We analyze elastic electron-atom scattering at intermediate and high energies by using a second-order optical-model potential together with the eikonal approximation. We devote particular attention to the role of long-range forces and formulate the theory in a way suitable for generalizations to complex target atoms. We also study the relationship between the optical eikonal model and the Born series, and include exchange effects to leading order in the inverse power of the energy. Our optical-model theory is then illustrated by a detailed analysis of elastic electron-helium scattering for incident-electron energies ranging from 100 to 500 eV. We find excellent agreement with experimental data without using any phenomenological parameter.

The photoelectric cross sections have been extracted from the total absorption cross sections. The total cross sections have been estimated by measuring the absorption in Al, Cu, Zr, Ag, Sn, Ta, Au, and Pb for 72.1-keV x rays resulting from the decay of ${}_{}{}^{203}{}_{}{}^{}\mathrm{Hg}$. The scattering cross sections are taken from recent tabulated values of Veigele for subtraction purposes. The photoelectric cross sections are compared with the values interpolated from the theoretical results of (i) Schmickley and Pratt and (ii) Scofield.

In view of experimental considerations, we give a model-independent argument that the novel tricritical points in multicomponent fluid mixtures, where three phases simultaneously become critical, are points on the boundary of a single two-dimensional surface of critical points. This result is corroborated by the Landau model suggested by Griffiths. The relationship between these tricritical points and the complex "higher-order" critical points proposed to exist in certain magnetic systems is elucidated.

The "subcritical" exponent ${\Delta }_{2s}$ for corrections to asymptotic scaling in the renormalization-group theory of critical phenomena, has been calculated for the continuous-spin versions of the classical, $d=3\mathrm{}$ Ising, $X-Y$, and Heisenberg models by numerical integrations of Wilson's approximate recursion formula. The results are ${\Delta }_{2s}\left(\mathrm{Ising}\right)=-0.640\mathrm{}$, ${\Delta }_{2s}(X-Y)=-0.644\mathrm{}$, and ${\Delta }_{2s}\left(\mathrm{Heisenberg}\right)=-0.647\mathrm{}$. Comparison is made with results from perturbation expansions in $\epsilon =4-d$ ($d$ being the dimensionality), high-temperature series expansions, and experimental measurements.

We Present detailed measurements of the electron-avalanche process in liquid xenon. The measurements were made by using liquid-xenon-filled proportional chambers with anode diameters of 2.9, 3.5, and 5.0 μ to detect 279-keV $\gamma$ rays and measure the photopeak pulse height as a function of applied voltage. The use of uniform pulses of electrons enabled us to discriminate against secondary Townsend processes. We present a table of the first Townsend coefficient $\alpha$ as a function of electric field $E$; a typical value is $\alpha =(4.5\mathrm{}\pm 0.3)\times {10}^4$ ${\mathrm{cm}}^{-1\mathrm{}}$ at $E=2\mathrm{}\times {10}^6$ V/cm. The electron avalanche occurs in liquid xenon at electric fields 27 ± 3 times smaller than would be predicted using measurements made in gaseous xenon and $\frac{E}{\rho }$ density scaling.

The effect of terms describing the anisotropic susceptibilities on the NMR shifts observed in superfluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is discussed. It is shown that they are such that the isotropic susceptibility in the expressions of Leggett is replaced by the correct temperature-dependent susceptibilities. The anisotropy energies of the Balian-Werthamer (BW) state are calculated and shown to be of order ${\left(\frac{\gamma H}{T_c}\right)}^2$ times those pinning the spin and orbit coordinates in either the BW or Anderson-Brinkman-Morel state.

The canonical partition function of the two-dimensional Coulomb gas interacting through the Coulomb potential —$q_i{q}_j\mathrm{In}{r}_{\mathrm{ij}}$ is considered in detail. The equation of state $\frac{\mathrm{PV}}{2N}=k_{B}T-\frac{q^2}{4}$ is shown to be meaningful above the critical temperature $T_c=\frac{q^2}{2k_B}$ through the use of upper and lower bounds (valid for all $T>\mathrm{}{T}_c$) for the canonical partition function $Q^{*}$ with lim $Q^{*}\sim N!{\left(Q_1^{*}\right)}^N$ as $T\to T_c^{+}$, $Q_1^{*}$ denoting the restriction of $Q^{*}$ to a pair (+ -). Below $T_c$, the equilibrium properties are investigated with the use of the binary approximation proposed by Hauge and Hemmer for charged disks. The resolution of the two-body Schrödinger equation allows us to consider point particles and place on a firm basis preliminary conclusions about the divergent behavior of the thermodynamic functions. The pair-correlation function $g_2\mathrm{}\left(r\right)\mathrm{}$ is investigated above $T_c$ for the one-component model within the framework of the Debye approximation, through a potential of average force $w_2\mathrm{}\left(r\right)\mathrm{}$, up to the third order in the plasma parameter $\frac{q^2}{k_B}T$. The short-range behavior of $w_2\mathrm{}\left(r\right)\mathrm{}$ appears as a renormalizable quantity, while the long-range behavior confirms and extends three-dimensional findings. The $T\to \infty$ limit of the corresponding thermodynamic functions coincides with exact results derived by Mehta for the same model restricted to the unit circumference. Finally, the Debye free energy is shown to fulfill a sufficient condition required by the existence of the thermodynamic limit.

General properties of the Sturm-Liouville equation and numerical methods are used to determine the eigenquantities of the Schrödinger equation of a (+ -) pair interacting via the two-dimensional Coulomb potential $q^2$ lnr. The spectrum is shown to be purely discrete and semibounded in its lower part with a density of levels of $\frac{dN\left(\lambda \right)}{d\lambda }\sim e^{\frac{2\lambda }{q^2}}$, while the wave functions behave like those of a harmonic oscillator. The spectrum is studied as a function of the coupling parameter $q$. Wave functions $\psi$ and radial densities $r{\left|\psi \right|}^2$ are plotted against $r$ and some matrix elements $〈\psi \left|r^{\nu }\right|\psi 〉$ are given. The $q=1\mathrm{}$ spectrum is used to evaluate the corresponding sum-over-states which allows us to give a clear meaning to the canonical thermodynamical functions of the two-dimensional Coulomb gas below the transition temperature $T_c=\frac{q^2}{2k_B}$.

The small-angle scattering of phonons with anomalous dispersion has been studied by evaluating the three-phonon collision operator. The characteristic scattering angle is used as a parameter for a new interpretation of sound propagation. The results indicate that the relationship most commonly used for anomalous dispersion is incompatible with the sound-absorption experiments at about 0.1 K.

For intense relativistic electron-beam propagation into low-pressure neutral gas in a metallic drift tube, it is shown for typical experimental parameters that the beam leaves the anode only when it is almost space-charge neutral, and that a fully propagating beam occurs only if it is completely space-charge neutral. Ion ionization effects are shown to play a crucial role in the charge-neutralization process, and a new interpretation of existing experimental data is given.

A 4-GW electron beam has been used to excite amplified spontaneous emission in hydrogen isotopes (ortho and para ${\mathrm{H}}_2$, HD, and ${\mathrm{D}}_2$). The laser energy has been measured with photodiodes, an ionization chamber, and film, and these different measurements are compared in detail. Analysis of the laser energy indicates the spectral linewidth is due to Doppler broadening, and, consequently, cooling the gas produces higher gain and power. This additional gain allows lasing to be observed at even shorter wavelengths (1098 ÅA as compared to 1161 ÅA) than reported previously. Also many (stimulated emission) spectral lines of the Werner and Lyman bands are reliably identified for the first time.

We present here, for the first time, the criteria for determining what field fluctuations are required to cause a bistable two-mode laser to flip from one mode to the other. Results (for a particular two-mode model) generated numerically are presented. Extensions of the method to more-refined two-mode models and multimode cases are discussed.

The normal modes of a cholesteric liquid crystal in the presence of a magnetic field are determined from the hydrodynamical equations. The damping constants of the orientation modes are found to be sensitive functions of the field and exhibit band gaps when their wave vector is an integral multiple of a reciprocal-lattice vector. The results disagree with those of an earlier calculation by Fan, Kramer, and Stephen and reduce to the correct result in the zero-field limit. The light scattered by the modes is discussed in the Born approximation.

A calorimetric and vapor-pressure study of the behavior of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ adsorbed on Grafoil in the temperature range 4 to 15 K is reported. These results have been combined with preexisting low-temperature heat-capacity data to form a complete thermodynamic description of the film. The Grafoil substrate evidently consists almost entirely of basal-plane graphite, with only a small fraction of energetically distinct adsorption sites. Techniques of semiempirical modelling are introduced which make it possible to eliminate the effects both of these inhomogeneities and of the formation of second and higher layers, so that a detailed picture may be formed of the behavior of the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ first layer on an ideal graphite substrate. The binding energy of a ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ atom on the graphite substrate is reported to be 143 ± 2 K, with a first excited state at 89 ± 3 K. A lattice-gas ordering transition occurs near 3 K at a coverage corresponding to one ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ atom for every three carbon hexagons in the graphite surface, and is used as a fiducial for calibrating our system relative to those of previous investigators. At both higher and lower densities the film seems little influenced by the crystal structure of the substrate. Particular attention is given to the high-coverage low-temperature region, which has been identified as a two-dimensional (2D) solid bounded by a melting-phase transition. The available data are combined with two-dimensional elastic theory to establish the presence of low-lying transverse sound modes, thus confirming the solidlike character of this medium. The behavior of the thermodynamic variables of state through the observed transition is also presented. The theoretical implications of the existence of a 2D solid are discussed, together with a dislocation theory of melting which gives rise to the well-known three-dimensional Lindemann empirical melting formula without an adjustable parameter. It is shown that at very low coverage the film does not form a low-density solid as previously suggested, but is rather dominated by substrate inhomogeneities. At intermediate temperatures and coverages the film is a fluid which is accurately described if a leading-order quantum virial correction is made to the 2D ideal-gas equation of state.

