Simulated sheared suspensions of particles with dipole interactions are found to adopt a number of different structural and rheological phases including a novel flowing crystalline phase. A crossover from Brownian to Stokesian transitions between phases is driven by partice-size effects.

We obtain the equations describing the swelling of an elastomeric sample when a good solvent diffuses in the elastomeric material. These equations predict the time evolution of the concentration profiles of the polymer. We consider explicitly the case of one-dimensional geometry (infinite slab) as well as the case of a spherical geometry in three dimensions and obtain numerical solutions for these cases. The experimental implications of our results are briefly discussed.

We provide a statistical-mechanical theory for a system of free polymer molecules in a colloidal solution. It is shown that three-body terms are required to obtain the shape of the polymer and the depletion-layer profile even when the dispersion medium is a good solvent for the polymer molecule. A semiquantitative analysis based on the density profile suggests that the addition of trace amounts (dilute) of free polymer induces the formation of weak flocs.

We have looked for a violation of time-reversal symmetry (T) in the molecule thallium fluoride using a rotationally cold beam from a jet source. Our method was to search for a frequency shift of the thallium nuclear magnetic resonance when an external electric field of 29.5 kV/cm was reversed with respect to a magnetic quantization axis. The measured shift, (1.4±2.4)×${10}^{\mathrm{-}4}$ Hz, was interpreted as a null result and constitutes a tenfold improvement in sensitivity over the previous measurement. Accordingly, our measurement has reduced the upper limits on the proton and electron electric dipole moments and on other T-violating weak couplings that can be deduced from the frequency shift.

Using methods of supersymmetry, we calculate the distribution of eigenvalues for random Hermitian band matrices. We show that, if the bandwidth b increases with the dimension of matrices N as b∝${\mathit{N}}^{\mathrm{\beta }}$ with some β>0, the resulting eigenvalue distribution is given by Wigner’s semicircle law as in the case of full random matrices of the Gaussian unitary ensemble.

The v-representability of the particle density for a system of noninteracting fermions is considered. It is shown that any reasonable spherical density for two spinless fermions is either the nondegenerate ground-state density or a linear combination of degenerate ground-state densities for some effective local potential, and is therefore ensemble v-representable. The results of model calculations are given that illustrate various possible situations for two-particle systems. An extension of this result for systems of more particles is made and the implications for density-functional theory are discussed.

We consider the v-representability of the particle density for a noninteracting system of spinless fermions by introducing the idea of proper order of a set of energy levels. It is shown that if ${\mathit{E}}_1$(λ), ${\mathit{E}}_2$(λ), and ${\mathit{E}}_3$(λ) are three energy levels associated with some local potential ${\mathit{V}}_{\lambda }$(r) that is a continuous function of λ=(${\lambda }_1$,${\lambda }_2$,${\lambda }_3$) over all possible points λ, where ${\lambda }_{\mathit{i}}$ is the occupation number of the ith state and M=${\lambda }_1$+${\lambda }_2$+${\lambda }_3$ is the total number of particles distributed over the three levels, then there must be at least one λ for which the three levels are in so-called proper order, in which the levels below the highest occupied level are filled. This result provides a basis for the proof of ensemble v-representability of some N-particle density for which the ground-state degeneracy of the system is no more than three. As examples, three- and two-dimensional central systems are examined, and an N-particle central density is shown to be ensemble v-representable for small N (N≤14 and N≤9 for three- and two-dimensional cases, respectively). The implications for density-functional theory are discussed.

Fine-structure intervals ${\mathit{np}}_{1/2}$-${\mathit{np}}_{3/2}$ (${\mathit{np}}_{1/2}$ is the ground state) are calculated for negative ions using relativistic many-body perturbation theory: ${\mathrm{Ca}}^{\mathrm{-}}$ 4p, 56 ${\mathrm{cm}}^{\mathrm{-}1}$; ${\mathrm{Sr}}^{\mathrm{-}}$ 5p, 178 ${\mathrm{cm}}^{\mathrm{-}1}$; ${\mathrm{Ba}}^{\mathrm{-}}$ 6p, about 460 ${\mathrm{cm}}^{\mathrm{-}1}$; and ${\mathrm{Ra}}^{\mathrm{-}}$ 7p, 1341 ${\mathrm{cm}}^{\mathrm{-}1}$. Comparison of the fine-structure interval with affinity: ${\mathrm{Ca}}^{\mathrm{-}}$ 10%, ${\mathrm{Sr}}^{\mathrm{-}}$ 22%, ${\mathrm{Ba}}^{\mathrm{-}}$ 30%; for ${\mathrm{Ra}}^{\mathrm{-}}$ the fine-structure interval is larger than the affinity. Thus the ${\mathrm{Ra}}^{\mathrm{-}}$ 7${\mathit{p}}_{3/2}$ state is a resonance in the continuous spectrum with energy 0.018 eV. This means that the relativistic spin-orbit interaction plays a determining role in slow electron-radium scattering.

