Search

The missing-mass technique has been used to study the spectra of neutral mesons produced by 2- and 3-Gev protons in the reaction $p+d\ensuremath{\rightarrow}{\mathrm{He}}^{3}+{x}^{0}$. Cross sections ($\frac{d\ensuremath{\sigma}}{{d\ensuremath{\Omega}}_{\mathrm{c}.\mathrm{m}.}}$) of about ${10}^{\ensuremath{-}34}$ ${\mathrm{cm}}^{2}$/sr were observed for the $\ensuremath{\pi}$, $\ensuremath{\eta}$, and $\ensuremath{\omega}$ for 3-GeV protons. A peak with a much smaller cross section was observed at a mass of 956 MeV. We have tentatively identified this peak as the ${\ensuremath{\eta}}^{\ensuremath{'}}$. Cross sections for the $\ensuremath{\pi}$ and $\ensuremath{\eta}$ were nearly a factor of 10 larger at 2 GeV than at 3 GeV. Deviations from simple phase space were observed near the two-pion threshold in both 2-GeV and 3-GeV data. Details of the experimental method and of the results are presented.

The parity-violating asymmetry of the total cross section for the scattering of longitudinally polarized nucleons from unpolarized proton targets is calculated for energies of 300 MeV-20 GeV. One-pion, $\ensuremath{\rho}$, and $\ensuremath{\omega}$ exchanges are included in the computation of the weak force between nucleons. Below energies of roughly 1 GeV, the Watson theorem is adapted to compute the asymmetry. At higher energies an absorptive model is used to take into account hadronic distortion effects.

We prove that $$\mathop {L_n \in Z_n }\limits^{\inf } \mathop \omega \limits^{sup^* } \mathop {f \in H_\omega }\limits^{\sup } \frac{{\left\| {f - L_n \left( f \right)} \right\|}}{{\omega \left( {\frac{\pi }{{n + 1}}} \right)}} = 1\left( {n = 0,1,2,...} \right)$$ (n=0,1,2,...), where $$\mathop {L_n \in Z_n }\limits^{\inf } $$ is taken over all linear polynomial approximation methods of degree not higher than n and $$\mathop \omega \limits^{sup^* } $$ over all convex moduli of continuity ω(δ).

Combinations of deformation, aging, and reversion heat treatments have been investigated as a basis for improving the strength and ductility of beta-stabilized titanium alloys. Suitable control over the volume fraction of the omega phase in the s-III alloy results in enhanced yield strength combined with some ductility. Deformation of the beta phase in the quenched s-III alloy promotes bi-modal precipitation of the alpha and omega phases. The stability of the fine alpha particles maintains high strength with some improvement of ductility after the omega phase has been reverted.

Single crystals of metastable BCC Ti-6.5 at.% Mo alloy have been aged at 350°C for varying times to precipitate the omega phase. The variation in volume fraction of precipitate was determined by a quantitative X-ray diffraction technique and correlated with transmission electron microscopy from thin foils. For Ti-Mo alloys the lattice misfit between omega and beta phases is small; reflections from parallel planes of both phases overlap necessitating the use of reflections from nonparallel planes. The 310 beta reflection and 31 4 1 and 30 3 2 omega reflections were selected. These two omega reflections occurred at 96° and 105° 2θ angles with CuKα radiation and required a 14° reorientation of the crystal.

The ion-implantation\char22{}perturbed-angular-correlation technique (IMPACT) has been used to measured the $g$ factor of the 204-keV ${\frac{3}{2}}^{+}$ level in $^{95}\mathrm{Mo}$ nuclei recoiled into ferromagnetic iron and cobalt hosts. The observed angular precessions were $\ensuremath{\omega}\ensuremath{\tau}(Fe \mathrm{Mo})=0.32\ifmmode\pm\else\textpm\fi{}0.05$ and $\ensuremath{\omega}\ensuremath{\tau}(Co \mathrm{Mo})=0.18\ifmmode\pm\else\textpm\fi{}0.03$. The available direct lifetime measurements for the 204-keV states and the NMR hyperfine field measurements for molybdenum solutes in iron and cobalt are used to obtain the gyromagnetic ratio $g(204)=\ensuremath{-}0.24\ifmmode\pm\else\textpm\fi{}0.03$. The sign of the hyperfine field for molybdenum in iron host was found to be negative.

