Novel phenomena in which two fields are of equal importance in determining electronic properties are considered through simple, semiclassical arguments. Both the range of field strengths where such "strong mixing" of fields sets in and the nature of the subsequent spectrum are established. Since this feature has not always been appreciated, implications for recent experiments in diverse situations in atomic and solid state physics are pointed out and further experiments to explore such phenomena suggested.

Cs vapor in He, Ne, and Ar buffer gases has been optically pumped in magnetic fields as high as 100 kG. The rate of electronic spin relaxation measured in Cs-Ar is approximately the same as that predicted by the low-field nuclear-spin-independent cross section for the relaxation of $〈S_z〉$ via the $\gamma \left(\overrightarrow{\mathrm{S}}·\overrightarrow{\mathrm{N}}\right)$ (spin-orbit) interaction. In the cases of Cs-He and Cs-Ne, considerably higher relaxation rates are measured at high fields than those that are predicted from the low-field cross sections. The differences are shown to be due to relaxation arising from the collision-induced modification of the Cs hyperfine interaction, $\delta a\left(\overrightarrow{\mathrm{S}}·\overrightarrow{\mathrm{I}}\right)$. Upper limits of the order of ${10}^{-13\mathrm{}}$ sec are set for the average durations of both the $\delta a\left(\overrightarrow{\mathrm{S}}·\overrightarrow{\mathrm{I}}\right)$ and the $\gamma \left(\overrightarrow{\mathrm{S}}·\overrightarrow{\mathrm{N}}\right)$ interactions in sudden binary collisions of Cs atoms with light noble-gas atoms. The average cross sections for the $\delta a\left(\overrightarrow{\mathrm{S}}·\overrightarrow{\mathrm{I}}\right)$ interactions are estimated to be 1.3 × ${10}^{-14\mathrm{}}$ ${\mathrm{cm}}^2$ for Cs-He, and 0.73 × ${10}^{-14\mathrm{}}$ ${\mathrm{cm}}^2$ for Cs-Ne.

We have measured Stark broadening and shift parameters for spectral lines of the ${\mathrm{C}}_1$ resonance multiplet $2p3s{}_{}{}^3{}_{}{}^{}P_{0,1,2}^o{}_{}{}^{}-2\mathrm{}{p}^2{}_{}{}^3{}_{}{}^{}P_{0,1,2}^{}{}_{}{}^{}$ as well as for lines corresponding to transitions to low-lying quantum states. The lines were emitted under approximately optically thin conditions from a dense equilibrium plasma (wall-stabilized arc; electron number density, $6.1\times {10}^{22} {\mathrm{m}}^{-3\mathrm{}}\le n_e\le 2.1\times {10}^{23} m^{-3\mathrm{}}$; temperature, $11700 \mathrm{K}\le T\le 16000 \mathrm{K}$). As predicted by the theory, the Stark widths and shifts for different lines of the resonance multiplet at ≈ 165 nm were found to be equal within the experimental uncertainty. The experimental values for these lines agree well with recent calculations by Griem. For $n_e={10}^{23}$ ${\mathrm{m}}^{-3\mathrm{}}$ the experimental (full) half-width amounts to (4.0±0.7) × ${10}^{-3\mathrm{}}$ nm and the red shift (1.9±0.3) × ${10}^{-3\mathrm{}}$ nm. A significant deviation from Griem's calculation was only found for ${\mathrm{C}}_1$ at 175.19 nm (${}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}-{}_{}{}^1{}_{}{}^{}S$), for which the measured shift is larger by a factor of 2. For this line, the calculations by Wilson and Nicolet approximately agree with the results of this study.

For the first time, the parametric coupling of the negative-energy cyclotron and space-charge modes to a fast coaxial waveguide structure is observed. The coaxial waveguide smooth center conductor is internally loaded to maintain a 5% ripple of 1.4-, 1.6-, or 2.0-cm periods on the background axial magnetic field throughout the interaction region of 70 cm. The parametric coupling may be considered a stimulated scattering process with the rippled magnetic field of zero frequency in the lab frame appearing as an electromagnetic pump wave in the beam frame, with 30-MW/${\mathrm{cm}}^2$ power density imparting to the electrons a quiver velocity $V_{\mathrm{os}}\simeq 0.1c$. As predicted by theory, the frequency of the microwave radiation generated by the negative-energy cyclotron mode decreases with increasing magnetic field while remaining constant for the negative-energy space-charge mode. Power levels from 1 to 5 MW have been measured at mm and cm wavelengths. Radiation at frequencies of $\frac{2{\gamma }^{2}V}{L}$, where $V$ and $L$ are the beam velocity and ripple period, respectively, has been observed at high magnetic fields with an exponential-growth rate consistent with parametric coupling theory. This mechanism could be employed as a tunable generator of millimeter and submillimeter wavelength radiation.

