrupole-allowed transitions, in the limit of large angular momentum, is presented. It is shown that the infinite sum over partial collision strengths, which gives the total collision strength, is asymptotic to a geometric series of ratio $k_{<}^2$/$k_{>}^2$, where $k_{>}^2$ and $k_{<}^2$ are the energies of the free electron before and after the collision.