Showing papers on "Energy (signal processing) published in 1970"

Bound Eigenstates of the Static Screened Coulomb Potential

Abstract: Accurate numerical solutions have been obtained for Schr\"odinger's equation for a two-particle system interacting through a static screened Coulomb potential (SSCP) $V(\mathcal{r})=\ensuremath{-}\frac{Z{e}^{2}{e}^{\ensuremath{-}\frac{r}{D}}}{\mathcal{r}}$. The numerical integration of the wave equation uses a one-dimensional difference method which is simple, accurate, and efficient. Solutions have been computed for 45 eigenstates, $1s$ through $n=9$, $l=8$, yielding the eigenfunctions and energy eigenvalues for a wide range of $D$, the screening length which characterizes the range of the interaction. Under screening, all energy levels are shifted away from their unscreened values toward the continuum, the energy increasing as $D$ decreases. For each $n$, $l$ eigenstate, there is a finite value of the screening length ${D}_{0}(n, l)$, for which the energy becomes zero. The value of ${D}_{0}$ for the ground state of a two-particle bound system in a potential of this type, such as the Debye or Yukawa potential, is 0.83991 $\frac{{a}_{0}}{Z}$ in agreement with certain previous studies. The total number of different energy levels is finite for any finite $D$, and is approximately linearly dependent on $D$. The number of bound $s$ states ${g}^{*}$ is given by the relation ${({g}^{*})}^{2}=1.2677$ $\frac{\mathrm{DZ}}{{a}_{0}}$. For given $n$, the $l$ degeneracy is destroyed, lowest $l$ levels lying lowest in energy. At sufficiently high $n$, this behavior results in level crossing, high $l$ levels of eigenstate $n$ having higher energies than low $l$ levels of eigenstate $n+1$. This produces increasingly complex deviations of the level order from the unscreened order, commencing with the $5s\ensuremath{-}4f$ cross-over. Because of the displacement of high $n$ states into the continuum, the density of states in the SSCP for any finite $D$ is lower than in the unscreened potential, especially near the continuum.

Electron Energy Distributions and Collision Rates in Electrically Excited N 2 , CO, and C O 2

Abstract: Electron energy distributions have been obtained for electrically excited ${\mathrm{N}}_{2}$, CO, C${\mathrm{O}}_{2}$, and their mixtures by numerically solving the Boltzmann equation for conditions typical of electric discharges. Reported electron cross-section data have been used in the calculation. The calculated distribution functions were found to be markedly non-Maxwellian, having energy variations which reflect the important electron-molecule energy exchange processes. Solution of the electron energy conservation equation using these distribution functions revealed that vibrational and electronic excitation of ${\mathrm{N}}_{2}$, CO, and C${\mathrm{O}}_{2}$ dominates electron-molecule energy exchange processes for average electron energy in the 1-3-eV range typical of electric discharges. Electron-molecule vibrational excitation rates were also evaluated for a variety of gas mixtures and discharge conditions. The importance of these results to molecular gas-discharge lasers is discussed.

Structure of Finite Nuclei in the Local-Density Approximation

Abstract: A new theory is presented for calculating the structure of finite nuclei from the nucleon-nucleon interaction. The essential features of the reaction matrix in finite nuclei are obtained from nuclear-matter theory through the local-density approximation. The resulting density- and energy-dependent effective interaction is justified in detail, and it is shown that the tensor force plays an important role in saturation. The effective interaction is cast into two different forms, one convenient for use in calculating matrix elements and the other specialized for a Hartree-Fock calculation in position space. The density-dependent Hartree-Fock equations are derived by variation of the ground-state expectation value of the energy, and in addition to the usual Hartree-Fock terms, one obtains rearrangement terms arising from the variation of the density appearing in the density-dependent interaction. The appropriate angular-momentum reduction for closed $j$-shell nuclei is performed. The need for modifying the effective interaction to account for higher-order corrections is discussed, and the constraints imposed on this modification by the properties of nuclear matter are examined. The results of this theory for ${\mathrm{O}}^{16}$, ${\mathrm{Ca}}^{40}$, ${\mathrm{Ca}}^{48}$, ${\mathrm{Zr}}^{90}$, and ${\mathrm{Pr}}^{208}$ are shown to yield very satisfactory agreement with experimental binding energies, single-particle energies, and electron scattering cross sections. The rearrangement terms in the density-dependent theory are demonstrated to have two essential effects on nuclear structure: a significant reduction in the central density of the nucleus, and a modification of the usual Hartree-Fock relation between single-particle energies and the binding energy. Equivalent local single-particle potentials are calculated and are shown to have significant state dependence.

