When discussing matter on an atomic level it is often useful to employ the notion of a three-dimensional lattice even if the x-ray diffraction pattern is diffuse and, hence, the long-range order characteristic of a crystalline lattice is absent. Phases in which this notion is particularly helpful are called paracrystalline phases. The theory of paracrystals has been applied to various solids and has recently been employed for analyzing the diffraction pattern from liquid metals. In this paper the theory is used for analyzing the diffraction pattern from liquid Cu at 1100°C, as measured by Ruppersberg. The radial density function out to distance of 25 Å is synthesized extremely well by means of the paracrystalline convolution polynomial made up only of first-neighbor or "coordination" statistics. These statistics are inhomogeneous in the sense that two different first-neighbor distances are employed. Forty percent of the first-neighbor distances are 10% larger than the others and arise from intercrystalline distances measured across the paracrystalline grain boundaries. Since, it is well known from inelastic neutron scattering that the lifetime of the paracrystalline domains is about ${10}^{-11\mathrm{}}$ sec, the intercrystalline distances include diffusive motion. The melt is described in terms of a fcc lattice and consists of microparacrystallites with a mean diameter (for copper of about 5 Å and for alkaline metals up to 100 Å) of about 5 Å. The results of the paracrystalline theory are compared with the model of Kaplow and Averbach which is based on the known structure of the solid. The two approaches agree in the assignment of the same lattice type above and below the melting point.

The problem of the time evolution of a closed system, consisting of a two-level atom and its field in a cavity, is investigated by a quantum formalism in which the field is assumed to be a part of the atomic source and is expressible directly in terms of source variables. The source and its field form an irreducible quantum system, that is completely representable within the two-dimensional Hilbert space of the atom. The behavior of the system has features that are similar to those predicted by conventional quantum electrodynamics.

The asymptotic distribution of the eigenvalues $k_n$ of the scalar wave equation $\Delta u+k^{2}u=0\mathrm{}$ is calculated for a three-dimensional finite domain of general cylindrical shape with Dirichlet and Neumann boundary conditions. In the limit of large $k$, the number $\overline{N}\mathrm{}\left(k\right)\mathrm{}$ of modes not exceeding $k$, smoothed in order to eliminate its fluctuating part, is determined. Four terms of the expansion of $\overline{N}\mathrm{}\left(k\right)\mathrm{}$ are obtained. The boundary effects for the thermal phonon radiation of thin films are discussed as an application. The respective results for the electromagnetic vector waves in a lossless closed cavity (blackbody radiation) are presented as well. Here the constant term in the expansion is independent of the shape of the domain and does not account for corners or connectivity. $E$- and $H$-type resonances have to be observed separately in order to yield the complete shape dependence of $\overline{N}\mathrm{}\left(k\right)\mathrm{}$. The edge- and curvature-dependent corrections of the Planck, Wien, and Stefan-Boltzmann radiation formulas are given.

The linearized Vlasov equation for a hot inhomogeneous magnetoplasma is solved through the particle-orbit theory using the techniques of Fourier transforms. An analytical integral expression in $\overrightarrow{\mathrm{k}}$ space is obtained for the current density for waves propagating across the static magnetic field. When inverse Fourier transformed, it gives rise to a differential expression which is accurate up to order ${\left(\frac{{\mathcal{r}}_c}{\lambda }\right)}^2$, ($\frac{{\mathcal{r}}_c^2}{\lambda L}$), and ${\left(\frac{{\mathcal{r}}_c}{L}\right)}^2$. The integral equation is solved numerically for the problems of Buchsbaum-Hasegawa resonances and the Bernstein modes propagating in an inhomogeneous magnetoplasma.

A search was made for Bose-Einstein condensation in superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ using neutron inelastic scattering. A two-component scattering distribution has been resolved for ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ at 1.2 °K giving direct evidence for the existence of the zero-momentum state. Analysis of the measured data leads to a condensate fraction of (2.4 ± 1)%, a value much smaller than previously estimated.

The sound velocity and attenuation of xenon near its critical point have been measured with a pulsed acoustic interferometer which incorporates phase-sensitive detection and signal averaging. Accurate data could be obtained over the frequency range from 0.4 to 7 MHz in spite of the very large attenuation. Results are given in detail along a near-critical isochore and are also reported along several isotherms.

A mode-locked neodymium-glass laser with a fast shutter was used to study light scattering from an absorbing liquid. Two equal high-intensity beams from the laser intersected at a small angle in the liquid, and the resulting stimulated diffractive scattering was observed. Scattering was found on two time scales: a fast effect, developing within the 10-psec duration of a mode-locked laser pusle, and a slow effect requiring many nanoseconds to develop. An analysis is presented which shows the slow effect to be a combination of stimulated thermal Rayleigh scattering and stimulated thermal Brillouin scattering. The fast effect is explained as a result of saturation of the absorbing liquid in an interference pattern.