The photoelectron energy distribution curves for CuCl, CuBr, CuI, and AgI have been measured for $\ensuremath{\hbar}\ensuremath{\omega}=16.8, 21.2, 26.9, 40.8, 48.4, \mathrm{and} 1486.6$ eV. By exploiting the strong dependence on $\ensuremath{\hbar}\ensuremath{\omega}$ of the photoionization cross sections of the atomic levels comprising the valence band, we have been able to determine the $s$, $p$, and $d$ partial densities of valence states. These results compare well with those obtained by x-ray fluorescence and x-ray photoemission, but have better resolution. It is found that the $d$ levels of ${\ensuremath{\Gamma}}_{12}$ symmetry remain corelike, while the ${\ensuremath{\Gamma}}_{15}$ $d$ levels band significantly. In the Cu compounds the ${\ensuremath{\Gamma}}_{15}$ levels of predominantly $d$ character lie above the ${\ensuremath{\Gamma}}_{12}$ bands, which in turn lie above the mainly $p$-like ${\ensuremath{\Gamma}}_{15}$ levels. This level ordering is reversed in AgI. The band structure and densities of valence states computed from a seven-function basis set, consisting of four bonding $s\ensuremath{-}p$ orbitals and three ${d}_{\mathrm{xy}}$ orbitals, are shown to reproduce the trends observed in the density of valence states of these compounds.

A general framework is set up for the description of quantum-mechanical scattering processes for the case that both the free hamiltonian H0(t)=H0+H1(t) and the full hamiltonian H(t)=H0(t)+V are time-dependent. In particular the existence of the various evolution operators is considered and the wave operators Omega +or-(s), which now depend on the initial time s, are defined. The consequences of a periodic time dependence are studied and for H1(t) of the type H1(t)=H1 cos( omega t+ delta ) it is shown that for mod omega mod to infinity the frequency-dependent wave operators converge to the wave operators which pertain to the case that H1(t) is absent.

The study of the dynamic stabilization of certain plasma confinement and fluid systems leads to equations of the form $$(X + 2A\cos (\omega t - \phi ))y(t) + \int_0^t {R(t - t')\dot y(t')dt' = 0} $$ , whereX andA are constants, ϕ an arbitrary phase andR(t) a singular response function. This equation is solved for all values ofA and the general stability properties of the system are discussed. General formulae are given which relate the perturbed spectrum of the system to the unperturbed system. For the case where the static system has well separated eigenfrequencies, a perturbation expansion is derived.

Sufficient conditions are given here for the existence and stability of a possibly infinite sequence of isolated periodic solutions of the nonautonomous system of differential equations \[ \ddot y_k + \omega _k^2 y_k = \mu f_k \left(y_1 , \cdots ,y_n ,\dot y_1 , \cdots ,\dot y_n ,t\right) \], where $0 < \mu \ll 1,k = 1, \cdots ,n$. An $O(\mu )$ estimate of the amplitude of each of these periodic solutions is also obtained.

Measurements have been made on different composition V2O5-P2O5 glasses in the frequency range 102 Hz to 105 Hz and in the temperature range 77K to 300K, for different times of annealing up to 300 degrees C. No effect of annealing was observed, indicating that the frequency-dependent AC conductivity is an intrinsic property of the material. A comparison of the measured AC conductivity sigma ( omega ) has been made with some of the models of hopping conductivity proposed earlier in the literature. It is observed that in vanadate glasses the measured AC conductivity sigma ( omega ), over the entire frequency and temperature region can be explained reasonably well by assuming two contributions sigma 1( omega ) and sigma 2( omega ) to the measured sigma ( omega ). The first, sigma 1( omega ) which dominates at low temperatures, may be due to hopping of carriers near the Fermi level and the second, sigma 2( omega ), which dominates at higher temperatures, depending on the frequency of measurement, may be due to the hopping of carriers excited to the conduction band edge and is responsible for the activated dielectric loss peak.

End-on framing photographs taken at the Garching 500-kV theta pinch during fast magnetic plasma compression [${n}_{0}=(1.5\ensuremath{-}4)\ifmmode\times\else\texttimes\fi{}{10}^{13}$ ${\mathrm{cm}}^{\ensuremath{-}3}$] show distinct radial filaments that are due to flute instabilities of high azimuthal-mode number. The observed wavelengths are of the order $\frac{c}{{\ensuremath{\omega}}_{{p}_{i}}}$ they decrease with increasing density, but no mass dependence is found. The flute instabilities are responsible for the existence of a plasma halo which surrounds the thermonuclear $\ensuremath{\beta}=1$ plasma column and has a major influence on its behavior.

