Phase Shift Data Research Articles

Relay oscillation method for estimation of sorption kinetics in the biporous adsorption

Estimation of sorption kinetics in a biporous adsorbent has been complicated by the difficulty in separating the effective macro- and micro-pore diffusivities. Often the two diffusivities are interrelated so that several combinations of the parameters yield virtually identical time responses. Since the effect of transport resistances in the macro- and micro-pore often occurs at the same frequency ranges, even the frequency response method which has been successful for many processes having multiple transport resistances also becomes ineffective in the estimation. To determine the two diffusivities simultaneously in the continuous flow adsorption process with bidisperse adsorbents, an improved frequency response method is proposed. The phase shift characteristic function is shown to have better sensitivity for the two diffusivities than the usual out-of-phase characteristic function in the frequency response method. To obtain the phase shift data accurately by reducing the effects of experimental disturbances, often pronounced in the open loop frequency response tests, closed loop tests with the relay oscillations whose frequencies are highly dependent on the phase shift of the process are proposed.

Relativistic unitary description ofππscattering

A unitary framework based on the Bakamjian-Thomas construction of relativistic quantum mechanics is used to describe two-pion scattering from threshold to 1400 MeV. The framework properly includes unitarity cuts for one-, two- and three-hadron states and provides an excellent description of the available data for pi pi phase shifts and inelasticities. The role and importance of three-hadron cuts are calculated and discussed.

Porous thin films for thermal barrier coatings

A new approach is described in the deposition of thin films for thermal barrier applications. Using controlled substrate motion, porous layers and capping layers were vacuum deposited in an alternating fashion, creating a new, multilayered film structure. Direct measurements of the thermal properties of these multilayers were made using the 3ω and Mirage techniques. In the 3ω technique, heat is introduced into the coating by an AC current flowing through an evaporated resistor with a frequency ω. A fit of resistor voltage as a function of frequency yields the thermal conductivity. In the Mirage technique, an oscillating temperature is induced immediately above the film using a pulsed laser. A second probe laser aligned parallel to the surface is deflected by these temperature variations, and the thermal diffusivity is then found by fitting amplitude and phase shift data to the solution of the three-dimensional diffusion equation. Typically, the 3ω and Mirage techniques measure thermal constants in directions normal and parallel to the substrate, respectively. Measurements using these methods led to estimates of a reduction in thermal diffusivity of as little as 9% of that of films deposited entirely at normal incidence. Thermal simulations of similar structures also predicted a substantial decrease in overall thermal conductivity. In a specific case, an improved conductivity of 18% of that of films deposited by standard techniques was estimated.

Scanning probe microscopy and enhanced data analysis on lignin and elemental-chlorine-free or oxygen-delignified pine kraft pulp

Fibres from conventional pine kraft pulp (KP), oxygen-delignified KP (KPO) and elemental-chlorine-free (ECF) bleached KP were characterized by scanning probe microscopy (SPM). The surface morphology of lignin isolated from the respective pine KP was studied. The data analysis of the phase-shift data measured by using different tapping mode imaging parameters enabled the study of both the surface amphiphility and stiffness as a function of delignification. The average phase-shift values were observed to correlate to the respective kappa values, when imaging with small tapping amplitude (30 nm), referred to the capability of SPM to follow local amphipilic (adhesion) differences on a wood fibre surface. The roughness (standard deviation) of the average phase-shift values was taken as a measure of the sample homogeneity. The mean morphological roughness was observed to increase with decreasing bulk lignin concentration. The surface of lignin appeared mainly granular but occasionally some linear structures were observed. The surface roughness of different fractions of flow-through residual lignin samples correlated quite well to the molar mass of the respective fraction. Each grain contained hundreds of lignin molecules. Most of the lignin samples were homogeneous as regards friction and phase-contrast images. The surface of the nondelignified pine KP was typically granular. ECF delignification was more effective than oxygen delignification in removing this granular phase. The decrease in the relative amount of the granular phase correlated to a decreasing kappa value of the pulp. The granular phase is thus suggested to correspond to lignin, but it cannot be ruled out that small amounts of hemicellulose, extractives or a mixture of these components are embedded in this phase. The surface concentration of the granular phase of the KPO samples was, according to the phase-contrast images, clearly higher than the bulk lignin concentration, as indicated by the corresponding kappa values.

σ and κ in Scattering Processes and New π^0π^0 Phase Shift Data(§2. ππ/Kπ Scattering,Possible Existence of the σ-Meson and Its Implications to Hadron Physics)

σ and κ in Scattering Processes and New π^0π^0 Phase Shift Data(§2. ππ/Kπ Scattering,Possible Existence of the σ-Meson and Its Implications to Hadron Physics)

π0π0 scattering amplitudes and phase shifts obtained by the π−p charge exchange process

The results of the analysis of the π 0 π 0 scattering amplitudes obtained with π − p charge exchange reaction, π − p → π 0 π 0 n, data at 9 GeV/c are presented. The π 0 π 0 scattering amplitudes show clear f 0(1370) and f 2(1270) signals in the S and D waves, respectively. The π 0 π 0 scattering phase shifts have been obtained below K K threshold and been analyzed by the Interfering Amplitude method with introduction of negative background phases. The results show a S wave resonance, σ. Its Breit-Wigner parameters are in good agreement with those of our previous analysis on the π + π − phase shift data.

