A possible canonical formulation of dynamics for classical particles with spin degrees of freedom is presented. The Klimontovich equation for an exact one-particle distribution function is derived, and its applications are briefly discussed.

The influence of the attractive part of the potential in the Weeks-Chandler-Andersen perturbation theory is tested in a molecular dynamics calculation. The simulation was carried out at the triple point of a Lennard-Jones system. The differences (not negligible) in the radial distribution function permit the use of perturbation theory, because the thermodynamic properties show the usual linear behavior.

It is shown that in two dimensions, the capillary-wave theory of the critical interface between fluid phases predicts that the interfacial thickness diverges with an exponent which differs strongly from that given by scaling theory. This is in contrast to the agreement between capillary-wave theory and scaling theory in three dimensions, which is shown to persist in four dimensions. Optical reflectivity measurements may be able to discriminate between capillary-wave and scaling theories in two dimensions, while they cannot in three dimensions.

The nonexistence of chaotic motions in a nonlinear oscillator with an externally modulated frequency which is exactly solvable is demonstrated analytically. By means of numerical investigations it is shown that the stabilizing effect is also present when the driving force belongs to a wide class not included in the demonstration. Surprisingly, chaotic behavior, present when the force is a periodic $\delta$ function, is destroyed if the amplitude of the pulses depends on the coordinate.

We investigate fluorescence light emitted in the reaction of He ($2^{3}S$) with ${\mathrm{N}}_2$. We conclude that the process of radiative collision is not active in this reaction as postulated in the literature.

Additional data is presented which shows that all of the observed ${\mathrm{N}}_2^{ +}\mathrm{}(B,v)\mathrm{}\to {\mathrm{N}}_2^{ +}\mathrm{}(X,v-1\mathrm{})+\hslash \omega$ emission bands have the same source of excitation at late times in a high-pressure helium, electron-beam discharge afterglow. The data presented in the preceding Comment, coupled with the data presented herein, indicate that our earlier observation of a radiative collision may have been a multiple-collision process.

It is demonstrated that the method of the fractional functional proposed by Takatsuka and McKoy, and the variational method of Moe and Saxon and of Kolsrud are identical. In particular, we show that the method is, contrary to Takatsuka and McKoy's claim, not free of anomalies; it implies the incorporation of the boundary conditions, it does not satisfy a minimum principle, and suffers from inconsistency. In order to illustrate the validity of our arguments, we investigate the $s$-wave scattering of electrons by Yukawa potentials.

In this paper we reply to the preceding Comment by Abdel-Raouf concerning several features of an amplitude-independent variational principle which we have recently proposed. The most substantive discussion concerns the nature of the singularities which can arise in one of these variational principles. The specific variational principle involved contains the Hamiltonian and not the Green's-function operator.

We show that the recent prediction of the García-Colín and Velasco [Phys. Rev. A 26 2187 (1982)] regarding the modification of the Rayleigh line, in the scattering of light from a fluid kept under a constant shear veloity gradient, is incorrect. A correct application of fluctuating hydrodynamics is shown to predict no such change.

A new technique to determine the final states and kinetic energies released in dissociative charge transfer is tested successfully on ${\mathrm{D}}_2^{+}$, ${\mathrm{D}}_3^{+}$, and ${\mathrm{O}}_2^{+}$ in a Cs vapor target. ${\mathrm{D}}_3^{+}$ yields both D+D+D and D+${\mathrm{D}}_2$ channel, ${\mathrm{D}}_2^{+}$ yields D+D from predissociation of ${\mathrm{D}}_2$($c{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$) and radiative dissociation of $a{}_{}{}^3{}_{}{}^{}\Sigma _g^{ +}{}_{}{}^{}$, and the $X {}_{}{}^2{}_{}{}^{}\Pi _g^{ +}{}_{}{}^{}$ and $a {}_{}{}^4{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ states present in ${\mathrm{O}}_2^{+}$ yield a surprisingly simple spectrum that is attributed to nearresonant- and Franck-Condon-type selection rules.

The widely used adiabatic nuclei approximation of electron-molecule scattering is shown to introduce serious errors into near-threshold $e$-${\mathrm{H}}_2$ vibrational-excitation cross sections. An alternative method, in which only the rotational motion of the nuclei is treated adiabatically, provides a computationally tractable procedure that yields highly accurate differential and integral cross sections.

The effect of the band shape of a light field on the multiphoton ionization is studied by use of the Karhunen-Loeve expansion of the Gaussian process. As an example, exact results are given for the non-Markovian chaotic field, which corresponds to a square spectrum. It is shown that the band shape of the field significantly alters ionization signals.

Laser-induced fluorescence on a beam of metastable ${\mathrm{N}}_2$ ($A{}_{}{}^3{}_{}{}^{}\Sigma _u^{ +}{}_{}{}^{}$) molecules has been used to study the hyperfine structure of the (10,6) band of the ${\mathrm{N}}_2$ ($B-A$) transition. The hyperfine structure of the $B{}_{}{}^3{}_{}{}^{}\Pi _0^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}\Pi _1^{}{}_{}{}^{}$ states was found to have an unusual, oscillatory $J$ dependence. This was explained by perturbation theory, and hyperfine-structure constants for the $B$ state were derived from a data fit. At the same time results from earlier, less-direct experiments on the $A$-state hyperfine structure were confirmed and extended.

We develop an efficient numerical scheme for integrating the equations of two-dimensional dendritic growth in the thermal-diffusion-limiting region. We use a Green's function representation to recast the problem as an essentially one-dimensional integro-differential equation which is solved numerically. We find that anisotropic surface tension is required to produce the stable tip behavior and repeated sidebranching of snowflakelike shapes.

Competition between Raman and line-center oscillations in off-resonantly pumped far-infrared lasers is studied by means of semiclassical laser theory. The observed preferential Raman line operation is shown to be caused by an inversion of the line-center gain when the Raman mode reaches intensities well below full saturation. This inversion is partly due to simple population effects. A further enhancement in the cross saturation at line center is caused by population pulsations. Numerical examples of mode competition are presented.

A novel optical interferometric technique is proposed for stabilizing and measuring a laser frequency in terms of an rf standard. In preliminary studies, a sensitive optical dual-frequency modulation scheme allows locking a laser to an optical cavity and the cavity in turn to a radio frequency reference with a noise level of 60 × ${10}^{-3\mathrm{}}$ Hz or 2 parts in ${10}^{10}$. In principle, the laser frequency ${\omega }_0$ can acquire the stability of the rf standard and being locked to a high-order multiple $n$ of the rf frequency ${\omega }_1$ facilitates the optical-rf division $\frac{{\omega }_0}{n}={\omega }_1$.

An exactly solvable generalization of the sine-Gordon equation involving an external arbitrary function is derived. A few examples of the effects of external electromagnetic fields or static potentials on the dynamics of the solition solution are studied. A particlelike interpretation is given which exhibits creation and/or annihilation processes.