By the use of relativistic many-body theory, the hyperfine structure of the $7p$ state of ${}_{}{}^{211}{}_{}{}^{}\mathrm{Fr}$ was calculated. By including polarization effects in all orders, good agreement for the magnetic dipole constant was obtained. In the same way, a new value of the electric quadrupole moment is obtained: $Q=-240\mathrm{}$ mb for ${}_{}{}^{211}{}_{}{}^{}\mathrm{Fr}\left({}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}\right)$.

Correlation functions between Fourier components with different $\overrightarrow{\mathrm{k}}$ vectors exist in nonequilibrium stationary states as a result of breaking translational invariance. Their nature, size, and experimental detectability by scattering light into two adjacent angles are discussed.

The equation for solitary waves in the continuum limit of a classical compressible Heisenberg chain is treated rigorously. It is proven that infinitely many coupled spin-lattice solitary waves exist. An explicit formula for the behavior of spin angles and lattice distortion is obtained. As an example of the general behavior, a particular case is worked out explicitly. The motion of spin and lattice coordinates is obtained rigorously in terms of a few well-defined integrals that are calculated numerically. The relevant solitary wave parameters-the speed, spin-precession rate, total energy, and total magnetization-are also obtained rigorously.

A mean-field theory of equilibrium polymerization of flexible polymers on a regular lattice with an arbitrary coordination number is presented. A merit of the model is that both polymer rings and excluded volume are incorporated. The drawbacks of the model are discussed.

We define a dynamical variable associated with the position of a particle representing the sine-Gordon soliton. Simple relativistic dynamic equations for this particle under the influence of forces are derived, including the case of dissipation. The fluctuation-dissipation theorem for this particle is obtained as well as some results on steady-state velocities and slowing of the thermalization time for ultrarelativistic solitions.

Nee and Roberts have measured the relative Rayleigh-scattering cross sections for various pulse durations. They give an explanation for different results found by Skowronek and Alayli. This is discussed and also some remarks are made on their experimental method.

Skowronek has commented on a Rayleigh-scattering cross-section measurement for various pulse durations made by us. His comments are discussed, and his questions on our experimental methods are answered.

In a previous paper we have pointed out that the common-translation-factor (CTF) method is the only one which, at present, and within the framework of the molecular model of atomic collisions, can be shown to be both convergent and computationally fast, even for many-electron systems. In this Communication we check that this second statement is correct, presenting, for the first time, a molecular calculation involving two-electron translation factors, for ${\mathrm{He}}^{+}$ + H collisions. A careful study of the sensitivity of the calculated cross sections to the choice of the CTF is performed, and conclusions on that sensitivity are drawn, for several types of processes.

Coupled-state calculations based upon a two-center expansion in atomic orbitals and pseudostates have been performed for ${\mathrm{H}}^{+}$+H in the 1-75-keV region. Cross sections for excitation and charge transfer to $n=2\mathrm{}$ states as well as total ionization cross sections are reported. It is shown that the calculated cross sections are not sensitive to the specific set of pseudostates included if the low-energy continuum states are reasonably well represented. The present results compare favorably with several sets of experimental data and with some large-scale calculations. The need for further experimental data in some areas is discussed.

Experimental evidence is presented to demonstrate that the energy at the peak of stopping-cross-section curves oscillates with target element of atomic number $Z_2$ when He ions and protons impinge upon these substances. A qualitative description is given in terms of outer- and inner-shell participation of the target atoms in the slowing down of the ion based upon existing theories and mechanisms.

The differential cross sections for excitation of atomic hydrogen isotopes to their $n=2\mathrm{}$ states by proton or deutron impact are found to follow a simple scaling relationship. The momentum-transfer-scaled differential excitation cross sections, for a projectile velocity of 1.26 a.u., produce one differential cross-section curve for all four possible hydrogen-isotope collision systems. The experimental results are in excellent agreement with our Glauber-approximation calculations.

A universal empirical scaling rule for electron-capture cross sections is reported for fast, highly charged ions in atomic and molecular targets. Projectiles range in energy from 0.3 to 8.5 MeV/amu, with charge states as high as 59+. This rule permits prediction of electron-capture cross sections for a wide variety of projectile-target combinations.

