Precise measurements of incoherently scattered light from a $\theta$-pinch plasma revealed a blue shift of the spectrum which could not be accounted for either by the diamagnetic drift velocity of the electrons or by the motion of the plasma as observed stereoscopically by a streak camera. We find that a major part of the blue shift can be attributed to a relativistic effect. We discuss the consequences of ignoring the relativistic corrections and point out the possibility of making large systematic errors in electron-temperature measurement in certain experimental arrangements employing Thomson scattering. Even at temperatures well below 1000 eV the effect is not negligible.

Fluorescence has been detected from Rb atoms following narrow-line excitation by a short coherent optical pulse. The fluorescence oscillates as a function of the pulse area $A$ with maxima for $A=\pi ,3\mathrm{}\pi ,5\mathrm{}\pi ,\dots$ and minima for $A=0,2\mathrm{}\pi ,4\mathrm{}\pi ,\dots$. In addition to demonstrating one of the simplest coherent optical effects, this experiment dramatizes the potential of the technique for determining dipole moments, pulse areas, relaxation times, and lifetimes. The details of the experimental apparatus are described. Results of a computer simulation of the experiment including the actuai excitation pulse shape, absorption frequency width, finite absorption (5-10% of pulse), and loss to a third level are given.

The resonance-fluorescence experiment described in the preceeding paper and found to be consistent with quantum electrodynamics is analyzed using the neoclassical theory (NCT) of radiation, i.e., the electromagnetic field is not quantized. We have not found a value of the dynamic shift for which the NCT computer simulation is consistent with the data. NCT predicts an increased radiative lifetime as appreciable excitation is achieved; the observed decay curves were simple exponentials with characteristic times independent of the fractional excitation. The observed oscillatory dependence of the integrated fluorescence upon input pulse area has not been reproduced by a NCT simulation either. Objections raised against this disproof of NCT are answered.

The degeneracy problem of a hydrogen atom in a uniform weak magnetic field $H$ is considered from the standpoint of the invariance group that the system obeys. Evidently the degeneracy space has a constant $z$ component of the angular momentum. Under such a classification, the dynamical invariance of the problem is shown to be an isomorph to the Lie group of the linear transformation of the straight line.

The phenomenon of coherent Raman beats observed recently by Shoemaker and Brewer is analyzed through solutions of the coupled Maxwell-Schrödinger equations. The effect arises in coherently prepared molecular samples where the level degeneracy is suddenly removed by Stark-pulse switching. The problem divides into two parts: (a) a steady-state preparative regime whereby the initially degenerate quantum levels are placed in superposition by a resonant laser field, and (b) a transient regime in which coherent forward Raman scattering decays in the presence of the same laser field during a nonresonant condition. The laser and Raman light thus propagate together and produce at a detector a coherent beat with a frequency that corresponds to the level splitting between initial and final states. The beat signal possesses the remarkable property of being entirely independent of longitudinal molecular velocity in the case of a plane-wave laser beam and of being almost so for milliradian divergence. It follows that relaxation involving velocity-changing collisions and that Doppler dephasing effects are absent in coherent Raman beats, in agreement with experimental measurements of the decay rate. The effect of off-resonance excitation on the dephasing time and on the period of the beat signal is also discussed, and the possibility of a small rotation of the plane of polarization of the scattered light is included. The subject presents a new aspect of Raman scattering which can now yield precise radio-frequency splittings directly and offers a selective way of examining relaxation phenomena.

By a simple change of variables, the scaling hypothesis of Widom is extended to apply not only to those liquid-vapor models for which it was originally designed, but also to those recently discovered models that violate the law of rectilinear diameters. "Corrections to scaling," i.e., additional terms in the equation of state beyond the homogeneous one, are shown in general not to make contributions to the singularities characteristic of these models, comparable to those coming from the change in scaling variables. Therefore, these models cannot be regarded as evidence in support of such proposed correction schemes. A more elaborate revision fo the scaling hypothesis proposed by Widom and Stillinger, is shown to be implied by the simple one proposed here.

