Showing papers on "Energy (signal processing) published in 1971"

Behavior of the Electronic Dielectric Constant in Covalent and Ionic Materials

Abstract: Refractive-index dispersion data below the interband absorption edge in more than 100 widely different solids and liquids are analyzed using a single-effective-oscillator fit of the form ${n}^{2}\ensuremath{-}1=\frac{{E}_{d}{E}_{0}}{({E}_{0}^{2}\ensuremath{-}{\ensuremath{\hbar}}^{2}{\ensuremath{\omega}}^{2})}$, where $\ensuremath{\hbar}\ensuremath{\omega}$ is the photon energy, ${E}_{0}$ is the single oscillator energy, and ${E}_{d}$ is the dispersion energy. The parameter ${E}_{d}$, which is a measure of the strength of interband optical transitions, is found to obey the simple empirical relationship ${E}_{d}=\ensuremath{\beta}{N}_{c}{Z}_{a}{N}_{e}$, where ${N}_{c}$ is the coordination number of the cation nearest neighbor to the anion, ${Z}_{a}$ is the formal chemical valency of the anion, ${N}_{e}$ is the effective number of valence electrons per anion (usually ${N}_{e}=8$), and $\ensuremath{\beta}$ is essentially two-valued, taking on the "ionic" value ${\ensuremath{\beta}}_{i}=0.26\ifmmode\pm\else\textpm\fi{}0.04$ eV for halides and most oxides, and the "covalent" value ${\ensuremath{\beta}}_{c}=0.37\ifmmode\pm\else\textpm\fi{}0.05$ eV for the tetrahedrally bonded ${A}^{N}{B}^{8\ensuremath{-}N}$ zinc-blende- and diamond-type structures, as well as for scheelite-structure oxides and some iodates and carbonates. Wurtzite-structure crystals form a transitional group between ionic and covalent crystal classes. Experimentally, it is also found that ${E}_{d}$ does not depend significantly on either the bandgap or the volume density of valence electrons. The experimental results are related to the fundamental ${\ensuremath{\epsilon}}_{2}$ spectrum via appropriately defined moment integrals. It is found, using relationships between moment integrals, that for a particularly simple choice of a model ${\ensuremath{\epsilon}}_{2}$ spectrum, viz., constant optical-frequency conductivity with high- and low-frequency cutoffs, the bandgap parameter ${E}_{a}$ in the high-frequency sum rule introduced by Hopfield provides the connection between the single-oscillator parameters (${E}_{0},{E}_{d}$) and the Phillips static-dielectric-constant parameters (${E}_{g},\ensuremath{\hbar}{\ensuremath{\omega}}_{p}$), i.e., ${(\ensuremath{\hbar}{\ensuremath{\omega}}_{p})}^{2}={E}_{a}{E}_{d} \mathrm{and} {E}_{g}^{2}={E}_{a}{E}_{0}$. Finally, it is suggested that the observed dependence of ${E}_{d}$ on coordination number and valency implies that an understanding of refractive-index behavior may lie in a localized molecular theory of optical transitions.

Hopping Conductivity in Disordered Systems

Abstract: By considering a model in which charge is transported via phonon-induced tunneling of electrons between localized states which are randomly distributed in energy and position, Mott has obtained an electrical conductivity of the form $\ensuremath{\sigma}\ensuremath{\propto}\mathrm{exp}[\ensuremath{-}{(\frac{\ensuremath{\lambda}{\ensuremath{\alpha}}^{3}}{{\ensuremath{\rho}}_{0}\mathrm{kT}})}^{\frac{1}{4}}]$. Here $T$ is the temperature of the system, ${\ensuremath{\rho}}_{0}$ is the density of states at the Fermi level, $\ensuremath{\lambda}$ is a dimensionless constant, and ${\ensuremath{\alpha}}^{\ensuremath{-}1}$ is the distance for exponential decay of the wave functions. We rederive these results, relating $\ensuremath{\lambda}$ to the critical density of a certain dimensionless percolation problem, and we estimate $\ensuremath{\lambda}$ to be approximately 16. The applicability of the model to experimental observations on amorphous Ge, Si, and C is discussed.

