The residual ranges of ${}_{79}{}^{197}{}_{}{}^{}\mathrm{Au}$ nuclei stopping in nuclear emulsions has been measured for nuclei with an incident energy of 991 MeV/amu. The mean ranges observed are appreciably less than those predicted from measurements made on energetic particles of lower charge. However, by the consideration of higher-order correction terms to the rate of energy loss, good agreement can be obtained between the predicted and observed ranges.

Measurements are reported for the He-like x-ray spectra of argon obtained in a deuterium tokamak plasma with $N_e=(1-2)\mathrm{}\times {10}^{14}$ ${\mathrm{cm}}^{-3\mathrm{}}$ and $T_e=1-2\mathrm{}$ keV. The results are interpreted with the help of computed excitation rates and other available atomic data. The plasma sensitivity of line-intensity ratios is discussed as well as the $Z$ dependence based on earlier observations of He-like S and Cl.

Analytically and numerically we give the general solution of the rotating harmonic oscillator. Our solution verifies the resolution of a disagreement in the literature, and can be understood physically. We point out that the solution demonstrates the incorrectness of the "energy equipartition theorem" for the ground state of all quantum oscillators.

A simple yet powerful method of obtaining averaged solutions to nonlinear Langevin equations with colored noise is presented. It takes advantage of the intimate relationship between an Ornstein-Uhlenbeck process and a quantum harmonic oscillator. Pertinent results for quadratic nonlinearity are easily obtained, and several applications are given, including noise-induced instability, one-photon ionization in an intense laser field, and the use of Bender-Wu results for anharmonic noise.

A new class of physical systems, those which can be described by piecewise-linear equations, are found to exhibit chaotic behavior similar to that found in previously investigated nonlinear dissipative systems. The example of a damped, sinusoidally forced harmonic oscillator with two possible spring-constant values is investigated in detail. The system exhibits period doubling to chaos characterized by Feigenbaum's universal exponents for a certain range of parameters and an iterated map similar to that in the Lorenz equations for another.

The eigenvalue equation for absorptive bistability in a ring cavity is analyzed in the mean-field limit. Perturbative solutions are obtained in two distinct limits: $\kappa \ll {\gamma }_{\parallel },{\gamma }_{\perp }$ and $\kappa \sim {\gamma }_{\parallel },{\gamma }_{\perp }$, where $\kappa$ and ${\gamma }_{\parallel }$,${\gamma }_{\perp }$ are field and atomic damping rates, respectively. For $\kappa \sim {\gamma }_{\parallel },{\gamma }_{\perp }$, the eigenvalues satisfy a cubic equation, derived previously in the theory of self-pulsing in absorptive bistability. For $\kappa \ll {\gamma }_{\parallel },{\gamma }_{\perp }$, while the "dressed-field-mode" eigenvalues are solutions to this cubic equation, the "dressed-atomic-mode" eigenvalues are not.

We devise a procedure to obtain an analytical treatment of self-pulsing in optical bistability, which is parallel to that of the dressed-mode theory but does not require evaluation of the eigenvalues of the linearized equations. Our analysis shows that the uniform—stationary-field approximation does not forbid our arriving at the correct final equations in the mean-field limit.

The successful experimental test of a two-crystal Bragg-case neutron interferometer that is topologically equivalent to a Jamin interferometer is reported. The intensity distributions behind the interferometer are found to be in excellent agreement with those expected from dynamical diffraction theory. The distinguishing feature of this interferometer type is the absence of Borrmann spreading in one of the interfering beams. This would facilitate the use of very narrow beams in neutron interferometry.

From an extensive set of Born-approximation calculations on the proton stopping power of atomic A1, I attempt to extract the inner-shell corrections of Bethe stopping-power theory. Analysis of the subshell calculations produces a leading term consistent with the expected behavior, and a Bethe mean excitation energy ($I$) slightly larger (132 eV) than that obtained by summing over optical oscillator strengths (124 eV). The inner-shell corrections found by this analysis are larger than those used earlier, but consistent with measured values in the 4-8-MeV region.

It is demonstrated by means of a specific calculation that a velocity-changing radiative collision can lead to efficient isotope separation. Compared with photodissociative or photoionization techniques, selective scattering affords the advantage of a greater degree of control over the initial conditions, hence greater scope for optimization. This advantage is particularly important at the collision temperatures (∼1 K), where radiative inelastic collisions are most efficient.