Pion-nucleon interaction in a covariant hadron-exchange model

We develop a relativistic covariant and unitary description of the pion-nucleon interaction in a hadron-exchange model. The model is based on the solution of a dimensionally reduced (quasipotential) Bethe-Salpeter equation for the partial-wave off-shell $\pi N$ scattering amplitudes with the potential consisting of the field-theoretical $s$- and $u$-channel nucleon, Roper, Delta, $D_{13}$, $S_{11}$ exchanges, and the $t$-channel $\rho$ and $\sigma$ meson exchanges. The contributions of the spin-3/2 Delta and $D_{13}$ resonances are treated within the Rarita-Schwinger formalism and different forms of the $\pi N\Delta$ vertex are investigated. The free parameters of the model are fitted to the $\pi N$ phase-shift data of the KH80 and SM95 partial-wave analyses in the region up to 600 MeV pion kinetic energy. The resulting on-shell solution provides a good description of the $\pi N$ scattering lengths, as well as the energy behavior of the S, P, and D partial waves. The sensitivity of the phase shifts on various model-dependent effects is examined.

A higher-order calculation of np scattering in cut-off effective field theory

We report a next-to-leading-order (NLO) chiral perturbation theory calculation of the neutron-proton scattering cross section in the 1S 0 channel using a cut-off regularization. The inclusion of two-pion exchanges in the irreducible diagrams – or potential – figuring at NLO is found to be important in enlarging the domain of validity of the effective field theory. We are able to reproduce the scattering phase shift data up to p=300 MeV, with an agreement which is superior to results of other effective field theory approaches. We also discuss the importance of the explicit pion degree of freedom in scattering process.

Analysis of partial-height ferrite-slab differential phase-shift sections

Rectangular waveguide loaded with transversely magnetized ferrite slabs is a classic arrangement used in the construction of high-power differential phase-shift circulators. The characterization of this structure is extended in this paper by using a combined magnetostatic/microwave finite-element method to evaluate propagation characteristics in terms of material parameters, frequency, and bias field. Magnetic flux density was found to vary by typically 20% across a partial-height ferrite slab. Experimental phase-shift data agreed to within 5% of numerical calculations for a 9.25-GHz device. Supplementary design data are presented for the first higher order mode in the cutoff plane, the effect of material properties on phase shift, and to compare below and above resonance operation.

Sub-CoulombαTransfers onC12and theC12(α,γ)O16SFactor

The {sup 12}C( {alpha}, {gamma}){sup 16}O reaction is crucial for the understanding of He burning in massive stars, but the low-energy cross section is highly uncertain. To address this problem we have measured at sub-Coulomb energies total cross sections for the {sup 12}C( {sup 6}Li, d){sup 16}O and {sup 12}C( {sup 7}Li, t) {sup 16}O reactions to the bound 2{sup +} and 1{sup -} states of {sup 16}O . The data are analyzed to obtain the reduced {alpha} widths of these states. Together with capture and phase-shift data, these results provide for a more accurate determination of the low-energy 12C({alpha}, {gamma}){sup 16}O S factor: S{sub E1}(0.3 MeV) =101{+-}17 keV b and S{sub E2}(0.3 MeV) =42{sup +16}{sub -23} keV b for the E1 and E2 multipole components of the reaction. (c) 1999 The American Physical Society.

Np→dγfor big-bang nucleosynthesis

The cross section for n+p -> d+gamma is calculated at energies relevant to big bang nucleosynthesis using the recently developed effective field theory that describes the two-nucleon sector. The E1 amplitude is computed up to NNNLO and depends only upon nucleon-nucleon phase shift data. In contrast, the M1 contribution is computed up to NLO, and the four-nucleon-one-magnetic-photon counterterm that enters is determined by the cross section for cold neutron capture. The uncertainty in the calculation for nucleon energies up to E ~ 1 MeV is estimated to be < 4%.

The a0(980), a0(1450) and [formula omitted] scalar decay constants and the isovector scalar spectrum

The scalar correlator Π(q 2)=i ∫ d 4x e iq·x〈0|T J(x)J †(0) |0〉 (with J=∂ μ d ̄ γ μu ) is studied using a class of finite energy sum rules shown recently to be very well satisfied in the vector isovector channel. The values of the a 0 scalar decay constants extracted in this analysis, which describe the couplings of the a 0(980) and a 0(1450) to the current J, are shown to be comparable, strongly disfavoring any scenario in which the a 0(980) is interpreted as a loosely bound K K ̄ molecule and the a 0(1450) is assigned to the same flavor multiplet as the K 0 ∗(1430) . The a 0 decay constants are also compared to the analogous decay constant describing the coupling of the K 0 ∗(1430) to the divergence of the strange vector current, J s=∂ μ s ̄ γ μu (which may be obtained from experimental K e3 and Kπ phase shift data) and implications of the relative magnitudes for the interpretation of the nature of the a 0 states discussed.