A complex fine structure has been resolved in the $K{\beta }_1{\beta }^{\prime }$ ($3p-1s$ transitions) x-ray emission spectrum of pure titanium metal. The measurement was performed with a double-crystal fluorescence spectrometer. The observed fine structure has been interpreted as originating from the interaction between the unpaired $3d$ electrons and the $3p$ hole in the final state of the $K{\beta }_1$ transition. The calculations are based on the relative energies and intensities for free-ion states of the $3p^{5}3d^{2}4s^2$ configuration in the Russell-Saunders coupling scheme with and without inclusion of configuration interaction. The Landé interval rule applied to these results has been found to be of minor influence on the appearance of the theoretical spectra.

Absolute transition probabilities of the stronger Xe I and Xe II lines between 3800 and 8400 Å are measured in emission. State variables of the shock-tube plasmas are determined by several independent methods. Accuracies for 25 neutral and 128 ionic $A$ values are estimated to be (22-50)%. Experimental Xe I line strengths are compared with theoretical predictions. The Xe II results are examined for conformity with quantum-mechanical sum rules and are compared with lifetime data from the literature.

We consider a degenerate system of fermions interacting via a Yukawa potential and confined within a slab of thickness $L$. Using the semiclassical random-phase approximation, we obtain the retarded density response function ${\chi }_{\mathrm{nn}}(\overrightarrow{\mathrm{k}},{\overrightarrow{\mathrm{k}}}^{\prime },\omega )$, which exhibits resonances corresponding to surface, as well as surface-bulk, or mixed, collective excitations. The surface and surface-bulk density fluctuations are spatially either of a symmetric or antisymmetric character. Their dispersion relations and collisionless damping are discussed, mainly in the strong-coupling limit. A symmetric surface mode which is phononlike at long wavelengths is found, but the antisymmetric surface mode ceases to exist below a certain value of ${\overrightarrow{\mathrm{k}}}_{\parallel }$, the wave vector parallel to the surface. The mixed modes all possess an energy gap at ${\overrightarrow{\mathrm{k}}}_{\parallel }=0\mathrm{}$. We also evaluate the dynamic structure factor $S(\overrightarrow{\mathrm{q}},\omega )$ which describes the inelastic scattering of particles in the Born approximation. Our calculations exhibit how crucially the nature of collisionless surface modes depends on the range of interaction between quasiparticles. We argue that our model calculations should be appropriate to liquid ${\mathrm{He}}^3$ in situations where the restricted dimension is of order 100 Å or larger.

Turbulent-plasma phenomena in laboratories and in the ionosphere are often associated with plasma inhomogeneities. As a plasma inhomogeneity, we consider a partially ionized gas with a mean density gradient in a nonuniform mean electric field and a strong magnetic field. Because of drift instabilities, the plasma becomes turbulent in the plane transverse to the magnetic field. We propose a method of a repeated cascade, and derive the spectral distributions for the turbulent density and field fluctuations in the production, inertia, and dissipation subranges of the universal spectrum. The results predict $k^{-3\mathrm{}}$, $k^{-1\mathrm{}}$, and $k^{-5\mathrm{}}$ laws in the respective subranges for the density spectrum, and a single $k^{-3\mathrm{}}$ law for the field spectrum. As the plasma inhomogeneity may be embedded in an atmospheric turbulence, we also study the effect of the atmospheric turbulence which drives the plasma inhomogeneity. The theoretical predictions are found to agree with data from laboratory plasma experiments.

The magnetic field dependence of the nuclear relaxation rate ${\tau }^{-1\mathrm{}}$ of an optically oriented ${}_{}{}^{199}{}_{}{}^{}\mathrm{Hg}$ vapor confined in a quartz cell is investigated both theoretically and experimentally. A theoretical expression is obtained for ${\tau }^{-1\mathrm{}}$ as a function of the static magnetic field, the average time of flight ${\tau }_f$, the average adsorption time ${\tau }_a$, and other physical parameters characterizing the atom-surface interaction. When the experimental values of ${\tau }^{-1\mathrm{}}$ in the presence of a field ranging between 0 and 1200 G are fitted by this expression, ${\tau }_a$, a good approximation for ${\tau }_f$, and information on the other parameters are easily obtained. The adsorption energy has been evaluated to within 20% using values of ${\tau }_a$ at various temperatures, for the case of an uncoated quartz cell and of a silicone-coated cell. They are 4 and 1.5 kcal/mole, respectively, while ${\tau }_a$ ranges from 5 μsec (at 288 K) to 1.8 μsec (at 328 K) in the former case, from 2.4 μsec (at 281 K) to 1 μsec (at 392 K) in the latter, with a 10% uncertainty.

Accurate measurements were made of the mobility of positive and negative charge carriers in ${\mathrm{He}}^4$, at pressures up to the melting pressure and temperatures in the range 0.27 ${\left(\frac{e}{\mu }\right)}_{\pm }=f_{\pm }\mathrm{}(P,T)\mathrm{}{e}^{ \frac{-\Delta \mathrm{}(P,T)\mathrm{}}{\mathrm{kT}}}$, where $\Delta \mathrm{}(P,T)\mathrm{}$ is the pressure- and temperature-dependent energy gap derived from neutron-scattering experiments. The measured pressure and temperature dependences of the prefactors $f_{\pm }\mathrm{}(P,T)\mathrm{}$ are discussed in light of recent theories for the scattering of rotons by the charge carriers.

The heat capacity at constant volume $C_{\nu }$ and the pressure coefficient ${\left(\frac{\partial P}{\partial T}\right)}_{\nu }$ were measured near the superfluid transition on six isochores. This work also yielded new results for the derivatives ${\left(\frac{\partial V}{\partial T}\right)}_{\lambda }$ and ${\left(\frac{\partial S}{\partial T}\right)}_{\lambda }$ along the $\lambda$ line ($V$ is the molar volume and $S$ the entropy). An essentially complete and detailed description of the thermodynamics of the superfluid transition at all pressures is provided by the data. In particular, the results were used to derive the heat capacity at constant pressure $C_p$, the compressibility $\kappa$, the thermal expansion coefficient $\alpha$, the ratio $\gamma \equiv \frac{C_p}{C_{\nu }}$, and the isentropic sound velocity $u$, along isobars. The heat capacity $C_p$ was examined carefully for its asymptotic behavior near $T_{\lambda }$. Although several interpretations of the data are possible with different assumptions about singular correction terms, it is clear that the exponents $\alpha$ and ${\alpha }^{\prime }$ are near zero, and that the ratio $\frac{A}{A^{\prime }}$ of the amplitude above $T_{\lambda }$ to the amplitude below $T_{\lambda }$ is greater than unity and pressure dependent. The results are compared with the predictions of scaling and universality. The assumption of a pure-power-law singularity in $C_p$ results in $\alpha \ne {\alpha }^{\prime }$ at some pressures, and thus yields disagreement with scaling. The inclusion of singular higher-order contributions to $C_p$ in the analysis increases the uncertainty in the exponents derived from the data, and the prediction $\alpha ={\alpha }^{\prime }$ of scaling falls within these larger uncertainties. The amplitude ratio remains greater than unity, and thus only nonzero exponents are consistent with scaling. The pressure dependence of $\frac{A}{A^{\prime }}$ is not removed by the type of correction terms considered in the analysis, and is contrary to universality. When recent calculations for the exponent of the correction terms are assumed valid, then only a negative leading exponent is permitted by the data. This implies a finite $C_p$ at $T_{\lambda }$. If $\alpha ={\alpha }^{\prime }<0\mathrm{}$, then the data permit a continuous $C_p$ at $T_{\lambda }$ and at all pressures only if, contrary to universality, $\alpha$ and ${\alpha }^{\prime }$ depend upon the pressure.