Calculations are reported of certain low-lying infrared transition frequencies in ${\mathrm{H}}_2^{+}$, ${\mathrm{D}}_2^{+}$, H${\mathrm{D}}^{+}$, H${\mathrm{T}}^{+}$, and D${\mathrm{T}}^{+}$. They take account of radiative, relativistic, and nonadiabatic effects and are made to the same level of accuracy (0.002 ${\mathrm{cm}}^{-1\mathrm{}}$) as the recent experimental measurements for H${\mathrm{D}}^{+}$; for the (1,0-0,1), (1,1-0,2), and (2,1-1,0) transitions for this molecular ion, the frequencies are 1869.135 (1869.134), 1823.534 (1823.533), and 1856.781 (1856.778) ${\mathrm{cm}}^{-1\mathrm{}}$, where the experimental results are shown in parentheses. We predict that the current values of the mass ratios $\frac{m_e}{m_p}$ and $\frac{m_e}{m_d}$ are good to ±2 in the sixth significant figure. The nonadiabatic energies are based on extremely large basis sets (up to and including 515 basis functions) and required special techniques for solving the generalized eigenvalue equation.

The technique of photoelectron spectrometry has been used to measure the ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}:{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ branching ratio in the photoionization of the $5p$ shell of xenon, using discrete UV lines and synchrotron radiation, in the entire energy range between 21 and 107 eV. A strong energy dependence is observed, with a minimum around 30 eV and a maximum, slightly higher than the statistical ratio, between 60 and 70 eV. Between 21 and 40 eV, the present data confirm the earlier calculations of Walker and Waber, using the Dirac-Slater model, which predicted a minimum in the branching ratio around 30 eV, in contrast to the conclusions of a previous experimental analysis which were that this branching ratio be constant in this energy range. The discrepancy between our data and these previous measurements might be attributed to pressure effects that are found to play a major role below 40-eV photon energy. New Dirac-Slater calculations by Desclaux reproduce the experimental behavior qualitatively between 40 and 100 eV.

Subthreshold operation of a one-dimensional laser having output coupling is analyzed quantum mechanically under the assumption of constant population inversion. The conventional quantum Langevin theory of the laser is improved in that the spatial behavior of the field is treated exactly by use of a multimode formulation of the field of the universe. This formulation allows the thermal noise to be derived automatically without introducing any artificial damping mechanism for the field; this noise comes from the statistical nature of the initial state of the field. The analysis shows that the cavity quasimodes are excited, that the linewidth formula differs from that of a conventional theory by a factor determined by the field distribution excited in the cavity, and that, outside the cavity, the quantum-mechanical coherence function is propagated with the velocity of light.

The polarization of photon echoes stimulated by linear-linear, circular-linear, and linear-circular excitation sequences has been studied in S${\mathrm{F}}_6$ with the $P\left(12\right)\mathrm{}$ through $P\left(26\right)\mathrm{}$ laser lines of C${\mathrm{O}}_2$ near 10.6 μm and in Si${\mathrm{F}}_4$ with the $P\left(28\right)\mathrm{}$ through $P\left(34\right)\mathrm{}$ lines near 9.6 μm. A linear-linear pulse sequence with angle $\beta$ between the linear polarizations produces an echo at angle $\varphi$ with respect to the second pulse. $\varphi$ rotates in the same sense as $\beta$ with $P\left(16\right)\mathrm{}$ in S${\mathrm{F}}_6$ and in the opposite sense as $\beta$ with the other lines in S${\mathrm{F}}_6$, and with the lines in Si${\mathrm{F}}_4$. A left-circular-linear sequence produces a right-elliptic echo with $P\left(16\right)\mathrm{}$ in S${\mathrm{F}}_6$, and a left-elliptic echo in the other cases. A linear-left-circular sequence produces a left-circular echo in all cases. These results are in accord with the large-$J$ polarization theory of Heer and Nordstrom. For a linear-linear excitation sequence, this theory predicts an unnormalized echo electric field $\overrightarrow{\mathrm{E}}\cong \mp \hat{X}\left(\frac{1}{2}sin\beta \right)+\hat{Z}cos\beta$, where the negative sign applies to a $P$- or $R$-branch transition, and the plus sign to a $Q$-branch transition. For a left-circular-linear sequence, the theory predicts an unnormalized echo electric field $\overrightarrow{\mathrm{E}}\cong \pm \frac{1}{2}i\hat{X}+\hat{Z}$, where the plus sign refers to a $P$- or $R$-branch transition, and the negative sign to a $Q$-branch transition. Echo decay rates determined from relaxation measurements are used to calculate molecular cross sections, and these cross sections are compared with calculations based on the refractive indices and the Slater-Kirkwood equation. Experimental cross sections are in general smaller than those found from the Slater-Kirkwood equation.