A discussion of an anisotropic ($p$ state) Fermi superfluid with a spatially varying order parameter is presented. We restrict ourself to the Landau-Ginzburg region and consider spatial variations governed by the linear gap equation. The kernel of the linearized gap equation is shown to be related to a current-current correlation function of quasiparticles in the normal state. This relation permits the calculation of the two coherence lengths ${\xi }_L$ and ${\xi }_T$ defined earlier in the framework of a phenomenological Landau-Ginzburg theory, and a discussion of boundary conditions for the order parameter at interfaces. A significant anisotropy in the coherence lengths is found (${\xi }_L=\sqrt{3}{\xi }_T$), which reflects itself in the nature of the supercurrents. The boundary conditions at specularly and diffusely reflecting surfaces lead us to expect that the vector $\hat{l}$, which describes the orbital angular momentum of a Cooper pair in an "axial" state, is anchored normal to the walls. Some consequences of these results on various experimental problems (fourth sound, monodomain production, Josephson couplings, behavior in thin capillaries) are briefly discussed.

A quantum theory of the laser is presented in which the coupling between atoms and field is retained in the treatment of the irreversible behavior of the atoms. A master equation for the optical field is obtained and compared with that resulting from the laser theory of Scully and Lamb, where atom-field correlations are neglected in describing the relaxation of the atoms. It is confirmed that for laser powers currently available the approximation employed by Scully and Lamb is valid.

Hydrodynamic instabilities of nematic liquid crystals with a negative dielectric anisotropy in ac electric fields are theoretically studied. The instabilities considered are due to the development of bend modes coupled with flow fields of equal periodicity (Carr, Helfrich). A simple numerical procedure is developed which allows a convenient and exact calculation of threshold curves and instability regions which depend essentially only on two parameters, the reduced cutoff frequency and the reduced decay time of the bend-shear mode. Results of numerical calculations are presented in stability charts using reduced field and frequency coordinates. Characteristic features of threshold curves are discussed and a general survey is given on the position and the extent of instability regions.

A microscopic theory of quasiparticle interactions in liquid helium is derived in terms of the density-fluctuation variables. The collective-variable approach follows closely the formalism of Sunakawa and co-workers, who have previously calculated in detail the three-phonon interaction. In this paper, the direct scattering of quasiparticles is calculated from first principles. The amplitude for the scattering of two excitations is derived in the general form to leading order in perturbation theory. It is then used to estimate the effective roton-roton coupling in terms of the analysis based on the collective-variable approach. The microscopic theory yields an attractive coupling of two rotons, but the coupling strength is an order of magnitude larger than the phonomenological estimates based on experiments. A renormalization procedure is outlined which reduces the strength of the roton-roton interaction, which may bring the coupling in closer agreement with previous estimates. Thus the renormalization of vertex functions and quasiparticle propagators is of great importance in relating microscopic theories to phonomenological parameters obtained from experiments.

We demonstrate that at all pressures, the resonant scattering emission in ${\mathrm{I}}_2$ vapor as excited by a 501.7-nm Ar-ion laser line is dominated by the combined effects of discrete-state resonant fluorescence and dissociative-state continuum resonant Raman scattering (RRS). The changes in the emission upon increased pressures, such as relative and absolute intensities of Stokes overtones, and the variation in depolarization ratios are demonstrated to be due to the gradual quenching of the resonance fluorescence at high pressure, while the dissociative-state RRS contribution remains unaltered.

From measurements of the spin diffusion, thermal conductivity, and viscosity coefficients in dilute solutions of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ in superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, we have phenomenologically determined the amplitude for ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^3{}_{}{}^{}\mathrm{He}$ quasiparticle scattering. Two different parametrizations of the amplitude have been used; one form depends only on the momentum transferred in the scattering event while the other depends on the initial momenta of the quasiparticles as well. The amplitudes are fitted to measurements at temperatures in both the degenerate Fermi-liquid regime ($T\ll T_{\mathrm{F}}$) and the classical regime ($T\gtrsim 2T_{\mathrm{F}}$), whereas most previously determined amplitudes are valid only in the low-temperature regime. Finally, the possibility that the scattering amplitude is ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-concentration dependent is investigated by fitting measurements at each concentration independently. This procedure indicates that there is an enhancement of the amplitude at small momentum transfer as the concentration increases.