Effective ionization rate coefficients of Ne vi, Ne vii, and Ne viii are derived from the time evolution of these ions in a transient helium plasma produced in a θ-pinch discharge. Good agreement is found with theoretical rate coefficients.

Using the asymptotic matching procedure of Dombre and Hakim, we determine properties of the steady-state cellular structures with deep narrow grooves observed in directional solidification experiments. The method is valid in the experimentally relevant region of small partition coefficient and finite Péclet number. An extension of the Scheil equation for the grooves is given, and the importance of conservation in determining the groove closing is pointed out.

The coupling between free and bound electrons under non-local-thermodynamic-equilibrium condition is analyzed. The cross sections of electron-impact ionization and excitation (${\sigma }_{\mathrm{ex}}$) are shown to be much larger than that of thermalization (${\sigma }_{\mathrm{ee}}$) between free electrons at high velocity range. As a consequence, the electron distribution function has a kink at an energy E=$E_k$, which is determined from ${\sigma }_{\mathrm{ex}\mathrm{\sim }3{\sigma }_{\mathrm{ee}}}$. In the course of time, the thermal part E<$E_k$ is rapidly cooled down, whereas the slope of the function for E>$E_k$ remains the same as that of the initial distribution.

The behavior of many fractal structures has been interpreted by a scaling hypothesis: The number of sites on a fractal of size R with a probability measure $R^{\mathrm{-}\alpha }$ scales as $R^{f\left(\alpha \right)}$. This defines a series of exponents f(α). If the measure subdivides in a self-similar manner over the structure, then it is shown that the set of sites with a given value of α do not themselves form a fractal, but have a more complicated geometry. The analysis is applicable to many growth processes including diffusion-limited aggregation, viscous fingering, and the screened-growth model. If the measure is defined on a static fractal, then the same conclusion applies to many other systems such as models of turbulence, random-resistor networks, and fractal aggregates in shear flow.

The Breit correction only accounts for part of the transverse photon exchange correction in the calculation of the energy levels in helium Rydberg states. The remaining leading corrections are identified and each is expressed in an effective potential form. The relevance to the Casimir correction potential in various limits is also discussed.

Using a formulation of quantum electrodynamics which is not second quantized, but rather based on self-fields, we calculate the energy shifts of an electron bound by a magnetic field in the vicinity of an infinite-plane conductor. We confirm the recent result of Kreuzer that the energy shift arising from the plate-induced change in the magnetic moment, Δμ/μ=-α/4Rm, is exactly canceled by a similar change Δm/m=-α/4Rm in the mass. Thus no change occurs in the spin-precession frequency to order α/Rm, in agreement with Brown et al. This cancellation of the two effects resolves an apparent controversy in recent literature over whether such a shift to the spin-precession frequency ${\omega }_s$ occurs. There is, however, a boundary-induced change in the cyclotron frequency ${\omega }_c$ which we calculate in the quantum result as Δ${\omega }_c$/${\omega }_c$=α/8Rm to order α. Our method of approach is novel in that it uses only the self-field to compute radiative corrections; there are no vacuum fluctuations.

The techniques of center of mass (c.m.) separation in a homogeneous magnetic field are tested on an exactly solvable problem: a bound system of arbitrary particles interacting with a general quadratic potential. An effective mass increasing with the field strength appears naturally in the collective energy and shows striking similarities for charged and neutral systems. In the charged case, the internal motion cannot be separated from the c.m. motion. These properties and several techniques discussed in the present paper are also valid for a Coulomb interaction. The present exact model provides a test of approximate separation methods employed in the Coulomb case.

The three-body Schrödinger equation is solved directly for the ground state of the positronium negative ion by using a rapidly convergent correlation function hyperspherical harmonic method, which involves no adjustable parameters. The inclusion of 169 hyperspherical functions yields the ground-state energy 0.262 004 86 a.u., which is converged to an error in the seventh significant figure. Expectation values of different functions of interparticle distances as well as the two-photon annihilation rate are calculated and compared with those obtained by variational calculations.

Representations based on the concepts of the theory of fuzzy sets are suggested to apply to a wide variety of problems in physics. A grade of membership is associated to each element in a set, which is a measure of its distance to a prototype. Fuzzy representations are thus adequate for dealing with situations where the belongingness of an object or a phenomenon to a class is uncertain, or to situations where the classes have no exact definition. An explicit relation is shown between fuzzy representation and dimensionality. Unambiguous definitions of the degree of fuzziness, cluster overlap, and isolated points are given on the basis of an anisotropic grade of membership function. The example is treated of collision cascades generated by xenon atoms incident on a polycrystalline gold surface with energies ranging from 20 keV to 1 MeV. The cascades are simulated in the binary collision approximation with the Marlowe computer code. They are shown to germinate from simultaneously growing collisions clusters. The displacement cascades are found to be only partially space filling. This is emphasized on the basis of their fuzzy geometrical characteristics, without need of any assumption concerning self-similarity. Their possible overlap and lumping are identified on the basis of the grade of membership of each vacated lattice site to each cluster. The final cluster pattern of the vacancy distributions is shown to depend on the degree of fuzziness. The sensitivity of several properties of vacancy clusters on the degree of fuzziness is discussed. This sensitivity is suggested to be a consequence of their granular structure. Consequently, their experimental characterization may be influenced by the resolution of the observation method. Fuzzy analysis is suggested as a tool to establish the relation between measures at different scales of the same phenomenon.