Slow-Electron Mean Free Paths in Aluminum, Silver, and Gold

Abstract: Beam-attenuation measurements were made on free-standing polycrystalline films of various thicknesses at energies between the work function and several electron volts above. The electron-electron collision mean free paths ${l}_{e}$ were determined by correction of the attenuation lengths for electron-phonon scattering lengths ${l}_{p}$ deduced from the attenuation temperature dependence. Imperfection mean free paths were negligible. The following results were obtained: for aluminum, ${l}_{e}\ensuremath{\sim}50$ \AA{} and ${l}_{p}\ensuremath{\sim}250$ \AA{} near 5 eV above the Fermi level; for gold, $45 \AA{}g{l}_{e}g15 \AA{}$ for energies between 5.5 and 10 eV; and for silver, $42 \AA{}g{l}_{e}g20 \AA{}$ for energies between 5.5 and 8 eV. In the energy range between 5.5 and 7.5 eV, it was found that ${l}_{p}\ensuremath{\sim}250$ \AA{} for gold and ${l}_{p}\ensuremath{\sim}400$ \AA{} for silver. All measured ${l}_{p}$ were only about two-thirds of the value near the Fermi level. Quinn's theory for ${l}_{e}$ in a dense free-electron gas predicts that for aluminum ${l}_{e}\ensuremath{\sim}60$ \AA{} at 5 eV. Exchange corrections in Kleinman's dielectric screening function tend to bring the value closer to the observed one. In silver and gold, considerable interaction of the beam electrons with the $d$ band occurred for which no theory is available as yet. The resulting data were compared with the energy dependence of ${l}_{e}$ deduced semiempirically by Krolikowski and Spicer from the density of states obtained from photoemission experiments. Reasonable agreement with presently available data was observed.

Limit of Cross Sections at Infinite Energy

Abstract: At infinite energy, we predict: (1) ${\ensuremath{\sigma}}_{\mathrm{tot}}$ approaches infinity; (2) the ratio of the real part to the imaginary part of the forward elastic amplitude approaches zero; (3) $\frac{{\ensuremath{\sigma}}_{\mathrm{el}}}{{\ensuremath{\sigma}}_{\mathrm{tot}}}$ approaches \textonehalf{}; (4) the width of diffraction peak approaches zero; its product with ${\ensuremath{\sigma}}_{\mathrm{tot}}$ is a constant. We give theoretical evidence based on massive quantum electrodynamics as well as experimental evidence in support of these predictions, and a physical picture for high-energy scattering.

Wave-Vector-Dependent Dielectric Function for Si, Ge, GaAs, and ZnSe

Abstract: The longitudinal wave-vector-dependent dielectric function $\ensuremath{\epsilon}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$ is calculated for Si, Ge, GaAs, and ZnSe. The energy eigenvalues and wave functions which are used have been obtained from energy-band calculations based on the empirical pseudopotential method. Explicit results are given in the [1, 0, 0], [1, 1, 0], and [1, 1, 1] directions in the range $0\ensuremath{\le}q\ensuremath{\le}(\frac{4\ensuremath{\pi}}{a})$. A comparison is made between the present results and the results of other calculations. Some comparisons with experiment are also made.

