The first experimental determination of excited-state dipole moments of an alkaline-earth monohalide radical is reported. Rotational transitions in the A ${\mathrm{}}^2$Π-X ${\mathrm{}}^2$${\Sigma }^{+}$ and B ${\mathrm{}}^2$${\Sigma }^{+}$-X ${\mathrm{}}^2$${\Sigma }^{+}$band systems of CaCl were studied in an external electric field. With the application of laser spectroscopy to a molecular beam the Stark shifts and splittings of individual lines were precisely measured. As the electric dipole moment of the ground state was known from previous investigations the excited-state dipole moments could be determined as μ(A ${\mathrm{}}^2$Π)=3.54(10) D and μ(B ${\mathrm{}}^2$${\Sigma }^{+}$)=4.026(60) D, the absolute error of the measurements given in parentheses.

Previous experimental and theoretical work has found electron capture to be a monotonically decreasing function of energy in fast ion-atom collisions. We report here the experimental observation of nonmonotonic behavior of the electron-capture cross sections in fast collisions of calcium ions, in charge states 16+ to 19+, with molecular hydrogen, in the energy range 97–368 MeV. The structure observed in the measured cross sections is attributed to the contribution of resonant transfer and excitation to electron capture.

A new technique is described which utilizes optical pumping in a time-resolved mode to study atomic hydrogen produced by a discharge. Initial measurements provide information about the equlibrium atomic-hydrogen density, its temporal evolution, and the diffusion coefficient for hydrogen atoms in molecular hydrogen.

The existence of isolated (in energy) field-induced nonlinear resonances is shown rigorously for a quantum particle in an infinite square-well potential and driven by a monochromatic external field. Above a critical external-field amplitude overlap can occur. The condition for appearance of resonance zones depends strongly on the size of the quantum system.

The author develops a theory of ac Stark (or Autler-Townes) splitting occurring in double optical resonances, one of which is a two-photon transition. It includes both laser bandwidth and collisional broadening effects. Theoretical results are in excellent agreement with Goldsmith’s observation of two-peaked structures in the multiphoton excitation spectra of atomic hydrogen in atmospheric-pressure flames. This is believed to be the first study demonstrating that the peak asymmetry in an ac Stark doublet can be reversed due to pressure broadening.

The effect of frequency perturbations on the stability of tuned, standing-wave gas lasers is determined, by use of the assumption of strong Doppler broadening. It is shown that such perturbations determine the instability threshold over a part of the parameter space, and that such thresholds correspond to bifurcations in the steady-state amplitude and frequency of the field. While the effect on the amplitude is found to be small, significant frequency bistability, resulting from the bifurcation, is indicated.

The density-matrix equation for a single atom interacting with a single mode of a cavity with finite Q is solved for the time dependence of various physical quantities using the dressed-atom approximation. The effect of the cavity damping on the collapse and revival phenomena and on the photon statistics is studied in detail.

The polymer-size distribution for the ensemble of kinetically growing branched polymers, in which molecules are labeled by the number of bonds they contain, is introduced and the Smoluchowski equation describing its time evolution is formulated. Analysis of this equation demonstrates the existence of a scale-invariant solution, with two independent scaling exponents, which we determined by the experimental measurement of the time dependence of the first two moments of the polymer-size distribution.

We propose a new and simple model for the formation of kinetic clusters. The model appears to have two critical points. The first one corresponds to a site percolation threshold, at which point a fractal structure appears for the first time, and below which the clusters stop growing after a finite time. The second critical point appears to be exactly the same as the site percolation threshold of the lattice in the directed percolation process, and at which point a qualitative change in the structure of the cluster appears. Various critical properties of the model are computed in two dimensions and they appear to be slightly but consistently different from those of random percolation. The clusters reduce to the Eden model in a special limit, and they appear also to have close connection with ballistic aggregation and cellular automata.

We use a recently developed renormalization-group formalism to study the global properties of the period-doubling attractor. The renormalization scheme can be written in closed form in terms of universal functions. The results of the calculation appear as a smooth spectrum of scaling indices in full agreement with direct numerical calculations. As a special result we obtain the fractal dimension of the attractor to be $D_0$=0.538 045 143 5, accurate to one part in ${10}^{\mathrm{-}10}$. The only input for the calculation is the Taylor expansion of Feigenbaum’s universal function.

We study the stability of a parallel array of Saffman-Taylor fingers in the limit of infinite viscosity contrast. We discover a modulatory instability which prevents the system from remaining in steady-state motion. We discuss how this instability signals the beginning of the coalescence of the finger array to the final single-finger steady-state configuration. Finally, we speculate on the importance of this global instability for the understanding of patterns in diffusion-limited growth.