The density-fluctuation spectrum and wave-vector distribution are calculated for a plasma subjected to the influence of two intense laser beams. The influences of the plasma ions, a possible external uniform magnetic field, the spectral intensity distribution of the mixed laser beams, and their finite diameter are taken into account. The spectrum is shown to consist of two contributions, of which one is recognized as the thermal-fluctuation spectrum while the other is induced by a force generated by the mixed laser beams. Both contributions simply add as a result of the incoherent nature of the thermal fluctuations. It is shown that the theoretical results are in agreement with recent experimental observations. Special attention is also directed to the case in which two beams, generated by the same laser, are mixed in a plasma, and it is shown that enhancement of the ion feature in the spectrum of more than two orders of magnitude against the thermal case can be produced by employing common $Q$- switched ruby lasers.

In this paper we derive the velocity distribution for an ideal gas, using the information-theoretic point of view, and the assumption that one can selectively measure the properties of molecules moving in different directions. In the equilibrium case, this reduces to the usual "canonical" formalism, where the collisional invariants of mechanics exhaust our information. In the case of a heat flow, we are logically forced to a new, bimodal, probability distribution, whose behavior is determined by observables which are not constants of motion, in the sense of mechanics. This is the first instance, to our knowledge, where the information-theoretic point of view leads to new results, which are not obtainable by the classical approach. A simple experiment is proposed, to verify our results.

A laser technique is proposed which may be useful for the assignment of molecular spectra in the visible and infrared regions. The method is based on the resonant interaction of two monochromatic fields with a Doppler-broadened three-level system. Under the appropriate conditions the absorption line shape of one of the transitions shows a complex structure over a narrow section of the Doppler profile, and for sufficiently high laser power the line shape splits into a number of narrow peaks. Analysis of the resulting intensity pattern leads to unambiguous assignment of the angular momentum quantum numbers of the three levels involved. A simple set of rules is given to facilitate interpretation of spectra. The line shapes discussed are also relevant to monochromatic optical pumping of gases and unidirectional laser amplifiers.

A new variational wave function is proposed for the ground state of Bose liquids. It consists of a Jastrow function multiplied by exponentials of three-particle functions. The form of the wave function is deduced from a formal analysis carried out for the weakly interacting Bose gas characterized by a strength parameter $\lambda$. By using the wave function proposed here, the energy obtained is exact to $O\left({\lambda }^4\right)$. Several useful and straightforward applications of the new method to liquid helium and Coulomb gases are suggested.

The velocity-distribution function of ions in a neutral gas is studied. A uniform electric field of arbitrary strength is assumed and only binary-ion-neutral-particle collisions are considered. Under these conditions part of the Boltzmann-equation collision operator is replaced by a kinetic model which enables the ion velocity distribution to be found in compact analytical form if the mean free time between ions and neutrals is independent of velocity. This velocity distribution exhibits the expected properties of drift, elevated ion temperature (as compared to the neutral gas), and skewness in the field direction. In addition, the velocity distribution obtained agrees with the known distributions in the extreme cases of (a) low fields and arbitrary masses and (b) arbitrary fields but extremely disparate ion and gas masses. Other tests are made for this distribution with satisfactory agreement.

Self-induced transparency (SIT) has been observed under the conditions of sharp-line absorption, i.e., with an inhomogeneous absorption width only one-fourth the spectral width of the pulse. A 5-nsec pulse from a ${}_{}{}^{202}{}_{}{}^{}\mathrm{Hg}$ ii laser intersected perpendicularly an atomic beam of natural rubidium. The beam slits reduced the Doppler absorption width to about 30 MHz. A particular resolved $M_{\mathrm{I}}$ transition of ${}_{}{}^{85}{}_{}{}^{}\mathrm{Rb}$ was scanned into coincidence with the laser pulse by a 75-KOe magnetic field. With peak absorption depths of 3-6, nonlinear transmission, pulse delays, pulse breakup, and peak amplification were seen and found to be in excellent agreement with sharp-line computer solutions of the Maxwell-Bloch equations. The experimental realization of the sharp-line SIT is of interest because analytical formulas for pulse evolutions are more plentiful and because sharp-line SIT might permit compression of picosecond pulses.

As lasers have an ability to deliver a large amount of energy very rapidly to matter, one can produce a plasma of thermonuclear temperature by laser bombardment of matter. We observed a neutron yield from a solid deuterium target irradiated by the beam of a glass laser, which had a power of 20 GW for 2 nsec. The theoretically estimated threshold laser power for anomalous heating owing to the parametric instability was in agreement with the experimental result. Above this threshold, an increase in the electron temperature, the appearance of a fast-ion group, and an anomaly in the reflection of light from the plasma were observed. These phenomena were closely correlated with the neutron yield. At the high-temperature region above a few hundred electron volts, the anomalous heating plays an essential role in reaching the fusion-reaction temperature.