Inertial-range transfer in two- and three-dimensional turbulence

Abstract: A simple dynamical argument suggests that the k−3 enstrophy-transfer range in two-dimensional turbulence should be corrected to the form \[ E(k) = C^{\prime} \beta^{\frac{21}{3}}k^{-3}[\ln (k/k_1)]^{-\frac{1}{3}}\quad (k \gg k_1), \] where E(k) is the usual energy-spectrum function, β is the rate of enstrophy transfer per unit mass, C′ is a dimensionless constant, and k1 marks the bottom of the range, where enstrophy is pumped in. Transfer in the energy and enstrophy inertial ranges is computed according to an almost-Markovian Galilean-in variant turbulence model. Transfer in the two-dimensional energy inertial range, \[ E(k) = C\epsilon^{\frac{2}{3}}k^{-\frac{5}{3}}, \] is found to be much less local than in three dimensions, with 60 % of the transfer coming from wave-number triads where the smallest wave-number is less than one-fifth the middle wave-number. The turbulence model yields the estimates C′ = 2·626, C = 6·69 (two dimensions), C = 1·40 (three dimensions).

Eight-Vertex Model in Lattice Statistics

Abstract: The solution of the zero-field "eight-vertex" model is presented. This model includes the square lattice Ising, dimer, ice, $F$, and KDP models as special cases. It is found that in general the free energy has a branch-point singularity at a phase transition, with a continuously variable exponent.

Relativistic Band Calculation and the Optical Properties of Gold

Abstract: The energy band structure of gold is calculated by the relativistic augmented-plane-wave (RAPW) method. A nonrelativistic calculation is also presented, and a comparison between this and the RAPW results demonstrates that the shifts and splittings due to relativistic effects are of the same order of magnitude as the gaps (approximately 1 eV). Various integrated functions, density of states, joint density of states, and energy distributions of joint density of states are derived from the RAPW calculation. These functions are used in an interpretation of photoemission and static reflectance measurements. It is shown that the photoemission results are extremely well described in terms of a model assuming all transitions to be direct whereas a nondirect model fails. The ${\ensuremath{\epsilon}}_{2}$ profile calculated in a crude model assuming constant matrix elements matches well the corresponding experimental results. The calculated interband edge ($\ensuremath{\hbar}{\ensuremath{\omega}}_{i}=2.38$ eV) agrees with experimental values, and the absorption tail below the interband edge which is found in experimental traces is also contained in the theoretical curve. By means of a calculation of the Fermi surface and the constant-energy-difference surfaces it has been possible to trace out the regions in $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ space where the edge and tail transitions occur. It is demonstrated that structure in the static reflection curves are not related to critical points in the band structure. The arguments are supported by calculations of temperature shifts of the critical-point energies and comparison to the observed temperature shifts of the elements of structure in the experimental ${\ensuremath{\epsilon}}_{2}$ function. Such structure may originate in extended rather than localized regions of $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ space. In contrast, critical-point transitions show up clearly in modulated reflectance spectra, and all elements of structure are fully accounted for by our band model. The temperature and strain responses in the band structure are determined by performing the RAPW calculation with two lattice constants and estimating the effects of the lattice vibrations by means of an OPW-LCAO (linear combination of atomic orbitals) scheme with pseudopotential Fourier constants reduced by the appropriate Debye-Waller factors. The phonon spectrum has been calculated for the latter purpose.

Neutron-Scattering Study of Soft Modes in Cubic BaTi O 3

Abstract: The soft optic phonons in the cubic phase of BaTi${\mathrm{O}}_{3}$ have been reinvestigated by the neutron-scattering technique. Measurements were carried out on major symmetry directions for a temperature range between 150 to 450 \ifmmode^\circ\else\textdegree\fi{}C. It is shown that, as in the case of the tetragonal phase, the lowest transverse-optic branches along the [111] direction and one of the branches along [110] rise rapidly with increasing wave vector $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}$. Phonons are well defined except for those at very small $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}$. On the other hand, in one of the branches along [110] and in the degenerate branches along [100] the phonons are overdamped as previously shown by Yamada et al. for small $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}$ values. The present study extends the measurement to the entire zone and corrects the erroneous picture previously given. The most important result of the present study concerns the interaction between the soft optic modes and acoustic modes. Unusual scattering cross sections for both optic and acoustic modes are explained by interference effects in a coupled phonon model with a highly damped optic component. The interference permits, for the first time, a determination of the phase as well as the amplitude of the dynamical structure factors of the phonons involved. The energy of the optically inactive ${\ensuremath{\Gamma}}_{25}$ mode at the Brillouin zone center was found to be (39 \ifmmode\pm\else\textpm\fi{} 2) meV.

Two electrons in a coulomb potential. double-continuum wave functions and threshold law for electron--atom ionization.

Abstract: The Schr\"odinger equation for two electrons in a Coulomb field is studied in the critical region where both electrons have near-zero kinetic energies. The main feature of this problem is that the mutual screening between the two electrons determines and is determined by the partition of the available energy between them. This energy-dependent screening can be taken into account to yield a complex potential in the radial variable $R={({r}_{1}^{2}+{r}_{2}^{2})}^{\frac{1}{2}}$ of the six-dimensional configuration space of the two electrons. Solutions of this equation are obtained and are shown to correspond to the classical orbits given in an early paper by Wannier. A possible way is indicated of using these wave functions to establish the Wannier threshold law which, for ionization of neutral atoms, is $\ensuremath{\sigma}\ensuremath{\propto}{E}^{1.127}$. Finally, the interplay between the total energy and the Coulomb potential is discussed both for this problem and for the case of one electron in the field of a nucleus.

Two-Dimensional System of Hard-Core Bosons

Abstract: As a model of a helium monolayer a system of hard-core bosons of mass $m$ and diameter $a$ constrained to motion in two dimensions is considered at absolute zero. In the low-density limit, the ground-state energy per particle and condensate depletion are found to be $\frac{E}{N}=\ensuremath{-}\frac{2\ensuremath{\pi}{\ensuremath{\hbar}}^{2}n}{m\mathrm{ln}n{a}^{2}}$ and ${n}_{0}=n(1+\frac{1}{\mathrm{ln}n{a}^{2}})$, where $n$ is the areal density of the system. The expansion parameter $\ensuremath{-}\frac{1}{\mathrm{ln}n{a}^{2}}$ is approximately equal to unity for real helium monolayers. The variation of the above results with temperature is discussed for a system of finite size.

Gravitational radiation from a particle falling radially into a schwarzschild black hole

Abstract: We have computed the spectrum and energy of gravitational radiation from a "point test particle" of mass $m$ falling radially into a Schwarzschild black hole of mass $M\ensuremath{\gg}m$. The total energy radiated is about $0.0104m{c}^{2}(\frac{m}{M})$, 4 to 6 times larger than previous estimates; the energy is distributed among multipoles according to the empirical law ${E}_{2l\ensuremath{-}\mathrm{p}\mathrm{o}\mathrm{l}\mathrm{e}}\ensuremath{\approx}(\frac{0.44{m}^{2}{c}^{2}}{M}){e}^{\ensuremath{-}2l}$; and the total spectrum peaks at an angular frequency $\ensuremath{\omega}=\frac{0.32{c}^{3}}{\mathrm{GM}}$.

Optical Properties of Single-Crystal Paratellurite (Te O 2 )

Abstract: Absorption at the fundamental band edge, the dispersion characteristics of the refractive indices, the optical rotatory power, associated temperature coefficients, and the photoelastic constants have been investigated. Absorption at the band edge has been found to obey the exponential Urbach rule up to 5 \ifmmode\times\else\texttimes\fi{} ${10}^{2}$${\mathrm{cm}}^{\ensuremath{-}1}$. Refractive-index data between 0.4 and 1.0 \ensuremath{\mu}m are excellently fitted to the two-term Sellmeier dispersion formula with oscillators located at 9.24 and 4.70 eV. The contribution of the former oscillator to the refractive index in the visible to infrared region is larger than that of the latter. The dispersion energy ${\mathcal{E}}_{\mathrm{di}}=\frac{{\mathcal{F}}_{i}}{{\mathcal{E}}_{i}}$ (where ${\mathcal{F}}_{i}$ is the oscillator strength factor and ${\mathcal{E}}_{i}$ is the oscillator position) defined by Wemple and DiDomenico has been determined as \ensuremath{\sim} 25 eV for the transition at 9.24 eV, and is in agreement with the value derived for the average single oscillator. Dispersion of the rotatory power has been also explained by the two-term Chandrasekhar's formula with oscillator positions nearly equal to those found from the refractive indices. Dispersion measurements of the photoelastic constants reveal that a large anisotropy exists between the changes of ${\mathcal{F}}_{i}$ and ${\mathcal{E}}_{i}$ induced by the strain ${S}_{1}$ and those induced by ${S}_{3}$. The main contribution to the positive value of the temperature coefficient of the refractive indices comes from an intrinsic temperature effect, and the contribution of the photoelastic effect associated with the thermal expansion is negative. Anomalous behavior has been observed in $\frac{\mathrm{dn}}{n}\mathrm{dT}$ and $\frac{d\ensuremath{\rho}}{\ensuremath{\rho}}\mathrm{dT}$ between 0.5 and 0.6 \ensuremath{\mu}m, and is probably attributable to extremely weak absorption peaks located in this wavelength region.