Energy intervals, g factors, and M1 amplitudes of the 6${\mathit{p}}^2$ configuration in Pb and the 6${\mathit{p}}^3$ configuration in Bi are calculated. All the corrections of second-order perturbation theory in residual electron-electron interaction are taken into account. The higher-order corrections are also investigated. In Pb we have calculated the most important corrections: the screening of external electrons interaction by closed-shell polarization. In Bi the higher-order corrections are treated semiempirically. Energy levels for a superheavy element with charge Z=114 are also calculated.

Simple expressions are obtained for diagonal matrix elements 〈n,l‖${\mathit{r}}^{\mathrm{\beta }}$‖n,l〉, for arbitrary β and fixed l, where l=n-1, n-2, n-3, n-4, n-5, n-6, and n-7. Off-diagonal matrix elements are also calculated for the special cases 〈n,l‖${\mathit{r}}^{\mathrm{\beta }}$‖n,l±1〉 and 〈n,l‖${\mathit{r}}^{\mathrm{\beta }}$‖n,l±2〉. The expressions are valid for any real β≥-(l+l’+2).

Cross sections for transitions between hyperfine-structure states of muonic hydrogen atoms in asymmetric collisions have been calculated. The interaction is described by the improved adiabatic representation. s waves dominate the cross sections except for the remarkable case of tμ(↑↑)+d where the p wave dominates even at liquid-hydrogen temperature. The quenching rates for the colli-sions in which the muon resides on the heavier isotope are λ[dμ(↑↑) +p→dμ(↑↓)+p] =5.5×${10}^2$ (6.4×${10}^2$) ${\mathrm{s}}^{\mathrm{-}1}$, λ[tμ(↑↑)+p→tμ(↑↓)+p]=3.1×${10}^2$ (3.2×${10}^2$) ${\mathrm{s}}^{\mathrm{-}1}$, and λ[tμ(↑↑) +d →tμ(↑↓)+d]=7.5×${10}^1$ (7.3×${10}^2$) ${\mathrm{s}}^{\mathrm{-}1}$ at 23 K (232 K) and liquid-hydrogen density. Although some experimental observations have been attributed to hyperfine quenching in asymmetric collisions, these rates are probably too slow to have had an effect in previous experiments. However, the rate for tμ(↑↑)+d is somewhat uncertain since it is found to be extraordinarily sensitive to the potential. As a by-product of this work, an independent value of the hyperfine correction to the binding energy of tdμ(J=1,v=1) is obtained: Δ${\mathrm{\varepsilon }}_{\mathrm{hfs}}$=-36.1 meV for the lowest hyperfine state.

The one-dimensional equation of motion for the canonical or Bloch density matrix is solved by the method of separation of variables for independent particles moving in a potential V(x). The solution is exact when third and higher derivatives of V(x) are zero, embracing thereby the examples of (a) harmonic potentials and (b) a constant electric field of arbitrary strength. The form of the Slater sum obtained involves then two functions of temperature only, to be determined. One obvious relation between these two functions is via the partition function. A further relation comes from the orthonormality of the wave functions appearing in the Slater sum: the analog of idempotency for the ground-state Dirac density matrix. These two conditions again are shown to lead back to the exact result for harmonic potentials. The results presented generalize the one-dimensional Thomas-Fermi theory to apply to a temperature range that is significantly wider than for the original method.

Theoretical calculations of several Auger, Coster-Kronig, and super-Coster-Kronig transitions of noble gases (such as Ne, Ar, Kr, and Xe) and of transition-metal atoms and their ions are presented using the recently developed relativistic and correlated local-density method [M. Vijayakumar, N. Vaidehi, and M. S. Gopinathan, Phys. Rev. A 40, 6834 (1989)]. The importance of relativistic and correlation effects on these transition energies is discussed. The results are compared with reported experimental results as well as with those obtained by semiempirical and ab initio methods. Predictions are also made of various Auger transition energies for processes like K-LL and L-MM transitions for some ions.