Photoreflectance Line Shape at the Fundamental Edge in Ultrapure GaAs

Abstract: Reflectance modulation produced by an intense secondary light beam (photoreflectance) has been studied for wavelengths near the fundamental edge in ultrapure epitaxial layers of GaAs as a function of doping, temperature, and intensity of the modulating light beam. As the doping increases, the built-in electric field at the surface increases and the photoreflectance line shape stretches, in qualitative agreement with the predictions of the Franz-Keldysh theory. These results show directly that the photoreflectance is due to the modulation of the electric field in the Schottky surface barrier by photoexcited carriers. Since the line shape is much narrower than earlier electroreflectance measurements, we arrive at a more accurate value for the band gap of 1.420 eV at 300 \ifmmode^\circ\else\textdegree\fi{}K. As the temperature is lowered, the spacing in energy between adjacent peaks in the photoreflectance spectrum decreases, indicating that the electric field at the surface is decreasing. This temperature dependence is explained by a simple model for the surface consisting of a large density of electron traps located a fixed energy below the conduction-band edge. For all but the purest sample, the line shape is independent of the intensity of the modulating beam, consistent with the model that the secondary light beam is only slightly modifying the surface electric field. However, in the purest sample available (${n}_{e}=1.65\ifmmode\times\else\texttimes\fi{}{10}^{13}$ ${\mathrm{cm}}^{\ensuremath{-}3}$), a new effect is observed at the highest intensities of the modulating beam (\ensuremath{\sim} 0.1 ${\mathrm{W}/\mathrm{c}\mathrm{m}}^{2}$). The qualitative features of the new line shape agree with the predictions for both the Burstein effect and exciton screening by free carriers. Since the discrete exciton is thermally quenched at 300 \ifmmode^\circ\else\textdegree\fi{}K, the new line shape may result from the Burstein effect.

Dominant Colliding-Beam Cross Sections at High Energies

Abstract: We report on our calculation of the energy and angular dependence of the cross sections for the production of various particles by two-photon annihilation processes in ${e}^{+}{e}^{\ensuremath{-}}$ and ${e}^{\ensuremath{-}}{e}^{\ensuremath{-}}$ colliding beams. For beam energy $E$ of more than 1 GeV, these cross sections [$\ensuremath{\sigma}\ensuremath{\propto}{\ensuremath{\alpha}}^{4}{(\mathrm{ln}E)}^{3}$] become increasingly more important than the usual one-photon cross sections [$\ensuremath{\sigma}\ensuremath{\propto}{\ensuremath{\alpha}}^{2}{(E)}^{\ensuremath{-}2}$] for hadron production.

Energy of a Boson Fluid with Lennard-Jones Potentials

Abstract: A more powerful version of a numerical method published before is given which permits the integration of the Schr\"odinger equation for a large ensemble of particles. A new method for obtaining quantum expectation values is outlined. Numerical results are tabulated for the energy of the ground state of a system of 32 bosons interacting by Lennard-Jones potentials and with periodic boundary conditions. This is a commonly used model of liquid ${\mathrm{He}}^{4}$. The present results are substantially lower and closer to experiment than variational estimates based on a Jastrow-type wave function.

Proposed Secondary-Standard Wavelengths in the Spectrum of Thorium*

Abstract: Energy levels of Th lines computed from weighted averages of interferometrically measured wavelengths data

H + + H − Mutual Neutralization Cross Section Obtained with Superimposed Beams

Abstract: The ion-ion mutual neutralization cross section for ${\mathrm{H}}^{+}$ + ${\mathrm{H}}^{\ensuremath{-}}$ has been measured over the barycentric energy range from 0.15 to 300 eV using a merged-beam technique. The results are compared with theoretical calculations and with a recent higher energy experimental measurement. An estimate of the thermal rate coefficient is made.

Electron Energy-Loss and Ultraviolet-Reflectivity Spectra of Crystalline ZnO

Abstract: A comparison between the ultraviolet-reflectivity spectrum and the characteristic energy-loss spectrum of ZnO has been carried out. Reflectivity measurements made over an energy range of band gap to 22 eV yielded a spectrum with structure at 3.34, 5.0, 7.3, and 8.4 eV, and in the region 11-15 eV. Energy-loss measurements made over the energy range of band gap to 50 eV using 10-keV electrons exhibited peaks at 3.82, 5.47, 9.56, 13.5, 18.8, and 35.5 eV. The dominant peak in this spectrum is that at 18.8 eV and has been associated with a plasmon excitation. The samples in both cases were hexagonal ZnO platelets at room temperature. A dispersion analysis has been performed on the reflectivity data yielding the optical constants $n$, $k$, ${\ensuremath{\epsilon}}_{1}$, ${\ensuremath{\epsilon}}_{2}$, the effective number of free electrons ${n}_{\mathrm{eff}}$, the effective dielectric constant ${\ensuremath{\epsilon}}_{0\mathrm{eff}}$, and the imaginary part of ${\ensuremath{\epsilon}}^{\ensuremath{-}1}$. The energy-loss function has been calculated and found to compare well with the energy-loss spectrum obtained from the electron-transmission measurements.