Effect of Fermi Surface Geometry on Electron-Electron Scattering

Abstract: In order to investigate the influence of Fermi-surface geometry on the lifetime of an electron due to interactions with other electrons, we have performed a calculation (using Fermi's "Golden Rule") of the energy- and temperature-dependent lifetime of an electron on a cylindrical Fermi surface. At zero temperature, the dominant energy dependence of the inverse lifetime or the decay rate is ${\ensuremath{\epsilon}}^{2}|\mathrm{ln}\ensuremath{\epsilon}|$ for small values of the parameter $\ensuremath{\epsilon}$ which is the electron energy relative to the Fermi energy $\ensuremath{\mu}$ measured in units of $\ensuremath{\mu}$. At finite temperatures the decay rate leads to an electrical resistivity proportional to ${T}^{2}|\frac{\mathrm{ln}\mathrm{kT}}{\ensuremath{\mu}}|$ instead of the ${T}^{2}$ dependence characteristic of a spherical Fermi surface. In addition, the similar calculation (using Fermi's "Golden Rule") for a spherical Fermi surface has been done exactly at zero temperature. The magnitude of the correction to the well-known ${\ensuremath{\epsilon}}^{2}$ term has been obtained. Furthermore, in an appendix, written with N. D. Mermin, the dominating influence of the density of states on the wave-vector dependence of the susceptibility is demonstrated.

Evidence for One-Dimensional Metallic Behavior in K 2 Pt(CN) 4 Br 0.3 . (H 2 O) n

Abstract: Single crystals of ${\mathrm{K}}_{2}$Pt${(\mathrm{CN})}_{4}$${\mathrm{Br}}_{0.3}$\ifmmode\cdot\else\textperiodcentered\fi{}${({\mathrm{H}}_{2}\mathrm{O})}_{n}$ show a Drude-type optical reflectivity for light polarized parallel to the crystal axis. The energy of the plasma edge indicates a metallic density of free carriers. The relatively small conductivity at dc and low frequencies and the photoconductivity at ${4.2}^{\mathrm{o}}$K can be understood in terms of a simple model assuming metallic strands interrupted by lattice defects.

Transport of Heat and Approach to Second Sound in Some Isotopically Pure Alkali-Halide Crystals

Abstract: The propagation of short thermal pulses has been studied in very pure samples of NaF, ${\mathrm{Li}}^{7}$F, and NaI in various crystallographic directions. In each of these crystals the flow of heat at high temperatures is by diffusion, and at the lowest temperatures, by the direct flight of phonons from heater to detector. In the ballistic region, the elastic anisotropy gives rise to a channeling of mode energy into certain preferred directions. Over a limited intermediate temperature range, the effect of normal-process scattering on the propagated heat pulse has been observed in NaF and ${\mathrm{Li}}^{7}$F: In the best NaF crystals the pulse velocity approaches the expected second-sound velocity. The observations can be explained satisfactorily in terms of the hydrodynamics of a weakly interacting phonon gas. Computer solutions generated to fit the observed thermal pulse shapes suggest that in NaF, the mean free path for normal-process scattering can be represented by ${l}_{N}=1.42\ifmmode\times\else\texttimes\fi{}{10}^{3}{T}^{\ensuremath{-}3.71}$ cm in the temperature range 10-20 \ifmmode^\circ\else\textdegree\fi{}K.

