$K\alpha$ x-rays of Si were produced by 30-MeV oxygen bombardment on a Si wafer. Nine $K\alpha$ lines are observed with an energy resolution of 2.5 eV at energies of 1739.78 ($K{\alpha }_{1,2}$), 1750.8 ± 0.5 ($K{\alpha }_3$), 1753.1 ± 0.6 ($K{\alpha }_4$), 1762.6 ± 0.5 ($K{\alpha }_5$), 1766.4 ± 0.6 ($K{\alpha }_6$), 1775.3 ± 0.6, 1778.8 ± 0.5, 1794.2 ± 0.6, and 1809.7 ± 0.8 eV. The intensity pattern is very nearly symmetric and the envelope approximately Gaussian. The energies of these lines are found to agree with Hartree-Fock-Slater calculated energies for $K\alpha$ transitions from Si atoms with initial configurations ${\mathrm{}\left(1s\right)\mathrm{}}^{-1\mathrm{}}{\mathrm{}\left(2p\right)\mathrm{}}^{-n}$ for $n=0, 1, 2, 3, 4, \mathrm{and} 5$.

A new model for ionizing collisions between slow protons and atoms has been proposed. $K$-shell ionization cross sections of oxygen atoms have been calculated and compared with available experimental data and with the results obtained by Gryzinski's formula. The proposed modification gives very good results for the cross section.

Cross sections for the production of ${\mathrm{Kr}}^{+}$, ${\mathrm{Kr}}^{++}$, ${\mathrm{Xe}}^{+}$, and ${\mathrm{Xe}}^{++}$ in collisions of ${\mathrm{H}}^{+}$, ${\mathrm{He}}^{+}$, and ${\mathrm{Ne}}^{+}$ with Kr and Xe have been measured for primary-ion kinetic energies $E$ between 0.5 and 100 eV. These cross sections rise rather sharply as $E$ is increased, reach a maximum, and then decrease rather slowly. Maximum values of the cross sections range from 0.1 to 40 ${\mathrm{\AA }}^2$. Production of the doubly charged ions must correspond to the production of a free electron; these ionization processes have apparent threshold energies 0-4 eV above the true threshold energies. Collisions of ${\mathrm{H}}^{+}$ with Kr and Xe do not produce doubly charged positive ions. The cross sections for reactions that release a free electron are not adequately represented by any of the theoretical expressions with which the experimental data were compared. Cross sections for the production of singly charged positive ions are larger for the more complex target atoms and lighter primary ions; these cross sections are well represented by the charge-transfer theory of Rapp and Francis when the experimental cross sections are large, but not otherwise. Rapp and Francis's formulas are not applicable to charge-transfer reactions having small cross sections. The present experimental data agree fairly well with previous experimental results.

The coupled equations of the adiabatic-state expansion method for quasiadiabatic transitions in atomic collisions are reduced in the eikonal approximations to a form that allows straightforward computation. The multistate eikonal approximation is then applied to the ${\mathrm{He}}^{+}\mathrm{}\left(1s\right)+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}\to {\mathrm{He}}^{+}\mathrm{}\left(1s\right)+\mathrm{H}\mathrm{}\left(2p\right)\mathrm{}$ excitation process. The partial and total $2p$-excitation cross sections as well as the polarization of the light emitted by the excited H atoms are calculated. Our results compare well with recent experimental measurements. The importance of final-state coupling is dramatically illustrated by the above $2p$-excitation process. The qualitative features of the nonadiabatic effects are also investigated in the eikonal Born approximation as functions of the position and distance of closest approach of the two adiabatic states.

The conventional formula determining x-ray production cross sections from thick-target yields has to be corrected for the effects of energy-loss straggling, x rays from recoil atoms, and nonstraight ion trajectories when heavy (keV and low MeV) ions are used as projectiles. The first two corrections are evaluated in this paper for the case where the last is small (negligible absorption). Carbon $K$ x-ray cross sections are deduced from published yield data. Large corrections, up to one order of magnitude, are found.

A numerical calculation has been performed for proton-hydrogen-atom scattering using $1s$, $2s$, $2p_0$, and $2p_1$ hydrogenic states in a two-center traveling-wave expansion in the impact-parameter method. Discrepancies with past work are pointed out and discussed. Cross sections for direct and exchange scattering into $1s$, $2s$, and $2p$ states, as well as the polarization, are presented for ion energies from 500 eV to 400 keV. Results are compared with other calculations using different expansion functions, both hydrogenic and "pseudostate."

In this paper a completely classical model for laser action is discussed. An active medium consisting of classical anharmonic oscillators interacts with a classical electromagnetic field in a resonant cavity. Comparison with the case of a medium consisting of harmonic oscillators shows the significance of nonlinearities for producing self-sustained oscillations in the radiation field. The results for the classical model are found to be similar to those for a semiclassical model of the ammonia-beam maser. The conclusion is that laser action is not intrinsically a quantum-mechanical effect. The classical-laser theory as given in this paper can also be applied to the case of the electron-cyclotron maser.