Four metastable states (1 ${}_{}{}^4{}_{}{}^{}\mathrm{\Pi }_{\mathit{u}}^{}{}_{}{}^{}$, 2 ${}_{}{}^4{}_{}{}^{}\mathrm{\Pi }_{\mathit{u}}^{}{}_{}{}^{}$, ${}_{}{}^4{}_{}{}^{}\mathrm{\Phi }_{\mathit{u}}^{}{}_{}{}^{}$, and ${}_{}{}^4{}_{}{}^{}$${\mathit{I}}_{\mathit{u}}$), resulting from two-electron attachments to the excited ${\mathrm{He}}_2^{+}$ core ${(}^2$${\mathrm{\Sigma }}_{\mathit{g}}^{+}$), are characterized using the numerical Hartree-Fock method. It is determined that such metastable states are formed when both valence electrons are placed into equally diffused orbitals, which have bonding charter, and whose angular momentum quantum numbers do not differ by more than 1.

Ti K-shell ionization probabilities have been measured for p, d, and ${\mathrm{He}}^{+}$ impact at energies of 0.5 MeV/u and at large scattering angles, where the influence of the target-nucleus recoil is most prominent. The data are compared with different semiclassical-approximation calculations including higher-order corrections. Good agreement is only obtained if two-center binding-energy corrections for the adiabatically relaxing state are taken into account.

We used the distorted-wave approximation (DWA) and first-order many-body theory (FOMBT) for the calculation of integral cross sections (ICS’s), differential cross sections (DCS’s), and electron-impact coherence parameters (EICP’s) for electron-impact excitation of neutral magnesium for several transitions. In the case of 3${\mathrm{}}^1$P excitation, we studied the basis-set dependence of the ICS’s, DCS’s, and EICP’s, we investigated the effect of unitarization on these quantities, and we compared the DWA with FOMBT. We also studied the principal-quantum-number dependence of the EICP’s for ${\mathit{n}}^1$P (n=3,4,5,6) excitation.

First-order Born cross sections for electron-positron pair production in relativistic heavy-ion collisions are calculated. Sommerfeld-Maue wave functions are employed to describe the continuum state of the emitted electron and positron in the field of the heavy target nucleus. Double-differential, single-differential, and total cross sections are presented in a wide energy regime from 1 GeV/u up to 20 TeV/u. We compare our results with first-Born calculations using a partial-wave expansion and with lowest-order QED calculations. The target-charge dependence is investigated.

Doubly excited ${}_{}{}^{1,3}{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ autodetaching resonances in ${\mathrm{Ps}}^{\mathrm{-}}$ have been calculated using the complex-rotation method, which has the advantage of giving resonance position and width at the same time. The wave function is of the Hylleraas type with number of terms up to 1330. Feshbach resonances associated with the positronium n=4, 5, and 6 thresholds are reported. In addition, we have also identified ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ shape resonances associated with the positronium n=4 and 6 thresholds, and a ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ shape resonance associated with the n=5 positronium threshold.

Feshbach-type ${}_{}{}^{1,3}{}_{}{}^{}$D resonances in two-electron systems, Z=2–10, have been investigated using the method of complex rotation. These states lie below the n=2 and 3 thresholds of hydrogenic systems. Wave functions containing up to 1230 Hylleraas functions have been used, giving accurate results for positions and widths. Comparisons between various calculations are given.

Singly excited states of sodiumlike argon and sulfur have been investigated by means of high-resolution 0° Auger spectroscopy at high projectile energies. The Auger-electron spectrum is due to the decay of states populated by monopole, dipole, and quadrupole excitation of the 2p and 2s electrons. Collision strengths calculated by means of the configuration-interaction Hartree-Fock program by Cowan [The Theory of Atomic Structure and Spectra (University of California Press, Berkeley, 1981)] in the plane-wave Born approximation (PWBA) have been used to describe the relative intensities found in the measured spectrum. The intensities due to monopole excitation are significantly higher than the prediction by PWBA for a Coulomb perturbation potential. The structure of the emitted electron spectrum is found to be significantly influenced by the configuration interaction.