Anistropy of the Constant-Energy Surfaces in n -Type Bi Te 3 2 and Bi 2 Se 3 from Galvanomagnetic Coefficients

Abstract: Low-field galvanomagnetic coefficients have been measured on single crystals of ${\mathrm{Bi}}_{2}$${\mathrm{Te}}_{3}$ and ${\mathrm{Bi}}_{2}$${\mathrm{Se}}_{3}$ at 76 \ifmmode^\circ\else\textdegree\fi{}K in fields to 9 kG. Using a six-valley ellipsoid model in the isotropic relaxation-time approximation, the mass parameters of the ellipsoids are calculated for both compounds. The discrepancy between previously reported galvanomagnetic data and de Haas-van Alphen data for ${\mathrm{Bi}}_{2}$${\mathrm{Te}}_{3}$ can be minimized by recalculating the mass parameters from the galvanomagnetic data and by not assuming complete degeneracy. The experimental data on ${\mathrm{Bi}}_{2}$${\mathrm{Te}}_{3}$ are in agreement with those reported earlier. There is also very good evidence of second-band effects at high electron concentrations (g ${10}^{19}$ ${\mathrm{cm}}^{\ensuremath{-}3}$), as has been previously suggested. The constant-energy surfaces undergo an apparent change in shape between low- and high-concentration samples. Data on ${\mathrm{Bi}}_{2}$${\mathrm{Se}}_{3}$ indicate that the constant-energy surfaces are more spherical than in the case of ${\mathrm{Bi}}_{2}$${\mathrm{Te}}_{3}$.

Relativistic balmer formula including recoil effects.

Abstract: It is shown that an approximate summation of the "crossed-ladder" Feynman diagrams for the scattering of two charged particles leads to the formula $s={{m}_{1}}^{2}+{{m}_{2}}^{2}+2{m}_{1}{m}_{2}{[1+\frac{{Z}^{2}{\ensuremath{\alpha}}^{2}}{{(n\ensuremath{-}{\ensuremath{\epsilon}}_{j})}^{2}}]}^{\ensuremath{-}\frac{1}{2}}$ for the squared mass of bound states. This formula neglects radiative corrections. It includes recoil effects properly, and reduces in the limit of one infinite mass to the corresponding spectrum of a relativistic particle in a static Coulomb potential. In the particular case of positronium, its expansion in powers of $\ensuremath{\alpha}$ coincides up to order ${\ensuremath{\alpha}}^{4}$ with the singlet energy levels. In an appendix we investigate some properties (gauge invariance, static limit) of this series of graphs.

Low-Temperature Critical Exponents from High-Temperature Series: The Ising Model

Abstract: First, a new method proposed by Baker and Rushbrooke is used to study the simple ferromagnetic Ising model at and below the Curie temperature. Of course, the properties of the Ising model are already well known, so that the main aim here is to assess the potential and reliability of the new method, since it has wide applicability to other models which have not been otherwise studied. Between 8 and 16 coefficients of exact high-temperature expansions for fixed values of the magnetization are derived for various two- and three-dimensional lattices. A Pad\'e-approximant analysis of these expansions at the critical isotherm and magnetic phase boundary enables us to estimate the critical exponents $\ensuremath{\beta}$, ${\ensuremath{\gamma}}^{\ensuremath{'}}$, and $\ensuremath{\delta}$, and plot the spontaneous magnetization. The results are in good agreement with previous calculations. Secondly, an analysis of the exact series expansions provides no support for the conjecture that the phase boundary is a line of essential singularities. However, the same expansions strongly suggest the existence of a "spinodal" curve, whose properties are in reasonable agreement with the predictions of various heuristic arguments (based essentially upon analyticity at the phase boundary and one-phase homogeneity in the critical region). Finally, structure and a mild extension of the proven analyticity of the free energy are used to show the $\ensuremath{\Delta}\ensuremath{\le}{\ensuremath{\Delta}}^{\ensuremath{'}}$, $\ensuremath{\gamma}\ensuremath{\le}{\ensuremath{\gamma}}^{\ensuremath{'}}$.