Assuming an anomalous phonon dispersion, the velocity shift and the attenuation of ultrasound in liquid ${\mathrm{He}}^4$ below 0.5 K are calculated by a direct numerical solution of the Boltzmann equation for the phonon distribution function. In order to account for the hydrodynamic regime the collision invariants are treated separately. The results are in qualitative agreement with the experiments and show a nonmonotonic increase of the velocity shift as a function of the applied frequency, but they are different from an approximate solution using relaxation times. The method developed to solve the Boltzmann equation can also be applied directly to calculate transport properties of phonons in solids.

A noniterative-integral-equation method (NIEM) is successfully applied to $S$-wave scattering of electrons by atomic hydrogen. Reactance-matrix elements and partial-wave cross sections are computed for energies above and below the $n=2\mathrm{}$ threshold. The results are stable despite the strong degenerate dipole coupling between the $2s$ and $2p$ channels. In addition, it is demonstrated, by locating the first ${}_{}{}^1{}_{}{}^{}S$ resonance, that the NIEM works in the resonance region below threshold.

We report the generation of sidebands in the energy spectrum of 14.4-keV $\gamma$ rays by a periodic modulation of the properties of the medium between the emitting and absorbing atoms. The observed spectrum agrees in detail with a "chopping" calculation that encompasses both amplitude and phase modulation, although the modulator may equally well be viewed as a moving multislit grating. This is the first experiment in which the observed sidebands in the $\gamma$-ray spectrum have been quantitatively understood.

The formalism developed by the authors for the variational determination of the expectation value of single-particle operators $W=\Sigma i^{}W\left({\overrightarrow{\mathrm{r}}}_i\right)$ via Delves's principle in the Hartree approximation is extended here to the Hartree-Fock approximation by employing a Slater-determinant-type trial wave function and an appropriately antisymmetrized auxiliary function. A set of coupled integral-differential equations for the components of the auxiliary function are obtained by a subsidiary variational minimization of a functional involving the trial wave function, the auxiliary function, the Hamiltonian, and the operator $W$. Owing to the antisymmetric nature of both the trial and auxiliary functions, an exchange term involving the specific single-particle operator in question appears in these equations. Decoupling approximations are discussed and the equations solved exactly for single-particle operators that depend on the radial distance only. Employing a single-parameter appropriately antisymmetrized product of the $1S$ and $2S$ hydrogenic functions as the trial wave function, the formalism in this Hartree-Fock approximation is then applied to both the helium $2 {}_{}{}^3{}_{}{}^{}S$ and $2 {}_{}{}^1{}_{}{}^{}S$ isoelectronic sequences to obtain analytic expressions for the expectation value of the operators $r^n$, $n=2,1,-1\mathrm{}$, and $\delta \left(\overrightarrow{\mathrm{r}}\right)$. The results of these calculations are observed to approximate closely the results of a 2300-parameter calculation due to Accad et al. and in the orthohelium case to be also equivalent to those due to Hartree-Fock.

Radiationless $K-L L$ transition probabilities have been calculated nonrelativistically in $j-j$ coupling and in intermediate coupling, without and with configuration interaction, for elements with atomic numbers $13\le Z\le 47$. The system is treated as a coupled two-hole configuration. The single-particle radial wave functions required in the calculation of radial matrix elements, and in the calculation of mixing coefficients in the intermediate-coupling scheme, were obtained from Green's atomic independent-particle model. Comparison with previous theoretical work and with experimental data is made. The effects of intermediate coupling, configuration interaction, and relativity are noted. Agreement of the calculated $Z$ dependence of $K-L L$ relative intensities with experiment has been somewhat improved.