Measurements of $K$-shell photoelectric cross sections of copper, zirconium, silver, tin, tantalum, gold, and lead for 279.1- and 411.8-keV $\gamma$ rays have been carried out using a well-type plastic scintillation spectrometer. The number of $K$-shell photoelectrons in each material is estimated by fitting a Gaussian to the respective resolved photoelectron spectrum, and hence the $K$-shell photoelectric cross sections are estimated. This method is similar to the one used for determining the $K$-shell photoelectric cross sections for 145-keV $\gamma$ rays which have been reported in an earlier paper by the authors. Also in the present investigation the cross sections are found to be in good agreement with the predicted values of Schmickley and Pratt, and the recently calculated values of Scofield at both energies.

A semiclassical theory of the vibrational Raman effect based on the idea of different time scales for the electronic and nuclear motions is given. The proposed model gives a physical insight into the polarizability theory intuited by Placzek, the role of the electronic polarizability being that of the perturbation which induces first-order transition of the nuclei between vibrational levels. Extension of the semiclassical theory to the resonance Raman effect is made for the case where the intermediate states are, or may be represented by, a vibrational continuum. The specific case of the parallel components of the 0 → 1 and 0 → 2 Raman transitions in ${\mathrm{H}}_2^{+}$ is considered.

Flügge, Mehlhorn, and Schmidt have suggested that the dependence of the atomic photoeffect on a bound-electron magnetic substate will have observable consequences for the angular distribution of subsequent Auger electrons. Because of the constraints of parity and time-reversal invariance, this possibility first arises for ejection from $L_{\mathrm{III}}$ and $M_{\mathrm{III}}$ subshells. We have calculated the relative probabilities of $\left|j_z\right|=\frac{3}{2}$ and $\left|j_z\right|=\frac{1}{2}$ ejection from these subshells, both with the relativistic Born approximation (Gavrila's formulation) and in the nonrelativistic dipole approximation. The ratio of these cross sections can have a dramatic energy dependence, ranging from 7 at high energies to 9/11 in the low-energy domain, and dropping to 1/3 near threshold if there is a Cooper minimum. Screening effects are discussed.

Photoattenuation coefficients are reported for high-pressure xenon and krypton at wavelengths in the red wings of the first resonant lines [$\mathrm{Xe}\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$, ${\lambda }_0=1470\mathrm{}$ Å and $\mathrm{Kr}\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$, ${\lambda }_0=1236\mathrm{}$ Å]. The measurements cover the range 2000-20 000 ${\mathrm{cm}}^{-1\mathrm{}}$ from the resonant lines. The photoattenuation spectra are interpreted in terms of Rayleigh scattering and photoabsorption by atoms, Van der Waals molecules, and unbound diatomic molecules—different portions of the spectra are dominated by different species and phenomena. Absorption by unbound diatomic molecules is interpreted via a quasistatic model of the molecule. Analysis of the data in this manner yields information concerning the structure and radiative lifetime of the lowest-bound diatomic states of $\mathrm{Xe}_2^{}{}_{}{}^{*}$ and $\mathrm{Kr}_2^{}{}_{}{}^{*}$. The significance of the results reported here in regards to dissociative noble-gas lasers (transition from a bound diatomic level to the repulsive ground level) is discussed.

Absolute apparent cross sections for electron impact excitation of the $4s^{\prime }$, $5s$, $3d$, $4d$, $5d$, $3d^{\prime }$, and $4d^{\prime }$ configurations of ${\mathrm{Ar}}^{+}$ from the ground state of Ar are presented by studying the vacuum uv photon decay of the states. The high-energy behavior of the excitation functions is demonstrated to reflect the two-electron nature of the initial excitation. Where cascade can be satisfactorily taken into account, excitation of states with the same orbital angular momentum and multiplicity is shown to be according to their statistical weights. Some significant discrepancies are exposed between theoretically calculated and experimentally measured relative transition probabilities. Configuration-interaction effects are demonstrated to exist in a number of instances and are quantitatively investigated for the ${}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ states.

The experiment presented measures the relative differential cross sections in helium for the energies between 1.0 and 10.0 eV and at the angles 10°, 15°, 20°, 25°, and 30°. The results are compared to the experiments of others and are also compared to the present theories. Since experiments do not overlap very well in this region, conclusions are difficult to draw. It is easier, however, to make comparisons to the theoretical predictions. It is shown that the results of this experiment do not agree well with the theoretical predictions.

The spectra of $K \alpha$ x rays emitted as a result of heavy-ion—atom collisions have been measured with a Bragg spectrometer using a variety of equal velocity (1.7 MeV/amu) heavy ions ranging from ${}_1{}^{}{}_{}{}^{}\mathrm{H}$ to ${}_{18}{}^{}{}_{}{}^{}\mathrm{Ar}$ incident on solid targets containing atoms of ${}_{13}{}^{}{}_{}{}^{}\mathrm{Al}$, ${}_{17}{}^{}{}_{}{}^{}\mathrm{Cl}$, and ${}_{19}{}^{}{}_{}{}^{}\mathrm{K}$. In the cases of Cl and K, the measured $K {\alpha }_{1,2}-K \alpha$ satellite energy differences for one through seven $L$-shell vacancies were found to be systematically larger than those calculated using the Herman-Skillman Hartree-Fock-Slater program. Values of the binomial probability parameter obtained by fitting the relative satellite intensities with binomial distributions have been compared to theoretical values calculated using an impact-parameter formulation of the binary-encounter approximation. In the Al spectra obtained with S and Ar ions, the $K {\alpha }_{1,2}$ peak is observed to have an intensity six to seven times larger than is expected on the basis of a binomial fit to the satellite peaks.

The absolute ionization probability at zero impact parameter has been measured in a coincidence experiment at incident Cl-ion energies of 50-100 MeV. Total $K$ -shell ionization cross sections are also reported over a larger energy range. The data are compared with theoretical predictions based on the assumption of pure Coulomb ionization as formulated in the binary-encounter approximation (BEA), the semiclassical approximation (SCA), and the plane-wave Born approximation. It is shown that the good agreement of the total cross sections with nonrelativistic calculations using a straight-line, constant-velocity projectile trajectory is to a large extent due to a fortuitous cancellation of the inadequacies of this oversimplified model. Recent impact-parameter formulations of the BEA model, including corrections for projectile retardation and deflection and an approximate treatment of relativistic effects, qualitatively reproduce the observed energy dependence of the cross sections and ionization probabilities but overestimate the absolute values by about a factor of 3. Approximate, closed-form, SCA results without these corrections also reproduce the energy dependence but underestimate the ionization probability by a factor of 2 to 3.

The projectile $K$ x-ray emission cross sections for fluorine ions were measured under single collision conditions for charge states ranging from +4 to +9 in a thin argon target. The dependence of these cross sections upon the energy and the initial charge state of the projectile was determined for fluorine ions with energies between 20 and 36 MeV. Over the entire energy range, the $K$ x-ray—production cross section for ${\mathrm{F}}^{+9\mathrm{}}$ ions was about 70% of the total electron-capture cross section determined in a separate experiment. The $K$ x-ray—production cross section for these fully stripped ions is attributed to electron capture to excited states of the projectile. Calculations of electron-capture cross sections within the Brinkman-Kramers approximation for these heavy-ion collisions are consistent with the observation of large cross sections for capture to excited states.

The density dependence of the viscosity coefficient of a dilute fully-ionized plasma is obtained. We associate the viscosity coefficient $\eta$ with the autocorrelation function of the off-diagonal elements of the stress tensor. The technique used is essentially equivalent to that used in a previous paper by the authors. The result of our analysis is $\eta =\Sigma {m=1\mathrm{}}^{\infty }{U}_m\mathrm{}\left(T\right)\mathrm{}\times {\left(\ln \rho \right)}^{-m}$, where the $U_m\mathrm{}\left(T\right)\mathrm{}$ are the solutions to well-defined algebraic equations. If one Sonine polynomial is used, the shear viscosity is given by $\eta ={\left[d_1\mathrm{}\right(T)\mathrm{}\ln \rho +d_2\mathrm{}(T\left)\right]}^{-1\mathrm{}}$.