Electron Capture into the n = 3 States of H by Fast H + Impact on Gases

Abstract: Absolute cross sections for electron capture into the $3p$ and $3d$ states of hydrogen have been measured for 10- to 100-keV proton impact on He, Ne, Ar, ${\mathrm{H}}_{2}$, ${\mathrm{N}}_{2}$, and ${\mathrm{O}}_{2}$. Improved $3s$ cross sections are presented for these gases from 10 to 120 keV. An apparent maximum in the $3p$ cross section occurs in this energy range for all gases. The $3d$ cross sections decrease monotonically with increasing impact energy according to an $\mathrm{exp}[\ensuremath{-}{(\frac{E}{K})}^{\frac{1}{2}}]$ relationship, where $E$ is the impact energy and $K$ is a constant, with the exception of helium which shows a maximum in the $3d$ cross section between 15 and 20 keV. The value of $K$ is identical for all the diatomic gases. Balmer-$\ensuremath{\alpha}$ cross sections are synthesized from these results. Polarization of the $3d\ensuremath{\rightarrow}2p$ radiation is reported.

Photoemission Properties of Simple Metals

Abstract: The predictions of the nearly free-electron model for the photoemission properties of simple metals are derived and applied to the available data on K, Ag, and Al. The optical transitions are taken to be direct. The energy distribution curve (EDC) of photoemitted electrons is then related to the energy distribution of the joint density of states (EDJDOS). In the one- and two-orthogonalized-plane-wave (OPW) approximations, the EDJDOS is predicted to be rectangular in shape with a width which increases quadratically with photon energy. The experimental data on K and on the "${L}_{{2}^{\ensuremath{'}}}\ensuremath{\rightarrow}{L}_{1}$" transitions in Ag show some agreement with this result. In the case of Al, the EDJDOS has been calculated numerically using Ashcroft's four-OPW band structure. The over-all rectangular features can still be discerned, but there is much additional structure due to the inclusion of the extra OPW's. The EDC's for Al at several photon energies are calculated by introducing appropriate threshold factors and are found to agree reasonably well with the data of Wooten et al. Only the three uppermost peaks in the theoretical EDJDOS are presently accessible to experiment, and these correspond fairly closely in energy with the three peaks in the density of states. The implications with regard to the alternative nondirect interpretation are discussed.

Angular Distribution of O- from Dissociative Electron Attachment to O2

Abstract: The angular distribution of ${\mathrm{O}}^{\ensuremath{-}}$ produced by electron bombardment of ${\mathrm{O}}_{2}$ has been measured in the electron energy range 5.75-8.40 eV. The results show a strong energy dependence and are consistent with the theory of O'Malley and Taylor if the final $\mathrm{O}_{2}^{}{}_{}{}^{\ensuremath{-}}$ repulsive resonance state is assumed to have the symmetry $^{2}\ensuremath{\Pi}_{u}$, and if only the first two allowed partial waves of the incident electron corresponding to $L=1$ and $L=3$ contribute. The results indicate that the $L=3$ term becomes more important as energy increases and thereby demonstrate that the single-term approximation for the angular distribution does not apply for this process.

Energy-Band Structure and Optical Spectrum of Grey Tin

Abstract: A first-principles relativistic orthogonalized-plane-wave calculation has been used to determine the energy eigenvalues of grey tin at seven key points of the reduced zone. An extended zone $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}$ method has been used as an interpolation scheme to map out the band structure in the remainder of the zone. Optical constants and derivative optical constants have been calculated from the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}$ parameters. The calculated normal incidence reflectivity is compared to experiment. A detailed critical-point analysis of the calculated optical spectra is presented. Valence-band mass parameters, effective masses, and $g$ factors at several points in the zone have been obtained and are compared to available experimental data.