We describe an efficient and general algorithm for simulating polymers, which can be used for single, large chains as well as many-chain systems. It allows us to distinguish solvent effects from interchain effects on the dynamics of the chains. The method is tested for linear and cyclic chains of 50 to 200 monomers. We have confirmed two theoretical results which have not been observed numerically or experimentally, namely the anomalous behavior of S(q) for rings and the $t^{0.54}$ power law for the motion of a monomer in a self-avoiding chain undergoing Rouse relaxation.

An incommensurate smectic-A phase (${\mathrm{SA}}_i$) made of two collinear independent density modulations at two incommensurate wave vectors is found to be stable in the phenomenological model of frustrated smectic phases of Prost in mean-field theory. The N-${\mathrm{SA}}_1$-${\mathrm{SA}}_d$-${\mathrm{SA}}_2$-${\mathrm{SA}}_i$ phase diagram is computed; its representation in appropriate axis (i.e., temperature, incommensurability) is fully compatible with the experimental topology recently reported in a binary mixture of 4-n-heptyloxyphenyl-4’-cyanobenzoyloxybenzoate (DB7OCN) and 4-octyloxy-4’-cyanobiphenyl (8OCB).

We analyze the time-dependent solution of the simplest Fokker-Planck equation which describes the action of Gaussian white noise in a single-mode laser. The pump parameter is linearly swept in time. Because of the critical slowing down, the time evolution of the probability distribution exhibits a delay with respect to the instantaneous value of the pump parameter. The delay turns out to depend crucially on the sweeping rate and to be essentially independent of the initial value of the swept parameter.

Coherent states for the Morse oscillator are constructed using generalized coherent states associated with the SO(2,1) noninvariance group for this potential. By using the path integral over these states, it is shown that the Morse oscillator may be viewed as a harmonic oscillator evolving in a fictitious time. To show that this picture is mathematically consistent, we compute the path integral for the Green’s function and recover the bound-state spectrum.

In order to investigate the potential precision of quantitative calculations using hyperspherical coordinates, we have reexamined this method in detail. By developing an analytic solution of the angular equation in the form of a series expansion in the variable x=tan(α/2), we are able to isolate the numerical errors in the solution from those caused by the truncation of the angular momentum expansion and by the exclusion of radial coupling terms, which we then examine separately. This new method enables us to extend the calculation of the potential curves and channel functions to the large-R region and to obtain asymptotic expansions for the potential curves and radial couplings. From these we determine general expressions for the boundary conditions of the radial equation. Finally, we present the first nonadiabatic result for the ground-state energy of helium.

We discuss quantum measurements and find a repeated-measurement scheme to monitor the free-mass position to an arbitrary accuracy.

To help simplify the many-electron problem, a new algorithm is presented which enables the generation of approximate ground-state electron densities and approximate ground-state energy differences of isoelectronic processes for interacting and noninteracting systems. This is accomplished starting exclusively from knowledge of the following: one isoelectronic ground-state ‘‘seed’’ density ${\rho }_A$, the external potential $v_A$ which generates ${\rho }_A$, and the external potential $v_B$ for which the ground-state energy $E_B$ and density ${\rho }_B$ are sought. Use is made of a matching theorem in conjunction with trial first-order density matrices (one-matrices), the virial theorem, and a variation of a Legendre-transform idea. Furthermore, knowledge of the exact energy $E_A$ enables the approximation of $E_B$ using either one of two energy-difference formulas which are approximations to the exact integrated Hellmann-Feynman energy difference. Initial tests for noninteracting electrons are constructed.

An analysis of some of the coupled-cluster methods has been undertaken for the calculation of first-order properties. In particular, it has been shown that Arponen’s variational extended exp(T) method truncated to the quadratic power in the cluster amplitudes gives a result identical to the average value of the property operator with the linearized coupled-cluster doubles (L-CCD) stationary state truncated to the quadratic power in amplitudes in the model where only two-body excitations have been included in the cluster amplitudes. In the same model it is also shown that Monkhorst’s nonvariational method gives results identical to the previously mentioned average value again truncated to the quadratic power in amplitudes with a full CCD stationary-state wave function.

In this paper we propose a possible explanation of the fact that certain molecules exhibiting symmetric configurations are localized in one of them, instead of being delocalized as predicted by a naive application of quantum mechanics. Our mechanism is based upon the instability, in the semiclassical regime, of delocalized states under small perturbations (among which we consider the reaction field due to the environment). This mechanism predicts, for example, a different behavior for ${\mathrm{NH}}_3$ and ${\mathrm{AsH}}_3$ (delocalized ground state in the former case, localized ground state in the latter case), and similar to the case of ${\mathrm{AsH}}_3$ we expect localized states in the case of optical isomers, in agreement with the empirical evidence. Possible consequences concerning the understanding of the ‘‘classical limit’’ in general are briefly outlined.