Fixed-nuclei, static-exchange calculations have been performed to study the vibrational-rotational excitation of HF by electrons from threshold to 5 eV. Our calculated, $R$-dependent $K$-matrix elements in ${}_{}{}^2{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$, ${}_{}{}^2{}_{}{}^{}\Pi$, and ${}_{}{}^2{}_{}{}^{}\Delta$ symmetry are combined with exact point-dipole and laboratory-frame first-Born-approximation results for higher symmetries to obtain converged, integrated cross sections. The calculations show strong threshold peaks which are related to the dependence of the ${}_{}{}^2{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$ $K$-matrix elements on internuclear distance at small scattering energies.

The doubly excited states of He, having both electrons in the same $n$ shell, are investigated by constructing a diagonal approximation for $R_{12}^2$ in terms of SO(4) operators. By inverting this operator and taking the square root, an approximate operator expression for $\frac{1}{R_{12}}$ is obtained. Energies of states in the ${\mathrm{}(n=3\mathrm{})\mathrm{}}^2$ shell of He are calculated using this expression and compared with results of more elaborate calculations. Good agreement is found in most cases.

The hyperfine structure (hfs) of ${\mathrm{N}}_2^{+}$ has been resolved for the first time, using Doppler-tuned laser fluorescence spectroscopy. Observations in the region of the (0,1) bandhead of the $B{}_{}{}^2{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}-X{}_{}{}^2{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ first negative system give hfs constants in reasonable agreement with calculations based on the wave functions of Cade et al. Preliminary values obtained for the spin-rotation constants are also presented.

For the Wigner-Weisskopf-Dicke Hamiltonian, the probability for the upper of two molecular levels to decay, under spontaneous emission of a photon, is analyzed as a function of time. Normal decay yields a quasi-Lorentzian line shape. "Anomalous decay," i.e., a nonvanishing survival probability of the initial state, occurs when level separation is smaller than the level shift and is identified as absence of any transitions, due to a Jahn-Teller-analogous symmetry breaking with two ground states corresponding to left- or right-handed phases (inequivalent representations of the canonical commutation relations for the field). Critical slowing down of the decay results in a line shape ${\omega }^{-1\mathrm{}}{\left(\ln \omega \right)}^{-2\mathrm{}}$ as $\omega \downarrow 0$.

The technique of phase-modulation laser spectroscopy is used to detect a coherent four-wave interaction in ${\mathrm{I}}_2$ vapor. A phase-modulated probe beam induces in the sample an oscillating population which in turn modulates a counterpropagating pump beam that reveals a characteristic two-resonance spectrum. The observations fully confirm an earlier density-matrix calculation.

By using transverse electromagnetic waves in plasma as an example, the particlelike nature of zero-frequency waves is demonstrated. It is shown that zero-frequency waves correspond to the free-particle state of normal coordinates, whereas finite frequency waves correspond to that of harmonically oscillating normal coordinates. It is emphasized that, for zero-frequency waves with $\omega =0\mathrm{}$, the energy is finite and does not go as $\hslash \omega$.

Any discrete process which maps the interval on itself and whose reverse process is double or multiple valued fulfills the Li and Yorke criterion for chaos. Sequences of numbers obtained by iteration of such processes are mirror images of paths of random walk in the reverse, branched processes. Discrete processes which transform one to one cannot produce chaos.

The hyperfine structure of the $2{}_{}{}^3{}_{}{}^{}S-5\mathrm{}{}_{}{}^3{}_{}{}^{}P$ transition in ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ at 294.5 nm was studied by Doppler-free intermodulated fluorescence spectroscopy with the frequency-doubled output of a cw dye laser. The experimental results for the $5{}_{}{}^3{}_{}{}^{}P$ state are in good agreement with semiempirical calculations. The Fermi contact term for the $5{}_{}{}^3{}_{}{}^{}P$ state was determined to be -4327.5 ±5.0 MHz.

Some results on the decay of correlation functions in certain unstable systems are presented which appear to confirm previous theoretical estimates.

Doubly differential cross sections have been measured for the production of 10-70-keV $\delta$ electrons and ∼10-50-keV continuum x rays generated in collisions between 65-MeV nickel ions and nickel foil targets. The data on $\delta$ electrons have been used to calculate corresponding yields of secondary-electron bremsstrahlung (SEB) including retardation effects. Magnitude, energy, and angular dependence of resulting SEB yields are discussed in detail. It is concluded that SEB contributions do not dominate experimental continuous x-ray spectra.

We describe a computer-assisted proof of the existence of a fixed point $\phi$ of the doubling transformation (functional composition) for area-preserving maps of the plane: $\phi$ is obtained from the solution $S$ to a fixed-point equation $\mathcal{R}S=S$ for generating functions of area-preserving maps. This establishes, with mathematical rigor, an important part of Feigenbaum universality for conservative, two-dimensional systems.

Using polarized light scattered at 45° from mixtures of chiral CB15 and nonchiral E9 liquid crystals, we have measured the Mueller matrices characterizing the Bragg reflections of blue-phase structures BPI, BPIIA, and BPIIB. Surprisingly, all of these structures possess essentially the same Mueller matrix, namely, that of an elliptical polarizer with axial ratio ≅0.7. The implications of the results on the allowed space groups of the blue phases is discussed in the context of the theory of Hornreich and Shtrikman.

Absolute differential cross sections have been measured for ${\mathrm{H}}^{-}$ formation in single collisions of ${\mathrm{H}}^{+}$ on Mg in the energy range from 0.5 to 5.0 keV. Total cross sections, obtained by direct integration of these differential cross sections, are in good agreement with earlier total-cross-section measurements of Morgan and Eriksen in the energy range common to the two experiments and are in good agreement with the calculated total cross sections of Olson and Liu. The differential cross sections are strongly peaked in the forward direction. The functional form and scaling properties of this forward peak strongly indicate that it is a glory maximum, which occurs when the classical deflection function changes over from attractive to repulsive at some finite impact parameter. The differential cross sections from 1.0 to 5.0 keV show no other structure, but below 1.0 keV a $\tau$-dependent structure is observed which becomes more pronounced as the collision energy decreases. 1982 The American Physical Society.

Electronic and nuclear spin relaxation of optically pumped K atoms has been measured in the presence of He and Ne gases. The nuclear-spin-independent cross sections for the destruction of electronic spin polarization in the $4{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ ground state of K are $\sigma \left[\gamma \right(\overrightarrow{\mathrm{S}}·\overrightarrow{\mathrm{N}}\left)\right](\mathrm{K}-\mathrm{He})=8.0\mathrm{}\times {10}^{-25\mathrm{}}$ ${\mathrm{cm}}^2$ and $\sigma \left[\gamma \right(\overrightarrow{\mathrm{S}}·\overrightarrow{\mathrm{N}}\left)\right](\mathrm{K}-\mathrm{Ne})=141\mathrm{}\times {10}^{-25\mathrm{}}$ ${\mathrm{cm}}^2$. The diffusion coefficients of K in He and Ne, corrected to 273 K, are $D_0(\mathrm{K}-\mathrm{He})=0.35\mathrm{}$ ${\mathrm{cm}}^2$ ${\sec }^{-1\mathrm{}}$ and $D_0(\mathrm{K}-\mathrm{Ne})=0.19\mathrm{}$ ${\mathrm{cm}}^2$ ${\sec }^{-1\mathrm{}}$. All measurements have an estimated uncertainty of ±10%. The relaxation of K is shown to be strongly affected by an anomalous process which is attributed to the modification of the K hyperfine interaction induced by the formation of K-He and K-Ne van der Waals complexes.

Drift-tube studies of the charge-transfer reaction of ${\mathrm{He}}^{+}$ with Xe show that the rate constant increases steeply from ${4\times 10}^{-12\mathrm{}}$ ${\mathrm{cm}}^3$ ${\sec }^{-1\mathrm{}}$ at 200 K to ${7\times 10}^{-12\mathrm{}}$ ${\mathrm{cm}}^3$ ${\sec }^{-1\mathrm{}}$ at 300 K and ${1\times 10}^{-9\mathrm{}}$ ${\mathrm{cm}}^3$ ${\sec }^{-1\mathrm{}}$ at 1 eV. The data join smoothly onto earlier beam studies of the total charge-transfer cross section. The cross sections for emission of excited ${\mathrm{Xe}}^{+}$ states formed in the reaction were investigated in the energy region 1-2000 eV. Here good agreement is found with data reported earlier at higher energies. The dependence of emission cross sections on ${\mathrm{He}}^{+}$ kinetic energy exhibits several maxima which can be explained on the basis of a Landau-Zener avoided-crossings model which is also consistent with other experimental features of the ${\mathrm{He}}^{+}$-Xe system.

The dependence on the hole quantum numbers of single-particle excited states of the alkaline-earth atoms Be, Mg, and Ca is studied within the Hartree-Fock frozen-core method. For a given orbital state of the outer electron, we find that the term values of all core excitations are nearly the same but they differ from that of the valence excitation. The similarity of the core Rydberg series is explained in terms of the electron-density relaxation. The first term of a Rydberg series is anomalous when the excited electron penetrates appreciably into the atomic core. Our findings are compatible with all available experimental data. The latter, however, are not accurate enough to confirm the predicted similarity among the core Rydberg series.

Relativistic generalizations are derived for the well-known nonrelativistic electric-dipole oscillator-strength sum rules. The relativistic sum rules include both positive- and negative-energy states. The derivations are valid for a Dirac electron in an arbitrary local potential. We also present a number of simple integral properties related to the relativistic virial theorem which are useful in the calculation of matrix elements.

The Čerenkov and transition radiation generated when a charged particle moves with constant velocity along a straight line through the center of a sphere is calculated. Comparison with experimental results is given.

It is shown that a class of dissipative dynamical systems with limit-cycle and chaotic behavior can be derived from a Lagrange function. A particular system is investigated numerically.

We discuss the introduction of constraints in a system of n noninteracting particles which obey the laws of nonrelativistic quantum mechanics. In this paper the particles are first thought of as being unconstrained (described by the $3n$ Cartesian coordinates of a flat space $R$), but subject to an external potential $V$ which, in a certian suitable limit, forces the system to remain in a curved subspace $V$ of $R$. This idea was already employed in a previous work where we have discussed the motion of one constrained particle. It was then shown that in order to obtain a meaningful result the particle wave function should be "uniformly compressed" into a surface (or curve), avoiding, in this way, the tangential forces which correspond to the dissipative constraints of classical mechanics. The resulting Schrödinger equation could then be separated in such a way that the part which contained the surface (or curve) variables was independent of the potential $V$ employed in the constraining process. In the present paper we show that this procedure cannot be carried out for all subspaces $V$ of $R$ in the case of a many-particle system, unless $V$ satisfies a certain geometrical condition. The many-particle Schrödinger equation (as was already the case of the one-particle systems) contains, besides the kinetic energy term, potentials which are not bending invariants, that is, cannot be obtained from the metric tensor $g_{\mathrm{ij}}$ of $V$ or its derivatives. This gives rise to different Schrödinger equations for isometric subspaces, in striking contrast with the usual quantization procedures which start from the classical Lagrangian of the constrained system.