TEMPERATURE DEPENDENCE OF THE WAVELENGTH MODULATION SPECTRA OF GaAs

Abstract: Wavelength-modulation spectroscopy is used to obtain the temperature dependence of the reflectivity spectrum for GaAs. Results are given in the regions of the ${E}_{1}$ doublet and the major ${E}_{2}$ peak at 5, 80, 150, 225, and 300\ifmmode^\circ\else\textdegree\fi{}K. The theoretical temperature dependence in these regions is obtained through use of Debye-Waller factors and thermal expansion coefficients in an empirical pseudopotential calculation of the ${\ensuremath{\Lambda}}_{3}\ensuremath{-}{\ensuremath{\Lambda}}_{1}$ and ${\ensuremath{\Sigma}}_{2}\ensuremath{-}{\ensuremath{\Sigma}}_{1}$ energy splittings.

Exact Calculation of the Penetrability Through Two-Peaked Fission Barriers

Abstract: The penetrability is computed exactly for a fission barrier $V(\ensuremath{\epsilon})$ defined in terms of two parabolic peaks connected smoothly with a third parabola forming the intermediate well. The potential is specified by the peak energies ${E}_{1}$ and ${E}_{3}$ and the minimum energy ${E}_{2}$ of the connecting curve, along with the constants $\ensuremath{\hbar}{\ensuremath{\omega}}_{1}$, $\ensuremath{\hbar}{\ensuremath{\omega}}_{3}$, and $\ensuremath{\hbar}{\ensuremath{\omega}}_{2}$ related to the curvatures of the three parabolas. For an incident wave of unit amplitude, the amplitude of the transmitted wave is determined by requiring that the wave functions (expressed exactly in terms of parabolic-cylinder functions) and their first derivatives match at the points where the parabolas are connected. The penetrability is then obtained from the amplitude of the transmitted wave. The transmission is essentially an increasing exponential function exhibiting narrow resonances at the positions of quasibound states in the intermediate well. The widths of these resonances are extremely small (\ensuremath{\sim}10 eV) for the levels near the bottom of the well but increase dramatically as the energy increases. This trend continues in some cases above the top of the barrier, producing broad peaks in the penetrability function. The exact penetrabilities are accurately reproduced by the WKB approximation for energies well below the barrier tops, but for energies near the barrier tops the WKB approximation is found to overestimate the penetrability for the cases studied.

Auger Electrons from Argon with Energies 150-210 eV Produced by H + and H 2 + Impacts

Abstract: Secondary electrons in the energy range 150-210 eV produced by 125-300-keV ${\mathrm{H}}^{+}$ and $\mathrm{H}_{2}^{}{}_{}{}^{+}$ impacts on argon gas are measured as a function of their energy and angle of emission. Discrete line spectra are due to Auger transitions from ${\mathrm{L}}_{2}$ and ${\mathrm{L}}_{3}$ vacancy states as well as satellite transitions from multivacancy states. The widths, energies, and branching ratios of the ${\mathrm{L}}_{2}$ and ${\mathrm{L}}_{3}$ vacancy states are presented. Widths of these states are appreciably greater than those obtained with electron impact excitation. This can be attributed to the recoil velocities of the target atom and to the presence of the proton in the vicinity of the emitting atom. The angular distribution of Auger electrons is found to be nearly isotropic, in marked contrast to electrons in the continum spectrum. The cross sections for the production of ${\mathrm{L}}_{2,3}$ and ${\mathrm{L}}_{3}$ vacancy states are determined as a function of impact energy.

Frequency interleaved video multiplex system

Abstract: Two video signals having substantially all their energy distributed at the same discrete line harmonics are interleaved to form a multiplexed output. One signal is processed to form a modified signal whose alternate lines are phase inverted so that its energy spectrum is displaced by one-half line frequency from the original harmonics. The modified signal and the other unprocessed signal are algebraically added to produce the multiplexed output. After transmission, the signals are separated by comb characteristic filters and inverse processing reconstructs the original signal.

Non-Muffin-Tin Energy Bands for Silicon by the Korringa-Kohn-Rostoker Method

Abstract: A method is proposed for removing the "muffin-tin" restriction from the Green's function or the Korringa-Kohn-Rostoker method of band calculation and, more generally, from multiple-scattering theory as formulated by Beeby and Edwards. The method is applied to a model for crystalline silicon involving a single parameter which is adjusted to reproduce the experimental indirect gap. The numerical results are in good agreement with a large number of experiments and in particular support the view that the $\ensuremath{\Delta}$ axis is important to the reflectivity peak at 3.4 eV. (The energy separation ${\ensuremath{\Gamma}}_{15}\ensuremath{-}{{\ensuremath{\Gamma}}_{25}}^{\ensuremath{'}}$ is found to be 3.04 eV.)

On the Balance Between Radial and Pitch Angle Diffusion

Abstract: The various attempts to mathematically describe the observed populations of trapped particles can be summarized by the following set of equations expressing conservation of particle number f and energy: $$\frac{\partial }{{\partial t}}f({x^\mu },t) = \frac{\partial }{{\partial {x^\mu }}}\left( {{D^{\mu v}}\frac{{\partial f}}{{\partial {x^v}}}} \right) - L({x^\mu }) + S({x^\mu })$$ (1) and conservation of electromagnetic wave energy e: $$\frac{\partial }{{\partial t}}\varepsilon (\omega ,t) = - {\text{div(}}\varepsilon {{\text{v}}_g}{\text{) + 2(}}\gamma {\text{ - }}l{\text{)}}\varepsilon$$ (1) . The variables x μ represent the adiabatic invariants which undergo small fluctuations by either interaction with the electromagnetic wave field or collisions. D μv is the diffusion tensor which so far has been considered mostly for L and pitch angle diffusion. S represents any internal particle source like the neutron albedo decay and L losses due to collisions.

Ferromagnetic Resonance in Thin Films. III. Theory of Mode Intensities

Abstract: A theory of surface-spin pinning and its effects on the ferromagnetic-resonance mode intensities is presented. The pinning by a surface inhomogeneity (e.g., a demagnetization field from surface imperfections or an inhomogeneous saturation magnetization) of thickness $\ensuremath{\epsilon}$ is considered. Roughly speaking, the modes are nearly unpinned for a thin-surface inhomogeneity (${\ensuremath{\epsilon}}^{2}\ensuremath{\ll}\frac{\ensuremath{\Lambda}}{\ensuremath{\pi}}$, where $\ensuremath{\Lambda}$ is the exchange constant in the exchange field $\ensuremath{\Lambda}{\ensuremath{ abla}}^{2}\mathrm{M}$), while the low-order modes are pinned by a thick-surface inhomogeneity (${\ensuremath{\epsilon}}^{2}\ensuremath{\ll}\frac{\ensuremath{\Lambda}}{\ensuremath{\pi}}$ not satisfied). The theory indicates that the low-order modes should be pinned unless great care is exercied in the film preparation. In 80% Ni-20% Fe permalloy, ${(\frac{\ensuremath{\Lambda}}{\ensuremath{\pi}})}^{\frac{1}{2}}\ensuremath{\cong}90$ \AA{}; thus, the surface region would have to be only a few lattice constants thick in order for there to be no pinning. These results are obtained by considering the equation of motion of the magnetization in the surface region as well as the bulk region. The intensities and frequencies of magnetostatic modes (negligible exchange energy) are relatively independent of surface-spin pinning, in contrast to the result for exchange modes (negligible microwave demagnetization energy) that pinning the surface spins gives rise to large intensities of even modes.

Far-Infrared Absorption of ZnS: Fe 2 + in Strong Magnetic Fields

Abstract: We have investigated several optical transitions between the $^{5}E$ energy levels of the orbital ground state of substitutional ${\mathrm{Fe}}^{2+}$ in natural crystals of cubic ZnS for magnetic inductions up to 14 T (140 kG) at liquid-He temperatures. In these experiments we have used both gas lasers and a Fourier-transform Michelson spectrometer covering the range 10-100 ${\mathrm{cm}}^{\ensuremath{-}1}$ wave numbers. The results show that simple crystal-field theory is adequate to account for the observed energy levels and their oscillator strengths as a function of the applied magnetic field. There is also evidence for local modes at 43 and 63 ${\mathrm{cm}}^{\ensuremath{-}1}$ wave numbers caused by trace impurities other than Fe.

Study of the (d,p) Reaction on the Even-A Barium Isotopes 130-138

Abstract: The ($d, p$) reactions on ${\mathrm{Ba}}^{130,132,134,136,138}$ have been investigated with 12.0-MeV deuterons from the Argonne Tandem Van de Graaff accelerator. Proton spectra were recorded in a broad-range magnetic spectrograph. Many new levels were observed. The ground-state $Q$ values (in MeV) for the ($d, p$) reactions (including the odd-$A$ targets) are found to be 5.269 for $A=130, 4.977$ for $A=132, 4.746$ for $A=134, 6.886$ for $A=135, 4.680$ for $A=136, 6.398$ for $A=137, \mathrm{and} 2.493$ for $A=138$. Proton angular distributions were measured for states up to an excitation energy of about 3 MeV. The observed angular momentum transfers were ${l}_{n}=0, 1, 2, 3, \mathrm{and} 5$, which correspond to the population of states of the $3{s}_{\frac{1}{2}}$ and $2{d}_{\frac{3}{2}}$ configurations below the closed neutron shell at $N=82$ and the $2{f}_{\frac{7}{2}}$, $3{p}_{\frac{3}{2}}$, $3{p}_{\frac{1}{2}}$, $1{h}_{\frac{9}{2}}$, and $2{f}_{\frac{5}{2}}$ configurations above it. From the observed $l$ values, it was possible to assign spins in some isotopes from a knowledge of the spin in other isotopes by taking account of systematic shifts in the $Q$ values of levels and also from shell-model expectations. Distorted-wave Born-approximation calculations were used to extract absolute spectroscopic factors. The problems and uncertainties arising in such calculations were studied in some detail. They derive, in part, from the need to use a sharp radial cutoff to fit the experimental angular distributions; calculations with nonlocal potentials and finite-range approximations did not yield satisfactory fits. Another source of uncertainty is the dependence of the spectroscopic factors upon the geometric parameters of the bound-state potential well. The results are interpreted with the help of pairing theory; centers of gravity and single-particle energies are deduced.

Modulated Piezoreflectance in Bismuth

Abstract: Piezoreflectance has been measured in single crystals of bismuth with light polarized in the basal plane of the crystal for photon energies in the range 0.6 to 4.5 eV. The stress modulation of the optical reflectance was achieved by cementing a nearly circular disk of bismuth onto a lead-zirconate-titanate disk set into radial oscillations at 22 kcps. Using the Kramers-Kronig analysis, the induced changes in the imaginary part of the basal component of the dielectric tensor ${\ensuremath{\epsilon}}_{\mathrm{i}j}$ have been computed from the piezoreflectance data. The energy dependence of the piezoreflectance ${(\frac{\ensuremath{\Delta}R}{R)}}_{11}$, as well as the computed changes in the dielectric constant $\ensuremath{\Delta}{\ensuremath{\epsilon}}_{11}^{\ensuremath{'}\ensuremath{'}}$, show an enhancement of the structure observed earlier by Cardona and Greenaway in the reflectivity spectrum. An assignment of the optical structure to direct interband transitions has been possible with the help of a comparison of the data with Golin's band-structure calculations.

Electronic distance measuring method and apparatus

Abstract: An electronic distance measuring device and method for determining the distance between two locations utilizing electromagnetic or light wave energy. The wave energy is transmitted from one location to the other and is reflected back toward the transmitting location. The reflected energy is detected and compared in phase with the transmitted energy, and the phase relationship between the transmitted and detected energy varied until a predetermined phase relationship exists. The predetermined phase relationship is selected so that the wave energy along the path between the transmitter, reflector and detector contains an integral number of wavelengths of wave energy. A time gate related to the propagation of the wave energy along this path is generated and distance is displayed digitally in response to the time gate and a highly stable reference frequency signal.