The inelastic x-ray scattering by $L$ and $M$ electrons in the vicinity of the argon $K$-absorption edge is analyzed with the use of a generalization of the Kramers-Heisenberg formula. The theoretical cross section is given as a superposition of scattering probabilities to final ${\mathrm{}\left(\mathrm{mp}\right)\mathrm{}}^{-1\mathrm{}}\mathrm{np}$, $n>~4$ discrete and ${\mathrm{}\left(\mathrm{mp}\right)\mathrm{}}^{-1\mathrm{}}\epsilon p$ continuum states for $m=2\mathrm{} \mathrm{and} 3$. The effect of the beamwidth on the spectrum of the scattered photons is discussed in detail. For a highly monochromatized beam the resolution is shown to increase by a factor of $\frac{{\Gamma }_{1s}}{{\Gamma }_{\mathrm{mp}}}$ as compared to $K$ photoabsorption measurements. Our work demonstrates the possibility of using the inelastic resonance scattering for a detailed study of Rydberg and exciton states in the x-ray region.

In the case of telegraphic noise $F_{\nu }\mathrm{}\left(t\right)\mathrm{}$, the activation rates for bistable flows of the type $x=f\left(x\right)+g\left(x\right)\mathrm{}{F}_{\nu }\mathrm{}\left(t\right)\mathrm{}$ can be calculated exactly. For a noise $F_{\nu }\mathrm{}\left(t\right)\mathrm{}$ of constant intensity, the activation rates are enhanced exponentially with decreasing correlation time $\tau =\frac{1}{\nu }$.

Spectacular accuracies have been achieved with single elementary particles trapped in hyperbolic Penning traps, but only after anharmonicities have been tuned out of these traps by varying the potential of extra compensation electrodes introduced into the traps. The relaxation calculation reported here is the first theoretical study of the electrostatic properties of such compensated Penning traps. Enough computations have been completed to clarify the basic physics involved in anharmonicity compensation and to provide useful, quantitative information for experiments in progress (especially for testing of anharmonicity systematics). The clearer picture of anharmonicity compensation which emerges suggests that the design of existing Penning traps could be significantly improved. An optimal electrode configuration is proposed which, in principle, makes the harmonic oscillation frequency of a trapped particle independent of changes in the compensation potential.

The exact solutions of the Klein-Gordon and Dirac equations are found by purely algebraic procedures for a charged particle embedded simultaneously in a plane-wave radiation field and in a uniform magnetic field which is directed parallel to the direction of propagation of the plane wave. Two cases of the solutions are considered: (i) the radiation field is a classical external plane wave and (ii) it is a quantized field. The connection with less explicit or more specific solutions of this problem known previously is established and possible applications are discussed.

By means of a canonical transformation that can be implemented as a unitary change of representation, we show how to quantize the damped harmonic oscillator.

An exact treatment of relativistic effects in bound-state problems in hydrogenlike atoms is given. In this paper we discuss the Zeeman effect and the Stark effect for relativistically bound electrons in a Coulomb field. For the Zeeman effect, the exact solution obtained by Darwin is used, and results of Crubellier and Feneuille for the Breit-Margenau correction are obtained in a simple way. For the Stark effect, the solution of Wong and Yeh is used. The exact expression can be readily compared with that of the Pauli approximation, and all correction terms can be identified. In the following paper we discuss interaction of the bound electron with radiation in an exact relativistic way. In the evaluation of the radial $r^K$ matrix elements with $n^{\prime }\ne n$, we present a closed-form expression as a sum over three parameters, derived from the method of the generating function of Laguerre polynomials.

An exact treatment of relativistically bound electrons in hydrogenlike atoms interacting with radiation is given. The simplified solution of the Dirac-Coulomb equation obtained by Wong and Yeh is used in the calculation. Transition probabilities and sum rules are obtained. Our results can be readily compared with those of the Pauli approximation, and all correction terms can be identified. New sum rules have been obtained for the relativistic case which can be compared side by side with the corresponding ones in the nonrelativistic case.