Mössbauer parameters, diffusion constants, and coefficients of viscosity for ${\mathrm{Fe}}^{2+}$ ions, dissolved from Fe${\mathrm{Cl}}_2$ · 4${\mathrm{H}}_2$O, in nominally dry glycerol, glycerol-5-wt% water, and glycerol-10-wt% water have been measured. The broadening of the Mössbauer line is observed to have a complicated temperature dependence, which we explain by assuming two mechanisms of diffusion. At low temperatures we postulate that diffusion is via a jumping process described by an Arrhenius relation, while at high temperatures, diffusion is via a gaslike motion obeying the Einstein-Stokes and Litovitz relations. A quantitative fit to the observed line broadening is excellent. A very rapid falloff in the quadrupole splitting and the logarithm of the recoil-free fraction is observed in the temperature region where diffusive broadening is measurable; this falloff is proportional to the observed broadening, with two distinct proportionality constants for the low- and high-temperature regions. These observations are explained by a phenomenological theory due to Jensen and by postulating that the average electric field gradient at the iron nucleus reduces in proportion with the iron diffusivity.

We have measured the resonant absorption of the 23.9-keV $\gamma$ rays of ${\mathrm{Sn}}^{199m}$ in a colloidal suspension of CoSn${\mathrm{}\left(\mathrm{OH}\right)\mathrm{}}_6$ in glycerol in the temperature range 110-323 °K. We measured the colloidal-particle radii with a scanning electron microscope, and found them to be 650±150 Å. We have also studied the fixed-temperature Mössbauer line broadening of our glycerol-based colloid, as a function of ethanol and water dilution. We find that the diffusive broadening of the Mössbauer line is proportional to the absolute temperature divided by the viscosity. The constant of proportionality is the same within the experimental errors, whether the sample viscosity is changed by varying the sample temperature, or by diluting the sol with ethanol or water. These results are in good agreement with the Singwi-Sjölander theory and the Einstein-Stokes relation. For this system we observed a rapid falloff in the recoil-free fraction in the temperature region where diffusive broadening effects were observed, similar to other earlier observations of this effect. Attempts to prepare large-particle sols of FeSn${\mathrm{}\left(\mathrm{OH}\right)\mathrm{}}_6$ in glycerol were made to try to see a breakdown in the Singwi-Sjölander theory. Some evidence for a failing in the theory was found for particle sizes of 1500 Å, but these results were not conclusive, as the sols were always unstable for these large colloidal particles.

The fluctuation-dissipation formula for the viscosity in terms of the stress-tensor fluctuations reproduces the experimental logarithmic temperature dependence of the hydrodynamic viscosity. Using the theoretical wave-number- and frequency-dependent viscosity in the problem of critical diffusion, we find that the effects of nonlocality and retardation practically cancel, resulting in satisfactory agreement with a recent light scattering determination of the effective viscosity.

The ground-state properties of an electron gas at metallic densities are investigated using the Wu-Feenberg theory of Fermi liquids. The correlation energy, the low-temperature specific heat, and the spin susceptibility are computed, and the ground state is found to be paramagnetic. The perturbative correction to the correlation energy owing to the particle-hole excitations in a correlated-basis-function formulation is found to be insignificant.

The density fluctuations in a molecular fluid are studied by treating the fluid as a multicomponent reacting mixture. The ordinary hydrodynamic equations for a reacting mixture form the starting point of the present derivation. The description is then contracted to that appropriate for the one-component molecular fluid. The resulting translational hydrodynamics theory contains memory effects due to the internal relaxation process. The results are compared with a recent kinetic model and with two previous theories of Mountain. The dynamic structure factor $S(k, \omega )$ and the roots of the dispersion relation are computed for parahydrogen gas and studied as a function of density. The results indicate that the treatment of the thermal-diffusivity mode in the theories by Mountain breaks down in the low-density region. It is suggested that Rayleigh-Brillouin scattering experiments on dilute parahydrogen gas at room temperature and densities between 5 and 30 amagats can quantitatively verify the predictions of translational hydrodynamics.

The correlation energy of a degenerate electron plasma in an extremely high magnetic field is calculated taking account of the dominant local principal plasmon mode's zero-point energy, as well as the statically shielded electron-electron interaction energy involving the quantum strong-field counterpart of the Debye-Thomas-Fermi static-shielding law. Other Plasmon-mode-resonance correlation-energy contributions are estimated in the quantum strong-field limit, and shown to be small for an extremely high magnetic field.