A theoretical model for the pressure dependence of the intensity of a gas laser is presented in which only velocity-changing collisions with foreign-gas atoms are included. This is a special case where the phase shifts are the same for the two atomic-laser levels or are so small that deflections are the dominant effect of collisions. A collision model for hard-sphere repulsive interactions is derived and the collision parameters, persistence of velocity and collision frequency, are assumed to be independent of velocity. The collision theory is applied to a third-order expansion of the polarization in powers of the cavity electric field (weak-signal theory). The resulting expression for the intensity shows strong pressure dependence. The collisions reduce the amount of saturation and the laser intensity increases with pressure in a characteristic fashion. It is recommended that the best way to look for this effect is to make the measurements under conditions of constant relative excitation.

A thorough reanalysis of the early measurements of pleochroic halos in light of today's standards and knowledge indicates that, contrary to widespread belief, these halos do not provide proof that the laws of radioactive decay are constant in time.

Closed analytical expressions for the orientation of the director and the total distortional elastic energy are given for de Gennes's model of a Grandjean-Cano disclination. The director expression is shown to be equivalent to de Gennes's infinite-sum solution. This model is generalized and similar expressions for single disclinations on one of the parallel surfaces and for double disclinations between the boundaries are derived. Approximate energies are computed for these singularities in the case of nonparallel surfaces, and comparisons are made to predict the conditions for their stability. A more realistic model where many equally spaced disclinations occur within wedge-shaped boundaries is proposed and elastic distortion energies are calculated for this case.

The complete solution is presented for the $N$-completeness problem, i.e., the problem of determining when a set of $p$-particle functions generates symmetric or antisymmetric functions without applying a symmetrizing or antisymmetrizing operator. Then it is shown that a symmetric or antisymmetric function has finite 2 rank if, and only if, it has finite 1 rank. Finally, the relation between $N$ representability of $N$ completeness is discussed.

Limiting temperature gradients at the breakdown of superfluid heat transport have been measured as a function of temperature for three configurations of insulated vertical channels. Values of the temperature gradient calculated from a vaporization hypothesis are in good agreement with the experimentally measured gradients, indicating that metastable superheating does not occur. Systematic discrepancies noted at low temperatures and high heat fluxes show that the vaporization hypothesis is not a complete description. Values of the Gorter-Mellink constant have been determined and are found to exhibit a systematic dependence on channel size as well as temperature. Limiting heat fluxes calculated using the experimentally determined Gorter-Mellink constant are in good agreement with experimental values above ∼ 1.6 K; deviations are observed at lower temperatures.

The lattice version of the Maier-Saupe model for the nematic-liquid-crystal transition consists of an array of unit vectors located at the sites of some regular lattice. The energy of interaction of nearby unit vectors is proportional to $P_2 \left({cos\theta }_{\mathrm{ij}}\right)=\frac{1}{2} (3\mathrm{}{{cos}^2\theta }_{\mathrm{ij}}-1)$, where ${\theta }_{\mathrm{ij}}$ is the angle between the vectors at sites $i$ and $j$ which represent the directions of the long axes of the molecules of the liquid. A discrete model which we call the dodecahedral model is defined by restricting the vectors to point in the directions of the faces of a regular dodecahedron. Monte Carlo results are obtained for this model, which is among the models discussed by Potts as interesting generalizations of the Ising model. It is also one of the sequence of models solved in the mean-field approximation and two-cluster approximation by Priest. The Monte Carlo results on a 10×10×10 simple-cubic lattice with periodic boundary conditions determine the transition to be of first order. The order at the transition $\mathrm{M}={\mathrm{P}}_2\left(cos\theta \right)$ is found to be 0.82. Attempts to obtain results on the model with vectors pointing in the six directions of the faces of a cube failed because the 10×10×10 lattice was too small in this case to discriminate between a first- and second-order transition.

We have recast a linear quantum-mechanical Boltzmann equation, describing the dynamics of a gas of $N$-level atoms absorbing light between an arbitrary pair of levels, into the form of a generalized master equation. The atoms are permitted to undergo both phase-changing and energy-changing collisions with a heat bath of inert molecules. The possibility of unimolecular decay is incorporated into the Boltzmann equation. The solutions of the generalized master equation give an accurate description of the system for short as well as long times and for arbitrary light-field intensity. Eigenvalues obtained from the solution of the $N$-level master equation are shown to have particular significance with regard to the scattered electromagnetic field, with the imaginary parts of the complex eigenvalues providing the location and the real parts of the eigenvalues giving the widths of scattered radiation bands. The dynamics and scattered field for a two-level system is discussed in detail. Two collision parameters giving the frequency of phase-changing and energy-changing collisions are important. For special values of these parameters, our results reduce to scattered field spectra calculated previously. When unimolecular decay is included, one identifies the smallest eigenvalue of the generalized master equation with the macroscopic rate constant. Observation of the scattered field for different incident field intensities would permit separation of radiative and thermal effects in an enhanced reaction rate, without requiring an accurate temperature measurement.