Fully automatic Omega navigation systems have been demonstrated and are beginning to be used operationally in aircraft and other vehicles. A natural question is the accuracy achieved by such systems. Concern over the probability of maintaining correct lane identification complicates this question. Use of the root-mean-square (rms) statistics is shown to be a misleading measure of operational performance. Alternate methods of specifying the navigational errors of automatic Omega navigators are discussed. Cumulative percentile plots are recommended for the specification of errors. Use of Weibull probability paper to study radial error trends is demonstrated. Illustrations of error analysis techniques are given, based on actual Omega flight test data.

Specific-heat and electrical-resistivity measurements in Ce${\mathrm{Al}}_{3}$ below 0.2 K reveal enormous magnitudes of the linear specific-heat term $C=\ensuremath{\gamma}T$ ($\ensuremath{\gamma}=1620$ mJ mole/${\mathrm{K}}^{2}$) and the ${T}^{2}$ term in $\ensuremath{\rho}=A{T}^{2}$ ($A=35$ \ensuremath{\mu}\ensuremath{\Omega} cm/${\mathrm{K}}^{2}$). We conclude that the $4f$ electrons obey Fermi statistics at low temperatures because of the formation of virtual bound $4f$ states.

A simple formula for $S(k,\ensuremath{\omega})$ which was originally established only as an approximation applicable to a boson system is found to hold exactly for any uniform macroscopic system of bosons or fermions. This is deduced by making elementary substitutions in equations written down by Huang and Klein several years ago. A general formula for moments of $S(k,\ensuremath{\omega})$ is derived, and examined for several special cases. The utility of some of these relations in specific perturbation treatments of $S(k,\ensuremath{\omega})$ for liquid ${\mathrm{He}}^{4}$ is discussed. They are also used here to derive a new approximate formula for the kinetic energy per particle in ${\mathrm{He}}^{4}$ in terms of the density and ${\mathrm{He}}^{4}$ liquid-structure fnction. A procedure for applying the formulas in semiphenomenological theories is also outlined.

The optical constants of clean thallium single crystals have been determined in the energy range 0.6 to 5.0 eV, at room temperature and at 80K, for polarizations parallel and perpendicular to the hexagonal axis. The results are discussed in terms of direct interband transitions with constant transition probability matrix elements. The joint density of states calculated from the band structure of Holtham and Priestley (1971) predicts the experimentally observed structure in omega 2 epsilon 2 at h(cross) omega =1.7 eV; however at higher photon energies the resemblance between the calculated and experimental structure in the optical spectra is found to be rather poor.

From energy loss experiments with 51 keV electrons the dependence of the aluminum plasmon energy on the wavevector q has been derived. The measurements are extended to q>qc=1.3 AA-1 (qc=critical wavevector) and reach q approximately=2.2 AA-1. For q qc, however, the loss energy shows only a weak dependence on the wavevector. The results are compared with calculations of the loss function. Im(- epsilon ( omega ,q)-1), using a dielectric function epsilon ( omega , q) that takes into account finite electron lifetime and local field corrections. It is shown that for large q local field effects have a strong influence. The halfwidth of the loss peak has also been obtained as a function of q. It shows a nearly steplike increase near the critical wavevector.

The model for $\ensuremath{\pi}N\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\omega}N$ scattering constructed in a previous paper is applied to the four quasi-two-body reactions ${\ensuremath{\pi}}^{+}p\ensuremath{\rightarrow}\ensuremath{\omega}{\ensuremath{\Delta}}^{++}$, ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}\ensuremath{\omega}n$, ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\rho}}^{0}n$, and ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{B}^{\ensuremath{-}}p$. It is found that reasonable agreement with the data is obtained for the features of the model which do not involve the $B$ meson. It is also found that $B$ exchange is too small to account for the unnatural-parity contribution to the two $\ensuremath{\omega}$-production reactions, indicating that the $\ensuremath{\rho}\ensuremath{-}\ensuremath{\rho}$ cut might be important in these processes.