The Lorentz deformation property of the phase-space distribution function is studied for harmonic oscillators. The overlap effect of two distribution functions is discussed in detail. It is shown that the Lorentz deformation of the phase-space distribution is responsible for the polynomial cutoff behavior of the proton form factor in the harmonic-oscillator quark model.

It is known from previous work that the total electron density matrix for closed-shell atoms in a bare Coulomb field is determined solely by the corresponding s-state contribution. In keeping with this philosophy, an expression is derived for the closed-shell electron density ${\rho }_n$(r) and kinetic energy density $t_n$(r) in terms only of s-state components ${\rho }_{\mathrm{no}}$(r) and $t_{\mathrm{no}}$(r) for arbitrary quantum number n. A proposal for the generalization of the present model for any central field of force is given in the Appendix.

Periodic orbit theory expresses, in a semiclassically approximate way, the trace of the energy-dependent Green’s function of a quantum-mechanical system in terms of a sum over periodic orbits of the corresponding classical system. In this paper a periodic orbit sum is carried out for a Hamiltonian describing the rotational dynamics of the ${\mathrm{SF}}_6$ molecule. Following Miller [J. Phys. Chem. 83, 960 (1979)], classically forbidden, or ‘‘tunneling’’ orbits are included in the sum. A closed-form expression for the trace of the energy-dependent Green’s function is obtained; it depends on the actions and Maslov indices of the classical orbits, as well as the irreducible representatives of the generators of the molecular point group. The expression reproduces the rich structure characteristic of the rotational spectra of symmetric molecules, including the exponentially near degeneracies for large angular momentum, and the periodicities in eigenvalue symmetry assignments. The methods used here complement the extensive studies of Harter and Patterson.

The rates of the Auger transitions between all bound states of the muonic molecular ion tdμ for the four initial configurations [(tdμ)e], [(tdμ)de${]}^{+}$, [(tdμ)d2e], and [(tdμ)2d2e${]}^{+}$ were calculated using new highly accurate variational three-body wave functions. Qualitative agreement with previous calculations was found. As a byproduct of the calculations we obtained an upper bound for the energy of the tdμ(20) state ${\varepsilon }_{20}$=-102.6489 eV, which is significantly lower than the best literature value.

The quantum-mechanical phase space of the surface-state electron is studied in the presence of a time-dependent field, for which the classical dynamics has been shown to be chaotic. A coherent-state representation of the Wigner function for the surface-state electron Hamiltonian is constructed. This is then used to compare and contrast phase-space characteristics for quantum states initially in regular and irregular regions of the classical phase space. In particular, the effects of the driving frequency on the dynamics are examined in detail. We confirm that at larger frequencies, for a fixed field strength, the quantum phase-space evolution is restricted or localized. This localization is in contrast with the diffusive behavior still present in the classical evolution. The quantal evolution, at higher frequencies, appears better characterized by tunneling rather than by diffusion.

Experiments with rotating systems are analyzed from the perspective of a test theory of the Lorentz transformations which permits, in principle, the verification of the latter’s simultaneity relation.

A detailed report on the current status of measurements of the Rydberg constant is given. Our recently reported value of $R_{\infty }$=109 737.315 73(3) ${\mathrm{cm}}^{\mathrm{-}1}$ has been confirmed by three other laboratories within experimental error. An additional check on the iodine cell, the heart of our wavelength and frequency reference, confirms a negligible pressure shift. The possible role of the Rydberg constant in fundamental atomic physics lies in tests of quantum electrodynamics and in improvement of the realization of the meter. We propose that the hydrogen spectrum be used to realize the meter in the optical domain, as an alternative to the current frequency chains. For the realization to be useful, improvement of the current precision of the Rydberg constant by a factor of 2 or more is required.

Differential cross-section measurements of charge-changing processes in small-impact-parameter collisions by 900-keV ${\mathrm{Ar}}^{\mathrm{q}+}$ (q=0–3) ions on He atoms were studied. Both scattered and recoiled particles were separated according to their charges and detected by a kinematical coincidence system. The distribution of the number of ejected electrons from the colliding system was also evaluated. A weak correlation between the charge-state distributions of the emerging projectile and recoil ions at a fixed impact parameter has been determined. This is not in contradiction to other measurements in which larger correlations were found and were attributed to the impact-parameter selection effect.

Exact one-photon nonrelativistic internuclear bremsstrahlung (INB) is investigated and compared with atomic bremsstrahlung (AB). Angular distributions and photon energy spectra of the INB of protons (and antiprotons) on aluminum and carbon targets are presented. Retardation effects are found to enhance the forward direction to the detriment of the backward one, where photon-induced x-ray emission (PIXE) measurements should be made. The crossing energies from where INB dominates on AB are calculated as a function of the photon angle. The present results define the backgrounds to be subtracted in measurements.

We examine the spectra corresponding to the secondary-electron bremsstrahlung produced by heavy ions penetrating thin solid foils. By using the Thompson approximation to describe the ionization process, and some other high-energy approximations, we develop a simple closed form, from which very useful information on the process can be obtained. A method results for reducing experimental data in a comprehensive way. The emerging universal shape function is compared with scaled experimental results, and the agreement is very satisfactory.

The theory of resonant dipole-dipole energy transfer in an electric field E indicates substantial differences between the collision velocities v∥E and v⊥E. For v∥E the cross section vanishes at exact resonance due to a destructive interference in the transition amplitude, producing a double-peaked line shape. The presence of the permanent dipole moments in the field produces slight shifts and asymmetries of the collisional resonance line shapes. A high-resolution experimental study of the cases v∥E and v⊥E indicates that the theoretical predictions are correct and further allows the resolution of the spin-orbit structure in the resonant collisions.