The second-order nematic to lamellar-smectic phase transition is studied in the micellar systems decylammonium chloride–${\mathrm{NH}}_4$Cl–water and cesium perfluoro-octanoate–${\mathrm{D}}_2$O, by measuring the electric conductivity of aligned samples and the density as functions of temperature. In the nematic range, for temperatures higher than about 1 °C above the transition, the data on cooling and heating coincide within experimental error. Closer to the lamellar-smectic phase significant differences occur between the values observed on heating and cooling. For the density, the difference between the two values in the smectic range is several ${10}^{\mathrm{-}4}$ g/${\mathrm{cm}}^3$. The processes responsible for the observed behavior have long relaxation times, estimated in the order of several hours to several days. A simple rearrangement of the micelles into layers should have relaxation times comparable to the relaxation times of the nematic to smectic-A phase transition in thermotropic liquid crystals; however, no such relaxation effect has been reported in thermotropic liquid crystals, even at very fast heating and cooling rates. Accordingly, the slow relaxation suggests significant change in the micellar structure at the nematic to lamellar-smectic phase transition, probably a divergence in the aggregation number, i.e., a transition to continuous lamellae. The observed long relaxation times reflect the slow approach to an equilibrium distribution of defects after the formation of the lamellae.

Recent experiments on colloidal suspensions of silica spheres in a water-lutidine mixture close to the consolute point have revealed interesting sphere-aggregation behavior that has been linked to wetting phenomena. We carry out a theoretical analysis of the phase behavior in such mixtures and suggest that the observed behavior is consistent with general expectations in three-component fluids.

We present the phase diagram of a system of hard spherocylinders, including the isotropic liquid and the nematic and smectic-A liquid crystals, calculated with a nonlocal-density-functional model for the free energy. We get first- and second-order nematic–smectic-A transitions, with a tricritical point at L/D=50, and a triple coexistence point (isotropic-liquid–nematic–smectic-A) for L/D=3.

The qth moment M(q) of the growth probability of diffusion-limited aggregates is studied for q<0 in terms of the value [M(q,N${\left)\right]}_{\mathrm{av}}$ obtained by averaging M(q) over the ensemble of all aggregates of a given number of particles N. For a range of structures that are susceptible to precise analysis, we verify that all moments, even those for q<0, obey asymptotic power-law scaling in N. Since we cannot analyze completely arbitrary structures, our analysis is not definitive. However, it does suggest the validity of a recent proposal by one of us that there is no Lifshitz-like anomaly (similar to that found for the distribution of currents in the random resistor network) leading to non-power-law scaling of the negative moments of the growth probability.

Simulations of spatially correlated ballistic deposition have been carried out using simple two- and three-dimensional lattice models. In these models particles are deposited, one at a time, from the ends of the steps in a Levy flight taking place in a line or plane above the surface of the deposit. For deposition on a line, the exponent α that describes the dependence of ξ (the surface width) on the lateral system size (L) is given by α=(1/2 for f≤1/2 and α=(1/2+(f- 1) / 2 )/3 for (1/2≤f≤2. Here f is the fractal dimensionality of the Levy flight. For deposition with transfer of the deposited particle (site) to the nearest local minimum (deposition with restructuring), α=(1/2(1+f) for 0≤f≤1 and α=1 for f>1. For deposition onto a plane the uncertainties are much larger, but our results suggest that α≃0.36 for f≤1 and that α grows linearly to a value of about (1/2 for f in the range 1≤f≤2. For deposition onto a plane with restructuring, α≃f/2. All of our simulation results are consistent with the scaling relationships α+α/β=2 for deposition without restructuring and α/β=2 for deposition with restructuring. Overall, our results are in good agreement with the theoretical predictions of Medina et al. [Phys. Rev. A 39, 3053 (1989)].

A renormalization-group theory is developed to study the fractal and the multifractal structures in the viscous fingering of a non-Newtonian displaced fluid at an infinite viscosity ratio. The effect of the non-Newtonian fluid on the multifractal scaling of the growth-probability distribution is investigated by using a finite lattice renormalization. The dependences of the α-f spectra of the growth-probability distribution are shown on the parameter k describing the different non-Newtonian fluids. It is found that the non-Newtonian fluid has important effects on the multifractal structure of the growth-probability distribution.

A renormalization-group theory is developed to study the multifractal structure of the growth probability distribution in the diffusion-limited aggregation on the multifractal lattice proposed by Meakin [Phys. Rev. A 36, 2833 (1987)]. The hierarchical lattices with two classes of multifractal heterogeneity are constructed using a diamond generator with two sets of weights $P_1$=1, $P_2$=Q, $P_3$=$Q^2$, and $P_4$=$Q^3$ and $P_1$=1, $P_2$=1, $P_3$=Q, and $P_4$=Q. Multifractal scaling exponents of the growth probability distribution are calculated using a finite-lattice renormalization. The effect of the multifractal heterogeneity on the growth probability distribution is considered. It is shown that the multifractal heterogeneity has important effects on the multifractal structure of the growth probability distribution.

A method described previously for obtaining upper and lower bounds for the eigenenergies of the Schrödinger equation for parity-invariant and central potentials is extended and applied to asymmetric one-dimensional potentials. The procedure consists of transforming the Schrödinger equation into a Ricati one for the logarithmic derivative of the wave function. The solution of the latter equation is approached by a series of Padé approximants. Approximate eigenenergies are obtained from the roots of associated determinants, and such roots are proved, in some cases, to be upper or lower bounds to the actual eigenenergies. The method is illustrated by calculations for several model potentials and the results compared with those obtained by alternative procedures.

Both single-well and multiwell one-dimensional anharmonic oscillators have provided an extremely fruitful testing ground for various modern techniques of microscopic quantum many-body theory and quantum field theory. They have served both as (0+1)-dimensional field-theory models of their important counterparts in a higher number of dimensions, and as algebraically simple yet highly nontrivial problems on which various approximation or truncation schemes could be tested to very high orders. Such techniques have included perturbation theory and its many possible resummation schemes, and the coupled-cluster method. In the present paper the spotlight is focused on variational methods, and we concentrate on their application to the particularly demanding double-well quartic anharmonic oscillator. We examine in detail both single-state and multistate variational calculations based on either orthogonal (uncorrelated) or nonorthogonal (correlated) basis functions. Particular attention is paid to the question of the sensitivity and accuracy of the results with respect to any nonlinear parameters that characterize the basis states. Practical schemes are suggested for their choice and are shown to be capable of very high accuracy. Use of this simple model also allows detailed comparisons to be made with other techniques of a perturbative or perturbative-variational hybrid character.

We have observed the narrow 1S-2S transition in hydrogen and deuterium with high resolution using Doppler-free two-photon absorption of continuous-wave 243-nm light. The transition frequencies were measured by direct comparison with accurately calibrated lines in the spectrum of the ${}_{}{}^{130}{}_{}{}^{}\mathrm{Te}_2^{}{}_{}{}^{}$ molecule. We find the 1S-2S interval to be 2 466 061 414.1(8) MHz in hydrogen and 2 466 732 408.5(7) MHz in deuterium. By combining these results with recent measurements of the Rydberg constant we obtain the values 8172.6(7) and 8183.7(6) MHz for the 1S Lamb shifts in hydrogen and deuterium, respectively. These are the most precise measurements of the 1S Lamb shifts in these atoms and they are in excellent agreement with the theoretical values of 8173.03(9) and 8184.08(12) MHz. Alternatively, if the 1S Lamb shift is supposed known from theory, our measurements determine the Rydberg constant as $R_{\infty }$=109 737.315 73(3) ${\mathrm{cm}}^{\mathrm{-}1}$.

Given any one-dimensional potential V(x) with n bound states, we construct an infinite number of isospectral potential families $V^{\left(a\right)}$(${\lambda }_0$,${\lambda }_1$,..., ${\lambda }_{n-1}$;x). The parameter a takes integer values and the n parameters ${\lambda }_i$ take real continuous values. All potentials have identical bound-state eigenvalues, but the reflection and transmission coefficients depend on the index a.

The solution of the coupled-cluster one- and two-particle equations by finite basis sets is demonstrated. The g-Hartree coupled-cluster equations are derived, and, as an example, the ground-state energy of Be is calculated, iterating the one-particle equation to infinite order coupled to the lowest-order two-particle function. This calculation is performed for the g-Hartree and the Hartree-Fock mean field, and the results are discussed.

A self-consistent treatment of rescattering effects of a nuclear subsystem in a μ-mesonic molecule is proposed. Strong nonlocality of the nuclear t matrix with respect to the μ-meson coordinate is established. This effect gives an essential contribution to the energy shifts of the Coulombic levels of a pdμ mesonic molecule. For a pdμ mesonic molecule the difference of energy shifts of levels with nuclear spins S=(1/2 and (3/2 equals 0.052 eV.

The scattering form factors for excitation of ${\mathrm{H}}_2^{+}$ in fast collisions are calculated in a sequence of approximations revealing their dependence on details of the initial- and final-state wave functions. Each approximate calculation is compared directly to the ‘‘exact’’ results obtained with separable, fixed-nuclei wave functions. Even for interproton separations larger than those for which the united-atom limit applies, the quasiatomic character of the final-state orbital dominates transition amplitudes to low-lying dissociative states. Possible applications to molecular dissociation by charged-particle impact at high energies are considered.

A new mode of transfer excitation (TE) process in high-energy ion-atom collisions is analyzed in which two or more electrons in the target system are involved incoherently in the excitation of the projectile ion and electron transfer. This uncorrelated TE mode (UTE) is shown to resolve the long-standing discrepancy in the high-energy tail of the resonant TE (RTE) cross section in the ${\mathrm{Nb}}^{31+}$+${\mathrm{H}}_2$ collisions, and explains satisfactorily the recent experimental studies of the system ${\mathrm{F}}^{6+}$+${\mathrm{H}}_2$ by Schulz et al. [Phys. Rev. Lett. 62, 1738 (1989)] for the uncorrelated transfer excitation followed by x-ray decay plus RTEX, involving radiative decay to a singly excited state, and of the low-lying states of ${\mathrm{F}}^{6+}$ with He by Zouros et al. [Phys. Rev. Lett. 62, 2261 (1989)] for the UTE involving Auger decay.

We show that a useful concept of the time spent by a quantum-mechanical particle in a given spatial region can be expressed in terms of a Hermitian sojourn time operator. Mean values of this operator give the mean sojourn time (dwell time) of the particle. We show that the sojourn time operators occur in a natural way in first-order perturbation theory for the barrier perturbed by any finite-range potential. The perturbed S operator, and also the effect of the perturbation on the change of observables due to the scattering, are, to a first-order approximation, fully expressible in terms of sojourn time operators. We anticipate that this result can be generalized to the case when the translational motion of the tunneling particle is weakly coupled to additional degrees of freedom. As a specific example of such a system, we explicitly reconsider the Larmor clock, originally proposed as a device measuring interaction times. We show that the change of the spin components, to a first-order approximation, is indeed fully expressible in terms of a sojourn time operator. In particular, when set as a clock, the system measures mean values of the sojourn time operator or real parts of some of its matrix elements.

The spin-destruction rates due to rubidium-rubidium and potassium-potassium collisions involving the $S_{1/2}$ ground states were measured. These spin-destruction cross sections decrease about an order of magnitude for the next lighter alkali-metal atom when comparing cesium, rubidium, and potassium.

Total cross sections and doubly differential probabilities for various two-electron processes resulting from protons colliding with helium are calculated using a new two-active-electron classical-trajectory Monte Carlo theory in which one electron moves under the influence of the projectile and target nucleus potentials as well as a time-varying potential due to the other electron. This results in a dynamic screening of the target nucleus by one active electron as seen by the other active electron. The results of calculations for the two-electron processes of ionization (including single and double), transfer ionization, ionization, and excitation, as well as double ionization, are presented. The double-ionization results are compared with recent experimental results and are found to have an improved agreement over any other results available to date.

The formation of positronium (Ps) in different states by the impact of intermediate energy (20–500 eV) positrons on atomic hydrogen is calculated using the distorted-wave Born approximation along with the first Born approximation. Differential and integrated cross sections for the formation of Ps(1s), Ps(2s), Ps(2$p_0$), and Ps(2$p_1$) have been evaluated individually and then 1/$n^3$ behavior for charge-transfer cross sections is used for n>=3 to obtain the total cross sections for positronium formation. The present results for positronium formation cross sections are in agreement with the results of other available investigations.

Slow Ar recoil-ion production cross sections by projectiles of 1.05-MeV/amu ${\mathrm{Ar}}^{\mathrm{q}+}$ (q=4,6,8,10,12,14) were measured using a projectile-ion–recoil-ion coincidence technique. The present results indicate that the average recoil ion charges 〈i〉 increase with increasing the incident projectile charge q and the number of the lost and captured electrons from and/or into projectiles, whereas the projectile charge-changing cross sections for loss ionization decrease steeply with increasing q for low-charge-state projectiles, and those for transfer ionization increase rapidly with increasing q for high-charge-state projectiles. For Ar projectiles with q=10, which corresponds to the equilibrium charge state of Ar projectiles at the present collision energy, the average recoil-ion charges are nearly the same in both loss and transfer ionization, and a pure ionization process plays a much more important role in producing highly charged recoil ions, in contrast to projectile electron loss or transfer processes, which play a role in other projectile charge states.