Measurement of spin polarization of photoelectrons from F${\mathrm{e}}_{3}$${\mathrm{O}}_{4}$ (MAG) and ${\mathrm{Li}}_{0.5}$${\mathrm{Fe}}_{2.5}$${\mathrm{O}}_{4}$ (LIF) up to $\ensuremath{\hbar}\ensuremath{\omega}=11$ eV shows that $B$-site $3d$ levels are higher in energy than $A$-site $3d$ levels. In MAG, unpolarized $2p$ electrons are not emitted up to 11 eV. Existing energy diagrams of MAG do not agree fully with the results. As a direct consequence of Hund's rule, the polarization spectra of MAG and LIF are very different because of the presence of ${\mathrm{Fe}}^{2+}$ in MAG.

The propagation of an electromagnetic wave in a direction perpendicular to both the applied static magnetic field ${\stackrel{\ensuremath{\rightarrow}}{B}}_{0}$ and the static electric field ${\stackrel{\ensuremath{\rightarrow}}{E}}_{0}$ in extrinsic indium antimonide (InSb), and wave instability are studied theoretically. The dispersion equation $D(\ensuremath{\omega},k)$ relating the wave angular frequency $\ensuremath{\omega}$ and the wave number $k$ is derived from Maxwell's equations, the equation of momentum transfer, and the continuity equation, using the magnetohydrodynamic approach and a one-dimensional linearized theory. With the aid of the dispersion relationship, the propagation characteristics of the slow electromagnetic wave in a collision-dominated semiconductor plasma is examined in detail, for both $n$-type and $p$-type materials. The range of parameters considered are $1\ensuremath{\le}f\ensuremath{\le}9$ GHz, $1\ensuremath{\le}{B}_{0}\ensuremath{\le}10$ kG, and $0\ensuremath{\le}{E}_{0}\ensuremath{\le}30$ V/cm, and the variation of the phase velocity of the wave, ${v}_{\ensuremath{\phi}}$, and the amplitude constant of the wave, $\ensuremath{\alpha}\ensuremath{\equiv}\mathrm{Im}(k)$, with the parameters ${B}_{0}$, ${E}_{0}$, and the wave frequency $f$, are investigated. It is shown that under proper conditions wave amplification, defined by $\ensuremath{\beta}\ensuremath{\alpha}g0$, where $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{k}=\ensuremath{\beta}+i\ensuremath{\alpha}$, and the wave instability, defined by ${\ensuremath{\omega}}_{r}{\ensuremath{\omega}}_{i}l0$, where $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\omega}}={\ensuremath{\omega}}_{r}+i{\ensuremath{\omega}}_{i}$, is possible. For example, under the conditions ${(\frac{{\ensuremath{\omega}}_{R}}{\ensuremath{\omega}})}^{2}l1+{\ensuremath{\mu}}_{s}^{2}{B}_{0}^{2}$ and $|\frac{\ensuremath{\nabla}{n}_{0}}{{n}_{0}}|\ensuremath{\ll}|k|$, the threshold condition for the wave amplification, the threshold condition for wave instability, the spatial growth rate ($\ensuremath{\alpha}g0$), the phase velocity ${v}_{\ensuremath{\phi}}$, and the threshold oscillation angular frequency ${\ensuremath{\omega}}_{0}={\ensuremath{\omega}}_{r}$ (for which ${\ensuremath{\omega}}_{i}=0$) as functions of ${E}_{0}$, ${B}_{0}$, $f$, and ${n}_{0}$ are derived, where ${\ensuremath{\omega}}_{R}$ and ${n}_{0}$ denote the dielectric-relaxation angular frequency and the carrier density of the material, respectively. ${\ensuremath{\mu}}_{s}$ denotes the carrier drift mobility which takes a negative value for the electron. The effect of the carrier density gradient on ${v}_{\ensuremath{\phi}}$, $\ensuremath{\alpha}$, and ${E}_{\mathrm{th}}$ (the threshold electric field for instability) is also briefly discussed.