A combined analytical and numerical analysis of the propagation of a step-function light pulse in a resonant medium is presented. It is found that the light pulse evolves into a steady-state amplitude-modulated wave train very closely approximated by the Jacobian elliptic function $\mathcal{E}=1.25\mathrm{} {\mathcal{E}}_{0}dn\left[\right(\frac{1}{\tau }\left)\right(t-\frac{z}{V}); \lambda ]$, where the modulus of the elliptic function $\lambda$ is equal to $\frac{4}{5}$ and ${\mathcal{E}}_0$ is the amplitude of the input pulse. This result is consistent with an earlier analysis which showed that the elliptic $\mathrm{dn}$ function represented one of two classes of functions which satisfy the equations of resonant-pulse propagation and correspond to the distortionless propagation of an amplitude-modulated wave train through an inhomogeneously broadened medium. Expressions for the period, velocity, and parameter $\tau$ of the elliptic function are found as functions of the intensity of the input pulse. The form of the steady-state wave train is found to be the same in either an attenuating or amplifying medium. It is found that the velocity of the pulse train becomes significantly less than the speed of light when the density of energy that can be stored in the resonant atoms becomes an appreciable fraction of the energy density of the electromagnetic field. The conditions necessary for observing the amplitude-modulated pulse train in gaseous S${\mathrm{F}}_6$ and Na vapor are discussed.

We continue our previous investigation of the properties of a system of either fermions or bosons interacting in one dimension by a two-body potential $V\left(\mathcal{r}\right)=\frac{g}{{\mathcal{r}}^2}$ with periodic boundary conditions. A method is introduced which provides a physically intuitive description of the excited states. The energies are given explicitly for finite and infinite systems, including all corrections due to quasiparticle interaction. The method is shown to apply to other one-dimensional systems as well. In particular, the results are applied to a classical one-dimensional $N$-body model of Dyson—the Coulomb gas in a Brownian medium.

The elementary excitations in superfluid helium have been studied in the wave-vector range $1.5<Q<\mathrm{}2.3\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$ by inelastic neutron scattering. The single-excitation scattering function ${\mathcal{S}}_1 (Q, \hslash \omega )$ was measured for pressures between 1 atm and the solidification pressure and for temperatures from 1.3°K to above the transition temperature $T_{\lambda }$. The dispersion curves were fitted to parabolas and the appropriate Landau parameters tabulated vs temperature and pressure. By accounting for the effect of the instrumental resolution it was possible to observe a line broadening at low temperatures which sets in when the slope of the dispersion curve equals the sound velocity. There are strong indications that this is due to the roton-phonon interaction proposed by Pitaevskii. The line broadening observed when the temperature approaches $T_{\lambda }$ is well accounted for by the roton-roton interaction as calculated by Landau and Khalatnikov. The results have been related through thermodynamics to other properties of the liquid and the spectral form of the excitations compared to those observed in magnetic systems close to the critical temperature.

We have obtained some evidence of the induced scattering of an electromagnetic wave by Compton collisions, and of its nonlinear propagation in a plasma. The interpretation of the modified spectral profile of the interacting radiation is compatible with plasma parameters.

The temperature dependence of specular-reflectance spectra of obliquely incident light reflected by a single-domain sample of a cholesteric liquid crystal in the wavelength range covering the first- and second-order Bragg reflection bands has been studied. The sample was a mixture of 4, 4′bis$n$-hexyloxy)azoxybenzene and optically active 4, 4′bis (2-methylbutoxy) azoxybenzene. The spectra of this sample are consistent with the Oseen-De Vries spiraling dielectric-tensor model and reveal that local dielectric tensors are ellipsoids of revolution to within our limits of resolution. Increasing the temperature increases the libration of the molecules and hence decreases the order parameter. This causes a decrease in eccentricity of the dielectric tensor which, in turn, produces readily measurable changes in the Bragg reflectance spectra. The observed changes are roughly in agreement with those predicted by assuming that the Maier-Saupe theory for temperature dependence of the order parameter in nematic liquid crystals also applies to cholesterics. We find it necessary to include a thermal-expansion coefficient to fit the data.

The effect of pressure on the mobility of the cavity-localized electron in solid helium has been studied to a pressure of 6660 atm. No delocalized electron state has been detected at this pressure below the melting point of the solid. It is shown that the results are consistent with the presence of electron bubbles at the highest pressures investigated. The nature of possible charge-trapping mechanisms that might account for the results is discussed.