The viscosity cross-section for elastic electron-xenon collisions including electron spin polarization

The results of the evaluation of the viscosity cross-section for elastic electron-xenon collisions, taking into account the spin-orbit interaction of the continuum electron, in the energy interval from 0.1 eV to 50 eV are presented and discussed. The calculations are performed on the basis of three theoretically derived sets of phase shift data obtained by different authors and on the deduced relativistic expression for the viscosity cross-section in terms of phase shifts discerning the spin-up and spin-down states of the scattered electrons. Comparison with viscosity cross-sections, as evaluated from non-relativistic phase shifts extracted from experiments, strongly favours the relativistic results. The assumption of isotropic scattering is critically examined and the error induced by its use is shown to persist to the same extent as in non-relativistic calculations, at least in the energy region considered.

Nucleon-nucleon effective field theory without pions

Nuclear processes involving momenta much below the mass of the pion may be described by an effective field theory in which the pions do not appear as explicit degrees of freedom. The effects of the pion and all other virtual hadrons are reproduced by the coefficients of gauge-invariant local operators involving the nucleon field. Nucleon-nucleon scattering phase shift data constrains many of the coefficients that appear in the effective Lagrangean but at some order in the expansion coefficients enter that must be constrained by other observables. We compute several observables in the two-nucleon sector up to next-to-next-to leading order in the effective field theory without pions, or to the order at which a counterterm involving four-nucleon field operators is encountered. Effective range theory is recovered from the effective field theory up to the order where relativistic corrections enter or where four-nucleon-external current local operators arise. For the deuteron magnetic moment, quadrupole moment and the np → dγ radiative capture cross section a four-nucleon-one-photon counterterm exists at next-to-leading order. The electric polarizability and electric charge form factor of the deuteron are determined up to next-to-next-to-leading order, which includes the first appearance of relativistic corrections.

LONG-RANGE CORRELATIONS IN THE PHASE-SHIFTS OF NUMERICAL SIMULATIONS OF BIOCHEMICAL OSCILLATIONS AND IN EXPERIMENTAL CARDIAC RHYTHMS

In biochemical dynamical systems during each transition between periodical behaviors, all metabolic intermediaries of the system oscillate with the same frequency but with different phase-shifts. We have studied the behavior of phase-shift records obtained from random transitions between periodic solutions of a biochemical dynamical system. The phase-shift data were analyzed by means of Hurst's rescaled range method (introduced by Mandelbrot and Wallis). The results show the existence of persistent behavior: each value of the phase-shift depends not only on the recent transitions, but also on previous ones. In this paper, the different kind of periodic solutions were determined by different small values of the control parameter. It was assessed the significance of this results through extensive Monte Carlo simulations as well as quantifying the long-range correlations. We have also applied this type of analysis on cardiac rhythms, showing a clear persistent behavior. The relationship of the results with the cellular persistence phenomena conditioned by the past, widely evidenced in experimental observations, is discussed.

Another look atππscattering in the scalar channel

We set up a general framework to describe $\ensuremath{\pi}\ensuremath{\pi}$ scattering below 1 GeV based on chiral low-energy expansion with possible spin-0 and -1 resonances. Partial wave amplitudes are obtained with the $N/D$ method, which satisfy unitarity, analyticity, and approximate crossing symmetry. A comparison with the phase shift data in the $J=0$ channel favors a scalar resonance near the $\ensuremath{\rho}$ mass.

Low energy theorems for nucleon-nucleon scattering

Low energy theorems are derived for the coefficients of the effective range expansion in s-wave nucleon-nucleon scattering valid to leading order in an expansion in which both ${m}_{\ensuremath{\pi}}$ and $1/a$ (where a is the scattering length) are treated as small mass scales. Comparisons with phase shift data, however, reveal a pattern of gross violations of the theorems for all coefficients in both the ${}^{1}{S}_{0} \mathrm{and}{ }^{3}{S}_{1}$ channels. Analogous theorems are developed for the energy dependence $\ensuremath{\epsilon}$ parameter which describes ${}^{3}{S}_{1}{\ensuremath{-}}^{3}{D}_{1}$ mixing. These theorems are also violated. These failures strongly suggest that the physical value of ${m}_{\ensuremath{\pi}}$ is too large for the chiral expansion to be valid in this context. Comparisons of ${m}_{\ensuremath{\pi}}$ with phenomenological scales known to arise in the two-nucleon problem support this conjecture.

Regularization and renormalization in effective field theories of the nucleon-nucleon interaction

Some form of nonperturbative regularization is necessary if effective field theory treatments of the NN interaction are to yield finite answers. We discuss various regularization schemes used in the literature. Two of these methods involve formally iterating the divergent interaction and then regularizing and renormalizing the resultant amplitude. