Collisional processes occurring within an atomic vapor can be conveniently described in terms of collision kernels. The population kernel $W_{\mathrm{ii}}({\overrightarrow{\mathrm{v}}}^{\prime }\to \overrightarrow{\mathrm{v}})$ gives the probability density per unit time that an "active" atom in state $i$ undergoes a collision with a perturber that changes the active atom's velocity from ${\overrightarrow{\mathrm{v}}}^{\prime }$ to $\overrightarrow{\mathrm{v}}$. For active atoms in a linear superposition of states $i$ and $j$, there is an analogous coherence kernel $W_{\mathrm{ij}}({\overrightarrow{\mathrm{v}}}^{\prime }\to \overrightarrow{\mathrm{v}}) \left(i\ne j\right)$ reflecting the effects of collisions on the off-diagonal density-matrix element ${\rho }_{\mathrm{ij}}$. In this work, we discuss the general properties of the collision kernels which characterize a two-level active atom which, owing to the action of a radiation field, is in a linear superposition of its two levels. Using arguments based on the uncertainty principle, we show that collisions can be divided roughly into the following two categories: (1) collisions having impact parameters less than some characteristic radius which may be described classically and (2) collisions having impact parameters larger than this characteristic radius which give rise to diffractive scattering and must be treated using a quantum-mechanical theory. For the population kernels, collisions of type (1) can lead to a large-angle scattering component, while those of type (2) lead to a small-angle (diffractive) scattering component. For the coherence kernel, however, assuming that the collisional interaction for states $i$ and $j$ differ appreciably, only collisions of type (2) contribute, and the coherence kernel contains a small-angle scattering component only. The absence of a large-angle scattering component in the coherence kernel is linked to a collision-induced spatial separation of the trajectories associated with states $i$ and $j$. Interestingly enough, the width of the diffractive kernel, as measured in the laboratory frame, is found to be insensitive to the perturber to active-atom mass ratio. To illustrate these features, a specific calculation of the kernels is carried out using a hard-sphere model for the scattering. The relationship of the present description of collisions to that of traditional pressure-broadening theory in which trajectory separation effects are ignored is discussed. It is explained why traditional pressure-broadening theory correctly describes collision effects in linear spectroscopy, but fails to provide an adequate description of some saturation spectroscopy and photonecho experiments in which velocity-changing collisions associated with the coherence kernel play a significant role. An expression for the collisionally modified photon-echo amplitude is derived which clearly displays the role played by velocity-changing collisions associated with the coherence kernel.

The photoionization of molecular nitrogen has been studied using a frozen-core Hartree-Fock final-state wave function with a correlated intitial-state wave function. The final-state wave function was obtained using the iterative Schwinger variational method. The effects of initial-state correlation were studied by comparing cross sections obtained using a configuration-interaction-type initial-state wave function with those obtained using a Hartree-Fock initial-state wave function. In this paper we compare our accurate single-center expansion results with other theoretical results. We find that earlier single-center cross sections were not well converged with respect to their expansion parameters. The results of the continuum multiple-scattering method and the Stieltjes-Tchebycheff moment-theory approach are found to be in qualitative but not quantitative agreement with the present results. We also compare our computed total cross sections as well as integrated target angular distributions with experimental results for photoionization leading to the $X{}_{}{}^2{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$, $A{}_{}{}^2{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$, and $B{}_{}{}^2{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ states of ${\mathrm{N}}_2^{+}$. We find generally good agreement, which is improved by the inclusion of initial-state correlation effects, especially in the resonant photoionization channel leading to the $X{}_{}{}^2{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ state of ${\mathrm{N}}_2^{+}$. We also report integrated detector angular distributions for these three channels.

A formula for the stopping power of matter for neutrinos and antineutrinos, interacting with electrons via the weak interaction in the context of both the $V-A$ theory and the Weinberg theory is derived in the high-$Q$ approximation and applied to study the solarneutrino anomaly. The result shows that neutrinos extending in energy from 1 to 10 MeV produced inside the sun escape it essentially without any loss of energy. In agreement with previous investigators, Rustgi, Leung, Turner, and Brandt, it is found that the neutrinos should retain the energy given them at their creation essentially forever and permeate the universe uniformly rather than cluster around galaxies.

Hyperfine splittings of inner-shell atomic energy levels are obtained analytically in a relativistic screened calculation. The approach is based on an analytic perturbation theory appropriate for describing electrons in the interior of the atom. Screening and relativistic effects can be separately identified. Screening is, for the most part, nonrelativistic in origin and largely (though not entirely) enters through the change of normalization. Good results may generally be obtained by correcting relativistic Coulomb results with the non-relativistic change in normalization due to screening.

Stark widths of the Mg I 2852.13-Å and of the Mg II 2795.53- and 2802.70-Å resonance lines have been measured in the ranges of electronic density and temperature 1.10-1.64×${10}^{17}$ ${\mathrm{cm}}^{-3\mathrm{}}$, 12 900-14 300 K. The light source is a stationary, optically thin, wall-stabilized arc burning in argon with a small addition of Mg vapor. Plasma parameters are measured with the use of line and continuum radiation of the argon plasma. Optical depth measurements are performed at the peaks of the investigated lines, and the Mg concentration is continuously controlled to minimize the reabsorption. High spectral resolution is achieved by use of a piezoelectric scanned Fabry-Pérot interferometer whose instrumental profile is measured and found to be Voigt shaped. The experimental profiles are analyzed using a least-squares fit of the Voigt function to all profile intensity points. The Stark width of the Mg I resonance line is found to be 30 to 50% lower than the existing semiclassical calculations. No quantum calculations and no other experimental values are available. As to the Mg II resonance doublet, its width is found lower by a factor of 2 than all the previous experimental values but those of Roberts and Barnard, and our value agrees well with the full quantum calculations of Barnes.

A novel phase-modulation technique which permits subkilohertz-laser stability and new levels of precision in laser spectroscopy was reported recently. For spectroscopy, the basic arrangement consists of a combination of an optical pump and a probe field which is phase modulated. The pump prepares the atomic sample by burning a narrow hole within the atom's inhomogeneous line shape, and the probe beam samples the prepared hole when its modulation sidebands are swept into resonance. Off resonance, the probe is balanced as pairs of sidebands produce heterodyne beat signals of opposite phase which just cancel. On resonance, the balance is upset and yields a nonvanishing beat signal with a Lorentzian absorption or dispersion line shape and with residual noise approaching the shot noise limit. Here we investigate the theory of phase-modulation spectroscopy. We treat the nonlinear response of an atomic two-level quantum system subject to an intense pump and a weak copropagating or counterpropagating phase-modulated probe beam. The density-matrix equations of motion are solved by a Laplace-transform method and by the novel use of a translation operator which allows the infinite hierarchy of coupled equations to close. A solution equivalent to the rate-equation result is developed and coherence corrections are found which predict new resonances that have just been detected in this laboratory. The delayed pump-probe technique encountered in solid-state laser spectroscopy is analyzed in this context for two- and three-level quantum systems. The response of a Fabry-Perot cavity to a phase-modulated light wave is examined also and reveals an unexpected absorption feature.

Cross sections for $7{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}\leftrightarrow 7{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}$ transfer in Rb, induced in collisions with He, Ne, Ar, and with ground-state Rb atoms, have been determined using methods of atomic fluorescence. Rb vapor, pure or mixed with a noble gas, was irradiated in a glass fluorescence cell with pulses of 660-nm radiation from a ${\mathrm{N}}_2$-laser-pumped dye laser, populating one of the ${}_{}{}^2{}_{}{}^{}D$ states by two-photon absorption. The resulting fluorescence included a direct component emitted in the decay of the optically excited state and a sensitized component arising from the collisionally populated state. Relative intensities of the components yielded the cross sections for $7{}_{}{}^2{}_{}{}^{}D$ mixing: $Q({}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}\to {}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{})=8.8,6.5,10.4, \mathrm{and} 30$; $Q({}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}\leftarrow {}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{})=5.8,4.0,6.9, \mathrm{and} 18$, in units of ${10}^{-14\mathrm{}}$ ${\mathrm{cm}}^2$ for He, Ne, Ar, and Rb, respectively. Cross sections for the effective quenching of the ${}_{}{}^2{}_{}{}^{}D$ states were also determined.

A new laser selective-excitation technique for the determination of absolute transition probabilities of weak allowed, intersystem, and forbidden atomic lines has been developed. It exploits the fact that the oscillator strength is proportional to the number of stimulated absorptions and emissions produced by a narrow-band laser pulse of known energy which is in resonance with an atomic transition. The method has been tested by studying the $3s^2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}-3s3p{}_{}{}^3{}_{}{}^{}P_1^o{}_{}{}^{}$ intersystem transition in Mg I. Magnesium vapor was produced in a resistively heated oven and excited with a Nd:YAG laser-pumped dye laser. The lower-level population was monitored with the hook method while the equivalent width of the ${}_{}{}^3{}_{}{}^{}P_{}^o{}_{}{}^{}-3s4d{}_{}{}^3{}_{}{}^{}D$ multiple was used to determine the ${}_{}{}^3{}_{}{}^{}P_1^o{}_{}{}^{}$ level population, which is equal to the number of stimulation absorptions. A laser-produced plasma was used as a background continum source. The laser energy was determined with a disk calorimeter. We show that multiphoton, collisional, and power-dependent processes and mode structure in the laser do not affect the measurement. Our result, $A=(2.19\mathrm{}\pm 0.30)\times {10}^{+2\mathrm{}}$ ${\sec }^{-1\mathrm{}}$, or $f=(2.06\mathrm{}\pm 0.29)\times {10}^{-6\mathrm{}}$, is in good agreement with theoretical and other experimental data. The technique could be applied to lines several orders of magnitude weaker than the MgI intersystem line.

In a previous article it has been shown how the variance of the distribution of the lines belonging to a transition array between two atomic configurations can be computed exactly. The agreement with experimental unresolved spectral patterns was good. We generalize the formal expansions obtained previously for simple arrays to cases with an arbitrary number of open subshells. The results are expressed in terms of the formulas already published [Phys. Rev. A 20, 2424 (1979)].

The complete reduction of a fourth-rank Cartesian tensor into parts wich are irreducible under the three-dimensional rotation group is presented. Results are given for the general case of a tensor without index permutational symmetry, and also for tensors with specific index symmetry properties. Applications in the realm of crystal physics are indicated with particular reference to four-photon absorption, and a table of irreducible tensor representations is provided for the seven crystal classes.

Photon echoes in gaseous media are explained with the use of a simple heuristic model in which the atoms behave like composite billiard balls. The laser providing the excitation pulses becomes an atom smasher which "splits" the atoms and then by judicious programming puts them back together again. The most general photon-echo reordering process is explained without recourse to formal analysis so that an intuitive feeling is obtained which works equally well for the ordinary two-pulse photon echo, the Raman echo, the trilevel echo, the grating echo, etc. A formal analysis of the billiard-ball echo model is presented in its support.

The theory of the interaction between radiation fields and atoms as applied to laser spectroscopy can be approached using either a bare-atom picture (BAP) or dressed-atom picture (DAP). In the BAP, the basis states are those of the free atoms and free field while, in the DAP, the basis states encompass some part of the atom-field interaction. The theory of saturation spectroscopy in three-level systems is discussed using both approaches. Whereas calculations are usually more easily done using the BAP, one can gain useful insight into the underlying physical processes from the DAP. Moreover, when the radiation field strengths (in frequency units) are larger than the relaxation rates in the problem, the DAP equations simplify considerably and lead to line-shape expressions which may be given a simple interpretation. The DAP is used to obtain resonance conditions for traveling-wave fields interacting with three- and four-level atoms and for a standing-wave saturator and traveling-wave probe interacting with a three-level atom. In addition, the DAP is applied to several problems involving optical coherent transients. A comparison is made between the various advantages of the BAP and DAP and an interesting duality between the two approaches is noted.

A free-electron laser with the guide magnetic field operating as an amplifier is analyzed. A simple dispersion relation, similar in form with or without the guide field, is derived. The study of the solutions of the dispersion relation indicates that the guide allows us to (a) enhance the spatial instability in the amplifier, and (b) significantly extend the frequency range of the instability to lower and higher frequencies. This improved operation of the amplifier with the guide field may be achieved at lower values of the pump helical magnetic field. An expression for the power gain in the amplifier as a function of its length is derived and applied in numerical examples to demonstrate the effects of the guide field.

The substantial ion heating of toroidal plasmas at rf frequencies between the ioncyclotron and lower-hybrid frequencies suggests that some additional process or processes must supplement conventional harmonic ion-cyclotron coupling of wave energy to particles. It is proposed in this paper that superthermal lower-hybrid turbulence excited because of the harmonic oscillating two-stream instability could contribute in a significant way to this observed heating. The threshold field strength for such a process to occur in the Elmo Bumpy Torus Scale is calculated. Specific tests of the theory, measurement of an enhanced lower-hybrid and quasimode spectrum, particularly at harmonics of the pump frequency, are indicated. The impact of the harmonic oscillating two-stream instability as allowing rf heating at frequencies a factor of 2 or 3 below the lower-hybrid frequency is described.

The scattering function $S\mathrm{}(Q,E)\mathrm{}$ for liquid bismuth at 305°C has been determined by neutron inelastic scattering in the wave-vector transfer range $1.6<Q<\mathrm{}7.2\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$ and for energy transfers $E$ up to about 20 meV. The measured $S\mathrm{}(Q,E)\mathrm{}$ satisfies the zeroth- and the second-moment relations within some few percent. The shoulder in the static structure factor $S\mathrm{}\left(Q\right)\mathrm{}$ gives rise to clearly visible effects also in the dynamical-scattering function. The full width at half maximum of $S\mathrm{}(Q,E)\mathrm{}$ exhibits an oscillation at a $Q$ value corresponding to the position of the shoulder. This fact together with some particular features in the same $Q$ range regarding the experimentally obtained spectrum of the longitudinal current-current correlation function indicates that the nature of the molecular dynamics in liquid bismuth is different as compared with simple liquid metals.

We present a comparison of approximate integral-equation and Monte Carlo pair-correlation functions in a nonuniform, one-dimensional classical fluid. The approximate correlation functions are obtained by solving the Percus-Yevick equation for a nonuniform system and also by evaluating the Percus-Yevick pair-distribution function for a uniform system at an appropriate average density. We find that the former agree very well with the results of Monte Carlo grand-canonical-ensemble simulations but that the latter frequently underestimates the correlations in the inhomogeneous fluid, independent of the averaging scheme employed. Some implications are drawn concerning the suitability of direct-correlation functions determined by these methods for use in density-functional applications.

We use the generalized Langevin approach to study the dynamical correlations in an inhomogeneous system. The equations of motion (formally exact) are obtained for the number density, momentum density, energy density, stress tensor, and heat flux. We evaluate all the relevant sum rules appearing in the frequency matrix exactly in terms of microscopic pair potentials and an external field. We show using functional derivatives how these microscopic sum rules relate to more familiar, though now nonlocal, hydrodynamiclike quantities. The set of equations is closed by a Markov approximation in the equations for stress tensor and heat flux. As a result, these equations become analogous to Grad's 13-moment equations for low-density fluids and constitute a generalization to inhomogeneous fluids of the work of Schofield and Akcasu-Daniels. We also indicate how the resulting general set of equations would simplify for systems in which the inhomogeneity is unidirectional, e.g., a liquid-vapor interface.

Pressure-volume-temperature measurements throughout the nematic phase for the first six members of the homologous series of di-alkoxyazoxybenzenes are reported. These data represent the first investigation of thermodynamic parameters in an homologous series, thus demonstrating the role of the end chains in a specific molecular geometry. Measurements at constant volume permit the conversion of previous orientational order studies at atmospheric pressure to constant-volume conditions. Measurements at constant temperature at the nematic-isotropic phase transition reveal the behavior of the specific volume, volume discontinuity, and volume dependence of the mean-field potential in this series. Finally, the implication of these data on several liquid-crystal theories is explored.

A classical theory of statistical mechanics of the Toda lattice is presented on the basis of soliton dynamics. Following the inverse spectral theory, the partition function of the Toda lattice is reconstructed from one-particle partition functions of soliton and ripple modes. Discussions are made on the contribution of these modes to the thermodynamic properties of the Toda lattice. At low temperatures, it is shown that the average number of excited solitons has the temperature dependence $T^{\frac{1}{3}}$. With the comparison of our results with those from the exact theory, several problems to be worked out are pointed out in our soliton-ripple gas-mixture model.

Longitudinal and transverse charge and mass current fluctuation spectra are calculated self-consistently for all wave numbers $q$ and frequencies $\omega$. The theory suggests a new generalized random-phase approximation which interpolates between the (large-$q$) kinetic regime and (the small-$q$) collision-dominated regime. The relaxation kernel governing the decay of current excitations at small wave numbers is approximated by a mode-coupling expression. The theory uses as input the pair potentials and the static pair and triplet correlation functions. For the latter a modified superposition approximation is employed. The results are compared with computer-simulation data.