The dissociation channels of ${\mathrm{H}}_3^{+}$ ions after a single dissociative collision in a gas target (Ar, ${\mathrm{H}}_2$, or air) were resolved by electronic coincidences and were characterized by the charge states of all the fragments. The dependence of the probabilities of the various channels on the bombarding ${\mathrm{H}}_3^{+}$ energy, the target gas, and the pressure of this gas was determined. Equations for the dissociation process are constructed and an interpretation of the complex dissociation process is given by the semiempirical model of geometric dissociation.

Photoionization of ${\mathrm{H}}_2$ by 304-Å radiation can produce the $2p{\sigma }_u$, $2p{\pi }_u$, and $2s{\sigma }_g$ repulsive states of ${\mathrm{H}}_2^{+}$. The angular distributions of energetic (> 2 eV) protons from these states have been measured relative to the incident unpolarized light beam using a rotatable hemispherical electrostatic analyzer. Axial-recoil conditions apply in this situation, so that the photofragment angular distribution would be ${sin}^2\theta$ for pure $\Sigma \to \Sigma$ electronic transitions and $1+{cos}^2\theta$ for pur $\Sigma \to \Pi$ electronic transitions. However, unlike photodissociation processes forming neutral products, the present process also involves the ejection of photoelectrons with alternative symmetries, each associated with one of the above characteristic photoion angular distributions. Consequently, measurement of the net photoion angular distribution in dissociative photoionization yields the branching ratio between the alternative (degenerate) channels available to the photoelectron. This type of information cannot be deduced by observing the photoelectron itself. The present results indicate that the formation of the $2p{\sigma }_u$ state ${\mathrm{H}}_2^{+}$ at 304 Å is accompanied by ejection of photoelectrons with significant $d$-wave character.

Quantum theory and selection rules of laser-induced predissociation of diatomic molecules without actual absorption or emission of laser photons are given. The rate of induced predissociation is a function of the externally controllable laser-field parameters: intensity, frequency, and polarization. Both perturbative and nonperturbative theories are used in the analysis, providing treatment for both low and high laser intensities. The region of validity of perturbative results is determined by comparison with the exact results and is given by a simple criterion. An approximate expression is given for the convenient calculation of the induced predissociation rate. Laser-induced predissociation without absorption or emission of laser photons also occurs in polyatomic molecules, and the analysis is similar.

The excitation spectrum arising from the interaction between two identical atoms (molecules), one of which is excited in the presence of a resonant strong electromagnetic field (pump field), is investigated. The excitation spectrum is found to consist of those describing the symmetric and antisymmetric modes, respectively. The form of both spectra depends on the relation between the distance $R$ separating the atoms and the wavelength $\lambda$ of the transition from the ground state to the excited state. For $R<\mathrm{}\lambda$, and when certain conditions prevail, the spectral function for the symmetric modes consists of three Lorentzian lines describing the central peak and the two sidebands whose radiative widths are equal to ${\gamma }_0$, $\frac{3{\gamma }_0}{2}$, and $\frac{3{\gamma }_0}{2}$, which are twice the corresponding ones arising from an isolated single atom interacting with the pump field. For the antisymmetric modes the central peak has a $\delta$-function distribution indicating the stability of the mode in question, while, when certain conditions are satisfied, the two sidebands are described by Lorentzian lines each having a radiative width of the order of $\frac{{\gamma }_0}{2}$, which is equal to the natural linewidth for a photon spontaneously emitted from an isolated atom. For both the symmetric and antisymmetric modes, the dipole-dipole interaction between the atoms brings about small energy shifts. For $R>\mathrm{}\lambda$, apart from the small energy shifts caused by the dipole-dipole interaction, the spectral functions for symmetric and antisymmetric modes are similar to that for the single atom interacting with the pump field.