A Green's-function theory of Raman-scattering line-shape asymmetries is developed here for a system in which a one-phonon (discrete) excitation is degenerate with intervalence-band (continuum) excitations. The scattering cross section is expressed in terms of a generalized dynamic form factor, $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{S}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}, \ensuremath{\omega})$, appropriate for the second Born approximation. The $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{S}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}, \ensuremath{\omega})$ is defined in terms of a composite Green's function which describes the quantum interference between the discrete and continuum states. Introducing a model electron-phonon interaction, the techniques of many-body theory are used to solve for $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{S}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}, \ensuremath{\omega})$ in the random-phase approximation. This automatically leads to an expression which yields the desired line shapes, i.e., gives antiresonances. Measurements of scattering line shapes for degenerate $p$-type silicon over a wide spectral range are described. This allows a fit of the theoretical and experimental line shapes. Examination of the analytic structure of $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{S}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}, \ensuremath{\omega})$ leads to the conclusion that there is a new collective excitation of the crystal. This is the result of the quantum interference between the discrete and continuum states. We associate the creation of this excitation with the onset of line-shape asymmetry in the Raman spectrum of the semiconductor.

Using Ti-Mn alloys, an investigation was made into the characteristics of slip and cracking in a structure containing various amounts of alpha in equilibrium with beta phase which was hardened by the precipitation of omega. Precipitation of omega in the beta resulted in total embrittlement of alloys containing 70 per cent beta or more but increasing the amount of alpha to 55 per cent resulted in an elongation of 5 per cent even though beta was still the matrix. Surface observations showed intense heterogeneity of slip within the omega hardened beta which appeared to initiate failure parallel to the slip band. Crack growth is arrested by the softer alpha phase accounting for the increase in ductility with increasing amount of alpha. Thin film transmission electron microscopy revealed a decreased density of omega particles within a slip band suggesting that slip causes a localized dissolution of omega. This would lead to a preferred path for further slip and account for the large heterogeneous offsets observed. It is concluded that the sequence of slip avalanche leading to localized shear failure or cracking is present for all volume per cents of hardened beta, but the observation of this phenomenon becomes more difficult with increased amount of beta due to the increased localization of slip.

Allowing for rotation about the Calpha-C' bond (i.e., variation of psi) and for some degree of freedom about the peptide bond (i.e., small variations of omega), the characteristic ratios, (R2)o/nl2, of the form I (cis) and form II (trans) poly(L-proline) chain have been calculated by a Monte Carlo method in which the conformational energies were used as weighting factors. The Monte Carlo method enabled short-range interactions (beyond those involved in a single residue) to be taken into account. The effect of the presence of a small amount of one form (say cis in a trans-rich chain) on (R2)o/nl2 was also investigated. The results for the trans-rich form are in good agreement with values observed experimentally in solvents in which the poly(L-proline) chain is predominantly in form II; the presence of a small amount of cis residues reduces the characteristic ratio of the trans-rich form of poly(L-proline) significantly.

Let (Ω,A) be a measurable space and Pθ, θ∈H be a family of probability measures on (Ω,A). Let {X n ,n≥1} be a sequence of real valued measurable functions on (Ω,A).A sequence of families of functions $$f_n^\theta :R \to \bar R,\theta \in \bar H,n \geqslant 1$$ ( $$\bar H$$ is the closure ofH $$\bar R = [ - \infty , + \infty ]$$ ) is said to be a sequence of families of contrast functions for {Pθ, θ ∈ H} corresponding to ≏Xn, n≧1≃ if inf {n:Eθ [f n τ (Xn)]−Eθ [f n θ (Xn)]} > 0 for all θ ∈ H, $$\tau \in \bar H$$ , θ ≠ τ. A minimum contrast estimator (MCE) is an estimator θn for which $$\theta _n (X_1 (\omega ),...,X_n (\omega )) \in \bar H$$ for every ω∈ό and $$\sum\limits_{i = 1}^n {f_i^{\theta _n } (x_i ) = \inf \left\{ {\sum\limits_{i = 1}^n {f_1^\theta (x_i ),\theta \in \bar H} } \right\}} $$ . Let {θn,n0 such that for all Θ∈K,n≧1,t∈R, $$\theta \in K, n \geqslant 1, t \in R, |P_\theta (n^{\tfrac{1}{2}} (\theta _n - \theta )< t \beta (\theta )) - \Phi (t)| \leqslant C_K n^{ - \tfrac{1}{2}} $$ where Φ is the standard normal distribution and β (Θ) is a function of Θ related to asymptotic variance. This result generalizes similar result ofPfanzagl in the i.i.d. case. An application to location parameter families is given.