Differential and Integral Cross Sections for the Electron-Impact Excitation of the a Δ g 1 and b Σ g + 1 States of O 2

Abstract: Electron-impact energy-loss spectra of ${\mathrm{O}}_{2}$ have been analyzed for incident electron energies from 4 to 45 eV, scattering angles from 10\ifmmode^\circ\else\textdegree\fi{} to 90\ifmmode^\circ\else\textdegree\fi{}, and energy losses from 0 to 5 eV. The inelastic processes observed were the excitation of the $a^{1}\ensuremath{\Delta}_{g}$ and $b^{1}\ensuremath{\Sigma}_{g}^{+}$ electronic states and vibrational excitation in some cases to ${v}^{\ensuremath{'}\ensuremath{'}}=13$. The excitation cross sections at each energy were made absolute by normalizing the sum of the integral cross sections (all inelastic, ionization, and elastic) to measured electron-${\mathrm{O}}_{2}$ total cross sections. The differential cross sections for the $a^{1}\ensuremath{\Delta}_{g}$ and $b^{1}\ensuremath{\Sigma}_{g}^{+}$ states show nearly isotropic behavior, as expected for optically spin-for-bidden transitions. The elastic differential cross sections are strongly forward peaked at higher energies, but become only slightly forward peaked at the lower energies. The integral cross sections for the excitation of the $a^{1}\ensuremath{\Delta}_{g}$ and $b^{1}\ensuremath{\Sigma}_{g}^{+}$ states reach their maxima near 7 eV and are more than an order of magnitude larger than previous estimates. The integral elastic cross section reaches its maximum at around 10 eV.

Signal detection in Gaussian noise of unknown level: An invariance application

Abstract: The concept of invariance in hypothesis testing is brought to bear on the problem of detecting signals of known form and unknown energy in Gaussian noise of unknown level. The noise covariance function is assumed to be K(t,u) = \sigma^2 \pho(t,u) where \rho(t,u) is the known form of the covariance function and \sigma^2 is the unknown level. Classical approaches to signal detection depend on the assumption that K(t,u) is known completely. Then, a correlation-type receiver that is the uniformly most powerful (UMP) test of H_o (signal absent) versus H_1 (signal present) can be derived. When \sigma^2 is unknown, there exists no UMP test. However, it is shown in this paper that there exists a test of H_o versus H_1 that is UMP-invariant for a very natural group of transformations on the space of observations. The derived test is found to be independent of knowledge about the noise level \sigma^2 , since the derived test (receiver) contains an error-free estimate of \sigma^2 . This utopian conclusion is reconciled by noting that the derived receiver can never be physically realized. It is shown that any physically realizable version of the receiver has a t -distributed test statistic. This permits choice of operating receiver thresholds and evaluation of performance characteristics.

Multiple Plasmon Effects in the Energy-Loss Spectra of Electrons in Thin Films

Abstract: The interaction of a fast electron (energy \ensuremath{\gtrsim} 1 keV) with collective modes in a thin metallic or doped semiconductor film is studied, taking explicitly into account bulk and surface effects. Reducing the problem to an exactly soluble quantum-mechanical model, we obtain results to all orders of the interaction and investigate the multiple-plasmon contribution to the electron energy losses. The theory is applied to transmission as well as to reflection and a complete description of the loss spectra is obtained. It is shown that the zero-energy plasmon mode does not cause singularities in the low-energy excitation spectrum. The strength of the many-body processes is given by the "fine-structure constant" $\frac{{e}^{2}}{\ensuremath{\hbar}{v}_{\ensuremath{\perp}}}$, where ${v}_{\ensuremath{\perp}}$ is the electron velocity normal to the surface, and in some cases multiple-plasmon emission becomes important, especially so in the specular reflection at grazing-angle incidence. For a thicker slab ($a\ensuremath{\sim}500\ensuremath{-}1000$ \AA{}), this results in a series of sharp peaks in the loss spectrum which have maximum strengths corresponding to several excited plasmons. For a thin slab ($a\ensuremath{\sim}\mathrm{few} 100$ \AA{}), the dominant contribution to the loss spectrum is a broad structure with a high-energy ($\ensuremath{\omega}g{\ensuremath{\omega}}_{p}$) tail, characteristic for the recombinational effect of many emitted low-energy plasmons.

Superheavy elements and an upper limit to the electric field strength.

Abstract: An upper limit to the electric field strength, such as that of the nonlinear electrodynamics of Born and Infeld, leads to dramatic differences in the energy eigenvalues and wave functions of atomic electrons bound to superheavy nuclei. For example, the $1{s}_{\frac{1}{2}}$ energy level joins the lower continuum at $Z=215$ instead of $Z=174$, the value obtained when Maxwell's equations are used to determine the electric field.

Electron-Tunneling Studies of a Quantized Surface Accumulation Layer

Abstract: This paper describes an experiment on electron tunneling through $n$-type InAs-oxide-Pb junctions and discusses in detail two results which are pertinent to the quantization of an accumulation layer at the InAs surface First, the tunneling curves $\frac{\mathrm{dI}}{\mathrm{dV}}$ vs $V$ and $\frac{{d}^{2}I}{d{V}^{2}}$ vs $V$ show structures reflecting the energy minima of two-dimensional electric subbands The bias position of these structures gives a direct measure of the energy of the quantized levels Second, when a quantizing magnetic field is applied perpendicular to the junction surface, oscillations are observed in the tunneling curves These oscillations reflect the Landau-level spectra of electrons in the electric subbands They give a direct measure of the effective mass of the surface electrons

Experimental Electron-Transfer Cross Sections for Collisions of Oxygen Ions in Argon, Nitrogen, and Helium at Energies of 7-40 MeV

Abstract: In the energy range 7-40 MeV, electron-capture and electron-loss cross sections have been determined for incident oxygen ions of charges +2 to +8 passing through argon, nitrogen, and helium. Thin-target conditions have been used in all cases. The analysis technique used to extract the cross sections allows relative cross sections to be obtained without consideration of the measurement of the gas target thickness. Multiple-transfer cross sections can thereby be determined reliably in the presence of cross sections three orders of magnitude greater. Double, triple, and quadruple transfers were observed. The electron-loss cross sections appear to pass through maxima when the velocity of the ion is in the vicinity of the velocity of the electron to be lost. Single-electron-capture cross sections have magnitudes as large as ${10}^{\ensuremath{-}17}$ ${\mathrm{cm}}^{2}$ at 40 MeV in argon, and depend on velocity approximately as ${V}^{\ensuremath{-}n}$, where $n$ lies between 3 and 6 for the heavy gases. The importance of capture from inner shells of the heavy gases is inferred by comparison with helium, in which $n$ is 8 or 9 and the cross sections are relatively small. The possibility of capture into the $K$ shell of the oxygen ion is suggested by the systematic differences observed in capture by +7 and +8 oxygen ions from capture by lower-charged ions.

Vibrational Excitation and Compound States in NO

Abstract: The cross section for elastic scattering by electron impact on NO shows resonances in the energy range 0-2 eV. These resonances, with a spacing of about 0.16 eV (${\ensuremath{\omega}}_{e}=0.17$ eV), are associated with vibrational levels of ${\mathrm{NO}}^{\ensuremath{-}}$, and there is a near-coincidence in energy between the 4th vibrational state of NO and the 6th vibrational state of ${\mathrm{NO}}^{\ensuremath{-}}$. The width of these resonances increases monotonically from 0.02 to 0.10 eV as the vibrational quantum number of ${\mathrm{NO}}^{\ensuremath{-}}$ goes from 1 to 6. The energy dependence of the vibrational cross sections exhibits peaks at the positions of these resonances, and the magnitude of these peaks is measured. The vibrational states of ${\mathrm{NO}}^{\ensuremath{-}}$ can decay by the emission of an electron into various vibrational levels of NO. The branching ratio for a few of these decays is measured. A potential energy diagram of ${\mathrm{NO}}^{\ensuremath{-}}$ is drawn, using the experimental evidence.

Temperature and Energy Dependence of Proton Dechanneling in Silicon

Abstract: The dechanneled fractions of protons impinging along the $〈111〉$ and $〈110〉$ axial directions of Si have been measured for ion energies between 0.3 and 1.5 MeV and for target temperatures ranging between 80 and 423 \ifmmode^\circ\else\textdegree\fi{}K. The dechanneled fraction is a linear function of the penetration depth $z$. Its dependence on beam energy $E$ and the target temperature $T$ can be described simply through the parameter $\frac{z{\ensuremath{\rho}}^{2}}{E}$, ${\ensuremath{\rho}}^{2}$ being the mean-square vibrational amplitude normal to the row. All the experimental points follow a unique linear trend if plotted vs $\frac{z{\ensuremath{\rho}}^{2}}{E}$. The dechanneled fraction for the $〈110〉$ axis is a factor of 2 lower than that for the $〈111〉$. A theoretical model has been developed to describe the dechanneling in terms of a steady increase in the transverse energy, accounting for both electronic and nuclear reduced multiple scattering. The initial transverse-energy distribution of the particle just beneath the crystal surface has been computed including the experimental angular spread, and both scatterings produced by the amorphous layers covering the surface and by the atomic string potential. The limiting transverse energy for the channeled-to-random transition has been taken from the experimental ${\ensuremath{\psi}}_{\frac{1}{2}}(T)$ values. The computed dechanneled fractions agree reasonably well with the experimental ones and justify their temperature and energy dependence. The calculated fractions differ from the experimental ones in their having an upward curvature; the significance of this disagreement is briefly discussed together with the approximations involved.

On‐Frequency Masking with Continuous Sinusoids

Abstract: The detectability of brief, 1000‐Hz sinusoids added in phase or in quadrature to a continuous tonal masker (pedestal) of the same frequency as the signal was examined in the presence of a continuous wide‐band noise. The effects of signal duration, shape of the signal's energy‐density spectrum, sound‐pressure level (SPL) of the pedestal, and noise spectrum level were investigated. For conditions in which the background noise level was low, two unusual phenomena were noted: (1) a complete absence of the customary trading relation between signal power and duration; and (2) an extremely shallow masking function relating signal SPL and pedestal level. These departures from the law of temporal integration and Weber's law are consistent with a simple filter model of the ear in which it is assumed that the location of the auditory filter is altered in response to changes in the parameters of the signal and masker. A basic assumption of the model is that the location of the filter is changed in order to maximize the ratio of signal energy to masker energy at the output of the filter. For detection of a tonal signal in the presence of another sinusoid, it appears that observers can listen at frequencies far removed from that of the signal, where signal energy is as much as 40 dB down from the peak.

Method and apparatus for actuating an electric circuit

Abstract: A field of electrostatic, electromagnetic or high frequency radiant energy is provided on a predetermined intermittent cycle in a confined space through which persons are directed. A tuned resonant circuit, concealed on merchandise being carried through the space, is activated by the energy field. During the time interval when the energy field is cut off, the decaying electric signal from the tuned resonant circuit is radiated to a receiver. The received electric signal functions to activate an alarm.

He 3 ( He 3 , 2 p ) He 4 Total Cross-Section Measurements Below the Coulomb Barrier

Abstract: Measurements of total cross sections for $^{3}\mathrm{He}(^{3}\mathrm{He},2p)^{4}\mathrm{He}$ have been made for center-of-momentum energies between 80 keV and 1.1 MeV. A continuously recirculating differentially pumped gas target system was employed to minimize uncertainties in energy loss and straggling. A calorimetric device was used to integrate the beam current within the target gas. Proton angular distributions were measured at seven energies. The measured cross-section factor, $S(E)$, was fitted to a linear function of energy for ${E}_{\mathrm{c}.\mathrm{m}.}l500$ keV: $S({E}_{\mathrm{c}.\mathrm{m}.})={S}_{0}+{{S}_{0}}^{\ensuremath{'}}{E}_{\mathrm{c}.\mathrm{m}.}$, where ${S}_{0}=({5.0}_{\ensuremath{-}0.4}^{+0.6})$ MeVb and ${{S}_{0}}^{\ensuremath{'}}=(\ensuremath{-}1.8\ifmmode\pm\else\textpm\fi{}0.5)$ b. The formula $S({E}_{\mathrm{c}.\mathrm{m}.})={S}_{0}+{{S}_{0}}^{\ensuremath{'}}{E}_{\mathrm{c}.\mathrm{m}.}+\frac{1}{2}{{S}_{0}}^{\ensuremath{'}\ensuremath{'}}{E}_{\mathrm{c}.\mathrm{m}.}^{2}$, with ${S}_{0}=5.2$ MeVb, ${{S}_{0}}^{\ensuremath{'}}=\ensuremath{-}2.8$ b, and ${{S}_{0}}^{\ensuremath{'}\ensuremath{'}}=2.4$ b Me${\mathrm{V}}^{\ensuremath{-}1}$ gives a good representation of $S(E)$ over the entire range of energies studied here.