Hydrodynamic equations of higher order, such as Burnett's equations, do not satisfy Onsager's theorem in its usual form. The reason for this is investigated, and is found to be related to the existence of "initial slip." A recent application of Onsager's theorem to the number of propagating hydrodynamic modes is generalized to apply to linear hydrodynamic equations of any order.

We have measured the optical Kerr effect and the intensity-dependent ellipse rotation in order to study the pretransitional behavior of field-induced molecular alignment in the isotropic nematic substances $p$-methoxy-benzylidene $p-n$-butylaniline (MBBA) and $p$-ethoxy-benzylidene-$p$-butylaniline (EBBA). The results agree well with predictions of the Landau—de Gennes model. Both the order-parameter relaxation time and the steady-state field-induced birefringence show critical divergence towards the isotropic → nematic transition with a ${(T-T^{*})}^{-1\mathrm{}}$ temperature dependence. In the case of MBBA, our results are also consistent with the results from light scattering, but the method we use is perhaps more straightforward and accurate. The nonlinear refractive indices and other relevant parameters of the materials are derived from the experiment.

We have carried out a detailed study of the frequency and damping of the oscillations in levels of two reservoirs of HeII which are coupled only via the mobile superfluid film. Our experiments cover the temperature range $1.2<T<\mathrm{}2.13\mathrm{}$ K and utilize several geometries under quasi-isothermal conditions. Below 2 K our results for the damping are in quantitative agreement with predictions based on a theory first proposed by Robinson. This indicates that the damping mechanisms proposed by Allen and by Calvani, Greulich, and Maraviglia are of minor importance under our experimental conditions. It is argued that the Robinson theory can explain the previous general agreement with the Allen theory.

The two-dimensional boundary-value problem associated with hydrodynamic effects in a dc electric field has been solved under the assumption of dynamic distortions. The time-dependent terms included in the equations of motion are viscous forces and torques as well as displacement currents. Inertial effects are ignored so that the calculations are performed in the zero-Reynold's-number limit. It is found that above a critical voltage, there is a band of domain wavelengths which grow exponentially with time. The fastest growing solution is identified with the physical solution. The domain wavelength and rise rates are calculated as a function of voltage, thickness, and relevant material constants. In particular it is found that turn-on rates for the Williams-domain mode are bounded by the space-charge relaxation time. These calculations are in good agreement with experiment for methoxybenzilidene-butylaniline (MBBA). It is found that the difference between a domain mode and a field effect can be correctly predicted on the basis of the dynamic analysis.

Sound velocity and absorption have been measured at frequencies of 0.6, 1, and 3 MHz for xenon along the liquid-vapor coexistence curve and along several near-critical isotherms. By simultaneously measuring the dielectric constant, the local density was determined at the level in the fluid where the ultrasonic results were obtained. The shape of the coexistence curve obtained from dielectric data gave a critical exponent $\beta$ of 0.357 ± 0.002. The critical sound absorption and dispersion have been analyzed in terms of our modification of Fixman-Kawasaki theory. It is shown that both absorption and dispersion data can be described in terms of a single reduced frequency. The thermodynamic sound-velocity values needed in the analysis of dispersion have been calculated from the linear-model parametric equation of state.

By measuring the resonant frequency of an azimuthal mode in a horizontal annular resonator, it was possible to determine the sound velocity in xenon at ∼ 1 kHz without difficulties caused by gravity-induced density gradients near the critical point. It was shown that the resulting velocity data along the critical isochore above $T_c$ and in the coexisting vapor below $T_c$ correspond to the thermodynamic (zero-frequency limiting) values. The experimental data were fitted with a theoretical curve based on the linear-model parametric equation of state, and the resulting value of 0.08 for the critical exponent $\alpha$ is in good agreement with the value determined previously from specific-heat data.

A linked-cluster expansion for the expectation values of operators between correlated wave functions of the Jastrow type is described. The expansion is based on the logarithm of the correlation function and leads to terms that are explicitly proportional to the particle number for infinite systems. The lowest-order terms for a weakly interacting system of spin-1/2 particles are calculated explicitly. From these, the Euler-Lagrange equations for the correlation functions have been calculated. The equation for the correlation function between particles of antiparallel spin can be solved by Fourier transform, and it is shown that for $r\to \infty$, the correlation function behaves like $1+\frac{A}{r^2}$. In the case of a system of particles interacting by hard-core repulsions, the logarithm of the correlation function does not exist inside the hard-core radius. It is then necessary to sum over ladder diagrams as in the derivation of the reaction matrix in many-body perturbation theory. This is carried out to provide a low-density approximation to the ground-state energy of the system and the Euler-Lagrange equation for the correlation function. It is argued that the correlation function again behaves like $1+\frac{A}{r^2}$ for large $r$. The expansion is applied to the problem of calculating the correlation energy of the electron gas. It is shown that a variational calculation based on the lowest-order terms in an expansion of the wave function leads to a divergent result (unbounded from below), but that a convergent result is obtained by summing over ring diagrams, which correspond to long-range polarization of the electron cloud. The result is similar to that of Gaskell obtained by a somewhat different method. It is shown analytically that at high densities the result behaves logarithmically, specifically as $0.0570\ln r_s-0.1324\mathrm{}$ Ry. The lowest-order exchange contributions have also been calculated and found to contribute 0.040 Ry to the energy at densities of physical interest.

The interactions between rotons in superfluid helium are similar to those between dipoles in a polar fluid. Models developed to describe polar fluids may therefore be used to study the influence of roton interactions on various physical quantities in helium II. In this paper we use the Onsager model of a dielectric to calculate the temperature dependence of the energy of the roton minimum in the excitation spectrum, the entropy density, and the normal fluid density, at three different pressures. The results obtained agree well with experimental values for temperatures up to a few tenths of a degree below the $\lambda$ temperature; the agreement becomes better with increasing pressure. Our theory contains only a single adjustable parameter, the roton hard-sphere radius, for which we find a value close to half the distance between nearest neighbors in the helium fluid.

An analysis is presented of the behavior of the hydrodynamic modes in a horizontal fluid layer subject to a downward-directed temperature gradient which, when reaching a critical value, drives the system into convective instability. It is found that the combination of this thermal constraint and gravity gives rise to a coupling between the heat-diffusion mode and the transverse mode ${\left(\mathrm{curl}\mathrm{curl}\overrightarrow{\mathrm{v}}\right)}_z$, with $\overrightarrow{\mathrm{v}}$, the velocity field, and the $z$ axis pointing in the vertical direction. As a result of this mode coupling, which is absent in a fluid at equilibrium, the damping factor of one of the coupled modes goes to zero when the temperature gradient increases to its critical value. On the basis of this mode analysis, the spectral distribution of the light scattered by the nonequilibrium fluid is then computed. The main features of the light-scattering spectrum consist of the appearance of an additional central component and the respective narrowing and broadening of the spectral components corresponding to the coupled modes as the instability critical point is approached.

An analysis of the theoretical efficiency of converting the nonlinear equilibrium thermal fluctuations of a system to a useful form of energy is made based on equilibrium distributions of statistical mechanics. For the model considered, electric energy fluctuations, as in a resistive material, are converted to a useful form of energy by combining these fluctuations with those from a nonlinear resistive material at another temperature. The system selected for the computed results uses two Alkemade diode models, each in contact with a heat reservoir, as the resistive materials. The resulting rectified current is calculated by deriving a master equation giving the probability of discrete electron jumps across the potential barriers of the diodes. From this, the efficiency is computed of the direct power conversion of thermal to electric energy and of electric to thermal energy as a function of the output or input voltage of the system. These results for the examples are in agreement with fluctuation theory and show that the conversion efficiency increases as the system size decreases to make the fluctuation energy a significant fraction of the total energy. The results also show that there are no theoretical limits on the assumed model in approaching the efficiency limitations of the Carnot cycle. Finally, the limitation on the available fluctuation power that could be provided from a unit area of a resistive film to an assemblage of small circuits was considered. It was determined that this very high limitation was of the order of ${10}^8$ ${\mathrm{W}/\mathrm{m}}^2$. This indicated the potential that, if the material and fabrication problems could be solved, this technique could yield practical amounts of power at high efficiencies over a wide range of temperatures.