We report an evaluation of the dipole matrix elements for radiative transitions ($2p, 3p\to 1s, 2s$) between atomic inner shells using a recently developed analytic perturbation theory for screened Coulomb potentials. The results are simple analytic expressions which display the dependence of the transition rate on charge $Z$ and ionic charge $Z_i$. Comparison with exact numerical calculations indicates that these analytic inner-shell predictions are reasonable for high-$Z$ elements and fairly reasonable for intermediate-$Z$ elements.

The visible emission bands from $\mathrm{K}\mathrm{}\left(5S\right)\mathrm{}\mathrm{Xe}$, $\mathrm{K}\mathrm{}\left(5S\right)\mathrm{}\mathrm{Kr}$, $\mathrm{Na}\mathrm{}\left(4S\right)\mathrm{}\mathrm{Xe}$, and $\mathrm{Na}\mathrm{}\left(4S\right)\mathrm{}\mathrm{Kr}$ excimers have been observed experimentally, the potassium excimers being produced by a violet ${\mathrm{Kr}}^{+}$ laser excitation and the sodium excimers by a discharge. These observed profiles are compared with calculated profiles based on Gallagher's quasistatic theory and Pascale's molecular potentials and oscillator strengths. Qualitative conclusions are drawn concerning the shapes and depths of the molecular-potential curves and the accuracies of the computed oscillator strengths. The theoretical emission profile is approximated by an analytical form, and the emission linewidth is predicted to vary as $T^{\frac{1}{2}}$, where $T$ is the absolute temperature. This is verified experimentally for KXe in a limited temperature range.

An expression is derived for the expected number of photon pairs separated by a time interval $\tau$ that are detected in photoelectric correlation measurements of an atomic beam, when due account is taken of the fluctuations of the number of radiating atoms and of the effect of their finite transit time through the field of view. The theoretical expression is checked against some recent measurements and good agreement is obtained.

We have used the beam-foil technique to measure the mean lives of the upper levels of: (i) the $2s{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}-2p{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2},\frac{3}{2}}^o{}_{}{}^{}$ resonance transitions (at 255 and 192 Å) in lithiumlike Fe xxiv and (ii) the $2s^2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}-2s2p{}_{}{}^3{}_{}{}^{}P_1^o{}_{}{}^{}$ intersystem transition (at 264 Å) in berylliumlike Fe xxiii. The measured mean lives are $\tau \left(2p{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^o{}_{}{}^{}\right)=0.55\mathrm{}\pm 0.02$, $\tau \left(2p{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^o{}_{}{}^{}\right)=0.235\mathrm{}\pm 0.01$, and $\tau \left(2s2p{}_{}{}^3{}_{}{}^{}P_1^o{}_{}{}^{}\right)=13\mathrm{}\pm 4$ ns. Oscillator strengths derived from the Fe xxiv results are in good agreement with recent relativistic multiconfiguration Hartree-Fock (MCHF) "length" gauge calculations; the Fe xxiii result is not in agreement with these MCHF calculations, but appears to be in agreement with recent intermediate coupling calculations.

The technique of level-crossing spectroscopy has been used to measure the fine-structure intervals in the $3{}_{}{}^3{}_{}{}^{}P$ state of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ through the observation of the level crossings at 2277 and 3700 G. The magnetic fields at the crossing points were used in conjunction with calculated $g$ values to obtain for the $3{}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}-3\mathrm{}{}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ fine-structure interval the value 8772.552 ± 0.040 MHz (4.5 ppm). These same data yielded for the lifetime of the $3{}_{}{}^3{}_{}{}^{}P$ state the value 97.6 ± 4.5 nsec and for the cross section for coherence-destroying collisions the value $(718\mathrm{}\pm 78)\pi a_0^2$.

The $S_0\mathrm{}\left(3\right)\mathrm{}$ pure rotational quadrupole transition of ${\mathrm{H}}_2$ has been observed using a tunable PbSnSe diode laser and a long-path absorption cell containing ${\mathrm{H}}_2$ at pressures in the range 0.1-0.9 atm. The observed linewidths (80-170 MHz full width at half maximum) were considerably narrower than the Doppler width (268 MHz for 297 K) owing to the effects of collisional (Dicke) narrowing. The line position was measured to be 1034.6702 ± 0.0007 ${\mathrm{cm}}^{-1\mathrm{}}$, and its intensity was found to agree well with that expected from ab initio calculations of the quadrupole moment of ${\mathrm{H}}_2$.

Millimeter resonances corresponding to single- and double-photon transitions have been observed between Rydberg levels of sodium with principal quantum number $n$ ranging from 23 to 41. The levels are prepared by laser excitation; transitions are induced by microwaves produced by a backwave oscillator working around 300 GHz; detection is performed through the selective field-ionization technique. Experimental values for quantum defects, fine-structure intervals, and polarizabilities are reported.

We study the properties of the laser field in the case where the cavity contains two cells, one which amplifies and one which absorbs the radiation. We adopt the simplest possible model, in which there is only one running mode in the cavity and all atoms are fixed and homogeneously distributed in space. We first set up a semiclassical description. In the frame of the stationary semiclassical (SC) theory the most striking feature is the occurrence of a domain in which three solutions coexist. A linear-stability analysis shows that two of these solutions are stable. This gives rise to an hysteresis cycle. Most of the results in this section are analytic. In the frame of a purely quantum description, we derive a generalized Fokker-Planck equation which is exactly solved in the stationary case. This yields a stationary quasiprobability distribution function for the field. In the domain where the SC theory predicts three solutions, the field-distribution function has two maxima and one minimum whose positions are precisely given by the SC intensities. With this distribution function we study the intensity and the intensity fluctuations: the intensity shows a rather abrupt increase when crossing the narrow transition region; in this region the intensity fluctuations are extremely high. By means of an approximate method to solve the time-dependent Fokker-Planck equation we study the linewidth and show that it drastically decreases above threshold. Finally we consider the linearized and quasilinearized Fokker-Planck equations which can be solved analytically. We show that the domain in which neither of these equations fits the results of the generalized Fokker-Planck equation is extremely small. The properties of the metastable states are analyzed in terms of the generalized and asymptotic Fokker-Planck equations.

It has been pointed out that heat flow in the slowly modulated dissipative steady state in some circuits far from equilibrium obeys a relationship $dQ-d{Q}_0=T_N\mathrm{dS}$. $d{Q}_0$ is the heat flow calculated in a macroscopic way by multiplying the ensemble averages of currents and voltages for the dissipative elements. $T_N$ is the temperature characterizing the fluctuations in the degree of freedom under consideration. $S$ is the entropy defined in the usual statistical-mechanical fashion. This relationship is illustrated through a particularly simple example: The divergent heat flow into a circuit as a second-order transition is approached from the high-symmetry side. The general case is more complex and discussed subsequently, with special attention to the complications caused by asymmetric distribution functions, and the fact that the dissipation in slowly shifted steady state differs from that in the exact steady state. The relationship, expressed in a form which involves entropy changes, is valid only if the distribution functions in the dissipative case mimic equilibrium distribution functions very closely. Other forms have a much broader applicability.

Using Hartree-Fock-Slater wave functions and the Sternheimer perturbation-numerical method, values of atomic quadrupole shielding factor $R_{\ominus }$ are reported for the $\mathrm{np}(n+1\mathrm{})s$ excited-state configurations of C, Si, Ge, Sn, and Pb. The perturbation terms up to second order have been included. In all the cases a shielding effect greater than +1 has been obtained.

Local thermodynamic equilibrium (LTE) is usually invoked if the rates of collision processes perturbing a system from equilibrium are several orders of magnitude slower than the rate of elastic collisions restoring the system to equilibrium. For coupled processes involving a common species, it is shown that this criterion for LTE may fail. The difficulty arises because average collision rates do not correctly reflect the relaxation rates of those energetic particles which make the largest contribution to the rate of processes with activation energy. This paper presents a study of two systems: the line-of-center cross section characterized with a threshold energy, and a model cross section applicable to nonresonant nuclear reactions. For both systems, it is found that (surprisingly) large departures from the equilibrium rate coefficients can occur for conditions for which LTE would ordinarily be considered to be valid.

A set of $n$ coupled two-dimensional area-preserving mappings in taken as a model problem for the study of the stochasticity of dynamical systems with $n$ degrees of freedom. The connectance of the system is defined as the percentage of two-dimensional mappings that are directly coupled. This work suggests that large complex dynamical systems may be expected to be stable below some critical level of connectance, but that as the connectance increases above that level they would become unstable.

A variational principle is applied to the generating functional of velocity correlations in an incompressible fluid described by the Navier-Stokes equations with random Gaussian stirring forces. The generating functional of velocity correlations gives, in a field-theoretic language, a complete statistical description of this driven, stationary Markov process in terms of path integrals and can be viewed as a generalized free energy. The statistical properties of velocity fluctuations generated by white-noise stirring forces whose energy-injection rate into the fluid is wave-number power-law distributed are investigated. A boundary dimension $d^{*}$ depending upon the forcing spectrum is found above which long-wavelength velocity fluctuations are weakly coupled. In the strong-coupling regime $d<\mathrm{}{d}^{*}$, static and dynamic exponents characterizing the wave-number dependence of long-wavelength fluctuations are evaluated. For $d>\mathrm{}{d}^{*}$, corrections to the linear theory caused by the nonlinear mode-coupling terms are determined. The results are compared with renormalization-group calculations. Turbulent velocity fluctuations are discussed in the limit of vanishing viscosity. The relationship between forcing and energy spectrum in $d$ dimensions is investigated and the results are compared with second-order closure approximations of statistical turbulence theories. A stirring-force spectrum $\sim k^{-d}$ leads to a Kolmogorov distribution of energy over wave number.

Cross sections for electron capture into the $4s$ state of hydrogen have been measured for 10 to 150-keV protons incident upon He, Ne, Ar, Kr, and Xe. The cross-section curves for each gas reach an apparent maximum in this projectile-energy range. The values for Kr and Xe are consistent with an $n^{-3\mathrm{}}$ scaling of previous $3s$ capture-cross-section measurements in this projectile range. The He, Ne, and Ar values are in excellent agreement with previously reported measurements above 60 keV but give consistently higher values than those measurements at the lower energies. There are no comparable Kr and Xe values in the literature. The shape and magnitude of the excitation functions for these gases indicate that the internal structure of the target atom is an important factor in the charge-transfer process.

By a Monte Carlo variational calculation, it is shown that the description of the ground-state properties of a hard-sphere Bose system is improved if the Jastrow wave function contains a correlation structure at distances intermediate between the first and the second shell of neighbors. We relate these correlations to the zero-point motion of rotons. We predict that the oscillations of the structure factor $S\left(k\right)\mathrm{}$ and of the radial distribution function $g\left(r\right)\mathrm{}$ increase at finite temperatures. Such intermediate-distance correlations improve the description of the solid phase by a Jastrow wave function, but the description is still not satisfactory compared to localized wave functions. Backflow associated with rotons induces explicit three-particle correlations in the wave function, and a new form for such correlations is proposed for variational calculation for ${}_{}{}^4{}_{}{}^{}\mathrm{He}$.

Several authors have, using a variety of approximations, predicted a sharp minimum in the angular distribution for the process $p+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}\to \mathrm{H}\mathrm{}\left(1s\right)+p$, over a wide range of energies. I have used the results of recent impact-parameter coupled-state calculations, in conjunction with the eikonal approximation, to calculate differential cross sections for this process in the energy range 15-200 keV; no sharp minima were found, but at the lowest end of the energy range there is some indication of the emergence of a dip. The present results are qualitatively consistent with the results of Glembocki and Halpern who used a Coulomb-projected Born approximation.