Multiple Scattering of Heavy Ions of keV Energies Transmitted through Thin Carbon Films

Abstract: This paper describes experimental studies of multiple scattering of 13 different heavy ions with $3\ensuremath{\le}{Z}_{1}\ensuremath{\le}30$ in the energy range of 200-1000 keV, transmitted through thin (8-25 \ensuremath{\mu}g/${\mathrm{cm}}^{2}$) carbon foils. The agreement between our experimental data, recent theoretical calculations, and published experimental data is found to be satisfactory, although a small systematic deviation exists for thicker foils.

Low-Energy Photo-Ionization of the 1 S 1 and 2 S 1 States of He

Abstract: The photo-ionization cross sections of the $1^{1}S$ and $2^{1}S$ states of He were evaluated in the energy regions 0.20-2.40 Ry and 3.15-3.30 Ry. The 56-term $^{1}S$ bound-state wave functions obtained by Pekeris were used for the initial states. An expansion into a complete discrete basis set (a modification of the close-coupling method used in electron-atom scattering) was carried out for the $^{1}P$ final-state continuum wave functions. Particular attention was given to the processes where the ejected photoelectron leaves the ${\mathrm{He}}^{+}$ ion in an $n=2$ excited state. The results obtained from the length and velocity expressions for the photo-ionization cross sections show an agreement to within 1% in the lower-energy region. Good accuracy is achieved for the negative-power moments of the oscillator-strength distributions.

Errors in Time Delay Measurements

Abstract: Simple delay and sum of sensors in a seismic array is an effective method for noise suppression. However, unless we have precise steering delays, much of the signal energy is lost during the beam forming process too. We have investigated possible error sources in time delay measurements, using a computerized cross-correlation procedure. Parameters perturbed are correlation window length and positioning, signal frequency content and signal to noise ratio (SNR). Our results indicate that relative low frequency waves and using the very first part of theP-signals give the most reliable and stable time delay values. High frequency bandpass filtering improves SNR, but signal correlation and the precision in beam steering corrections decrease. Significant loss of high frequency energy during beamforming seems to be unavoidable.

Ergodic Boundary in Numerical Simulations of Two-Dimensional Turbulence

Abstract: In numerical calculations, we observe a dichotomy in the time evolution of solutions of the high-Reynolds-number, two-dimensional, incompressible Navier-Stokes equations using power-law initial modal energy spectra $E(\ensuremath{\kappa},0)\ensuremath{\sim}{\ensuremath{\kappa}}^{\ensuremath{-}{\ensuremath{\mu}}_{0}}$. The boundary is expressed in terms of critical values of viscosity ${\ensuremath{ u}}_{\mathrm{cr}}$ and microscale ${\ensuremath{\lambda}}_{\mathrm{cr}}$. For both parameters initially above critical, $\ensuremath{\mu}$ approaches 4. For both parameters initially below critical, $\ensuremath{\mu}$ approaches 1 at large $\ensuremath{\kappa}$, consistent with equipartition of the vorticity spectrum. In the former case, large-scale vortex states form after a long time; and, in both cases, energy flows to the lowest wave numbers.

Position locating systems

Abstract: Position location and plotting is mechanized and accurately accomplished in a system employing a movable transmitter of acoustic signals and at least two acoustic receivers whose position is fixed The system measures transit time from the transmitter to the receivers It measures propagation velocity of the acoustic signal to determine distance from the transmitter to the two receivers and ultimately locates the transmitter''s position relative to the two receivers A signal of a kind that is more rapidly propagated than acoustic signals is generated simultaneously with initiation of the acoustic signal to form a start signal Receipt of the acoustic signal at the receivers is made the occasion for generating a stop signal and the distance computation is made on the basis of the time interval elapsing between the start and stop signals In the preferred embodiment the transmitter comprises a spark gap and the start signal is an electrical signal which is provided as an incident to current flow through the gap A second spark gap, and means for developing a second start signal, has a fixed position relative to the two receivers That arrangement is utilized to provide a high order of accuracy To enhance accuracy even more, the two spark gaps are miniaturized and the structure for supplying energy currents to them and for developing start signals are made similar and the two systems are energized alternately from a common source Special microphones receive acoustic signals at a known distance from a reference position whereby point-to-point distance and direction is accurately measured