The behavior of the momentum distribution function is discussed theoretically in the small-signal regime of the free-electron laser (FEL). The distribution function is derived analytically following a series of approximations that reduce this problem to the Klein-Gordon equation. The distribution function changes in nontrivial ways that may play an important role in the efficiency of the FEL.

Three experiments are described in which high-intensity ruby and Nd: glass laser beams were analyzed for spectral purity. The aim of the experiments was to verify whether the nonlinear relation for photon energy $\epsilon =\frac{h\nu }{[1-{\beta }_{\nu }f(I\left)\right]}$, previously used to explain ionization phenomena in gases irradiated with laser beams, admitted an interpretation in terms of change of light frequency as a function of intensity. Standard methods of frequency measurement, namely spectroscopic, interferometric, and filtering methods, were used. The results consistently exclude the idea of monochromatic laser beams and seem to indicate that, at the intensities used in the experiments, which ranged from a few hundred kilowatts/${\mathrm{cm}}^2$ to a few gigawatts/${\mathrm{cm}}^2$, the laser line is broadened by several hundred angstroms.

A high-intensity single-mode gas laser is analyzed by several mathematical methods. Exact numerical results are best obtained by solving for the coefficients of a Fourier series solution by using a backward recurrence scheme or a successive convergents method for evaluating a continued fraction. Numerical integration techniques can also be used to convert the periodic boundary conditions to initial conditions and then solve the resulting initial-value problem. Direct analytic integration leads to exact solutions in terms of Bessel functions for the special case of zero detuning, equal decay rates, and neglecting of collision broadening. For general single-mode operation, an improved analytic approximation [the second recursion relation approximation (2RCRA)] is obtained by taking an additional term in the recursion relations for the Fourier coefficients. This approximation predicts the existence of one of the secondary resonances in graphs of the spatially averaged population inversion and quadrature polarization coefficient densities and matches the exact solution from the position of the first resonance and outward independent of the intensity. The 2RCRA also matches the exact detuning curve except at small detunings. The first-order ("rate equation") approximation, by comparison, does not predict any secondary resonances and does not match the exact solution at higher intensities. A physical interpretation for the appearance of the secondary resonances is presented in terms of multiphoton interactions and a prediction for the positions of the resonances for the special case discussed above is obtained. As predicted by Greenstein the exact detuning curves show quantitatively that the Lamb dip decreases and disappears as the intensity increases for high excitations.

The complete solution of the Maxwell-Bloch equations by the inverse scattering transform as given by Ablowitz, Kaup, and Newell is compared with the McCall-Hahn theory, and others. Not only it is shown that the earlier results are contained in the complete solution, but also several new results are obtained. Among these are an infinite set of "nonlinear moments" which evolve similar to the McCall-Hahn area, a closed-form solution for the nonlinear transmission, how one can determine absolute time delays, why the threshold area for lossless propagation is still exactly $\pi$ (even when the initial profile is off resonance but unchirped), and first-order effects of relaxation on $2\pi$ hyperbolic-secant pulse propagation. For the last-mentioned results, we find that in general if a $2\pi$ hyperbolic-secand pulse is initially off resonance, it will move away from resonance. Also, we find that the McCall-Hahn result for first-order effects on the time delay must be modified for small-amplitude $2\pi$ hyperbolic-secant pulses.

We report a computer simulation of simple shear flow in order to investigate the transport properties of a two-dimensional microscopic model of a fluid. The numerical results exhibit nonlinear profiles for the fluid velocity, and the viscous resistance depends linearly on the shear rate. These experiments confirm that, in two-dimensional fluids, the Navier-Stokes equations do not exist in their usual form. We propose a phenomenological expression for the viscous part of the pressure.

An equation is obtained for the energy loss of ions to electrons in a high-density plasma of arbitrary degeneracy. The quantum-mechanical form of the dielectric function is used to produce a formula that is free of the usual Coulomb divergence, so that the introduction of ad hoc cutoff parameters is not required. The results show a decrease of 20% to 50% in the energy-loss rate when compared with other formulas that use the standard Coulomb logarithm.

Dynamic renormalization-group methods are used to study the large-distance, long-time behavior of velocity correlations generated by the Navier-Stokes equations for a randomly stirred, incompressible fluid. Different models are defined, corresponding to a variety of Gaussian random forces. One of the models describes a fluid near thermal equilibrium, and gives rise to the usual long-time tail phenomena. Apart from simplifying the derivation of the latter, our methods clearly establish their universality, their connection with Galilean invariance, and their analytic form in two dimensions, $\sim \frac{{\left(logt\right)}^{-\frac{1}{2}}}{t}$. Nontrivial behavior results when the model is formally continued below two dimensions. Although the physical interpretation of the Navier-Stokes equations below $d=2\mathrm{}$ is unclear, the results apply to a forced Burger's equation in one dimension. A large class of models produces a spectral function $E\left(k\right)\mathrm{}$ which behaves as $k^2$ in three dimensions, as expected on the basis of equipartition. However, nonlinear effects (which become significant below four dimensions) control the infrared properties of models which force the Navier-Stokes equations at zero wave number.

A molecular theory of liquid crystals is developed within the framework of statistical mechanics for classical liquids. Coupled Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) equations are derived and solved for anisotropic systems of molecules interacting via a pairwise, orientation-dependent potential. Solutions representing isotropic and nematic phases are obtained. Among the quantities calculated are the temperature- and density-dependent orientational order parameters. Besides serving as a prototype calculation, what is presented here also provides a theoretical background in which the mean-field approximation can better be understood.

For a system of dipolar hard spheres, comparisons are made among new Monte Carlo results and the results of several approximation schemes developed to describe the pair correlation function in simple dipolar liquids. A self-consistent Ornstein-Zernike approximation (SCOZA) proposed by Høye and Stell gives results that appear to be nearly exact for all values of the dipole moment at which relevant Monte Carlo results are currently available ($\lambda =\frac{\beta {\mu }^2}{R^3}\le 2.75$, where $\beta =\frac{1}{\mathrm{kT}}$, $\mu$ is the dipole moment, and $R$ is the hard-sphere diameter). Results are also given for a linear approximation (LIN) as well as for a higher-order cluster series approximation ($L3\mathrm{}$) of Verlet and Weis and for an approximation of Høye and Stell (the PPA) based on the use of a Padé approximant for the thermodynamics. These provide much less overall accuracy, but each satisfactorily reproduces certain key features of $h\left(12\right)\mathrm{}$, the pair correlation function. The orientationally averaged PPA correlation function is highly accurate over a large range of $\lambda$ when used with appropriate thermodynamic input, while the angular components are much less adequate. The LIN and $L3\mathrm{}$ results require no thermodynamic and dielectric input and are of interest chiefly because of this, and because of the dielectric constants ${\epsilon }_{\mathrm{LIN}}$ and ${\epsilon }_{L3\mathrm{}}$ associated with them. The Wertheim expressions for $\epsilon$, ${\epsilon }_{\mathrm{LIN}}$, and ${\epsilon }_{L3\mathrm{}}$ are compared. Monte Carlo estimates seem to be closest to ${\epsilon }_{\mathrm{LIN}}$ for $\lambda \le 1$. For higher $\lambda$ there is some evidence that all three expressions may yield values of $\epsilon$ that are too low. All are clearly more accurate than the Onsager expression.

A theory is developed to describe the effect of simultaneously occurring vibrational relaxation on intermolecular excitation transfer in the presence of radiative and nonradiative sinks. The basis is a master equation whose rates are combinations of the Förster-Dexter transfer rates and the Montroll-Shuler relaxation rates. Exact solutions are obtained for the probabilities of occupation of single vibrational levels as well as of site occupation, and for quantum yields and differential photon count rates. It is shown how phenomena exhibiting dependence of quantum yields or similar quantities on the wavelength of initial excitation can be quantitatively approached with the help of this analysis. The concept of time-dependent transfer rates is developed, and it is shown that at long times the transfer rate could tend to a value different from the thermalized Förster-Dexter rate. It is also shown how the relaxation process can result in an effective transfer rate (for singlets) whose dependence on the intermolecular distance $R$ is other than $R^{-6\mathrm{}}$.

A direct perturbation method is developed in order to study the interactions of $N$ solitons with imperfections and with each other in the presence of imperfections. The leading-order effects are obtained directly from the $N$-soliton waveform without invoking methods from inverse-scattering theory. The method is based upon a Green's function and a "two time" procedure from classical perturbation theory. An example of a single soliton is developed in detail. Finally, this perturbation method is compared with other approaches in the literature.

A mechanism is proposed which explains the nonexponential decay $2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}\to 1{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}+\gamma \mathrm{}\left(M1\mathrm{}\right)\mathrm{}$ recently observed in beam-foil experiments on He-like atoms. This mechanism suggests that the nonexponential nature of this decay is due to the inclusion of unresolved $M1\mathrm{}$ satellite photons from Li-like ions. By using models of excited-state populations which are suggested by recent beam-foil experiments, we are able to calculate a decay profile of heliumlike sulfur which agrees with the experimental results.