The dielectronic recombination cross section has been estimated for the ${\mathrm{B}}^{2+}$ target and projectile electron energies in the range 0.1 ∼0.5 Ry, corresponding to the $2s\to 2p$ ($\Delta n=0\mathrm{}$) excitation accompanied by capture of the continuum electron into a high Rydberg state ($\mathrm{nl}$). Contributions from $n\lesssim 400$ and $l\lesssim 15$ are estimated with the use of an improved theoretical procedure. For a typical electron energy resolution of 2.0 eV, the cross section with $n\lesssim 20$ is 1.6×${10}^{-19\mathrm{}}$ ${\mathrm{cm}}^2$.

Two-photon free-induction decay (FID) was experimentally investigated in a two-level electron-spin system by revealing the second-harmonic wave emitted by the system. Oscillatory FID signals were detected for large-area pulses of the input power, analogously to recent observations by Kunitomo et al. for single-quantum resonances. Moreover, the measured decay time of the FID signal following a steady-state preparation was found to be larger than the theoretical value by a few orders of magnitude.

A generalized Euler transformation (GET) is introduced which provides a powerful alternative method of accurately summing strongly divergent Rayleigh-Schrödinger (RS) perturbation series when other summability methods fail or are difficult to apply. The GET is simple to implement and, unlike a number of other summation procedures, requires no a priori knowledge of the analytic properties of the function underlying the RS series. Application of the GET to the difficult problem of the RS weak-field ground-state eigenvalue series of the hydrogen atom in a magnetic field (quadratic Zeeman effect) yields sums of good accuracy over a very wide range of field strengths up to the most intense fields of ${10}^{14}$ G. The GET results are compared with those obtained by other summing methods.

From new measurements of the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ $1s2p-1s3d$ lines, we have determined the $3{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}-3\mathrm{}{}_{}{}^3{}_{}{}^{}D_2^{}{}_{}{}^{}$ separation to be 102 459(15) MHz. The corresponding nonrelativistic $1s3d$ singlet-triplet separation is 102 196(15) MHz, as compared with the value 102 116(5) MHz previously determined for the equivalent ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ separation. The difference of 80(16) MHz agrees with the predicted isotopic difference of these separations, the main contribution being a mass-polarization difference of 79 MHz as recently calculated by Drake. The experimental difference for $1s3d$ is consistent with the rough trend of such isotopic differences of $1snd$ singlet-triplet separations determined in previous experiments. We infer that mass-polarization shifts probably contribute significantly to the previously observed differences, at least up to $n\simeq 8$.

We discuss the critical behavior in the vicinity of the uniaxial-biaxial phase transition. In particular we investigate the consequences of a static cross coupling between the order parameter and the uniaxial director, and we demonstrate that this coupling introduces a very slowly decaying transient which explains why the expected $x-y$ exponents have not yet been seen experimentally. By application of a sufficiently strong magnetic field parallel to the uniaxial director this transient can be removed.

The critical behavior of a three-component water-in-oil microemulsion was studied by small-angle neutron scattering. Intensity spectra were analyzed by the treatment of critical scattering as arising from concentration fluctuations of polydisperse spheres. We propose a model capable of fitting the data over five decades of intensity variation. The critical exponents were determined to be $\nu =0.72\mathrm{}\pm 0.04$ and $\gamma =1.61\mathrm{}\pm 0.09$. The average droplet size and width of the size distribution exhibited little temperature dependence.

Solitary waves are observed to mediate the transition between the two states with opposite polarization of chiral smectics. For samples thicker than the pitch, electric fields as high as ${10}^6$ V/cm do not completely unwind the helix of ferroelectric liquid crystals because the vanishing of domain walls in these layered phases, unlike in the cholesteric phase, requires the nucleation of an array of dislocations with a large Burger's vector. In addition, samples thinner than the pitch but still ≳ 10 μm are not bistable as we have experimentally verified.

A critical analysis is made of the arguments that the Bethe mean excitation energy ($I$) for solid A1 is 163-169 eV. The arguments for this $I$ value are shown to be nondefinitive. Using recent measurements and inner-shell corrections established in the preceding paper, I suggest that the solid-Al $I$ value is in the range of 145-150 eV.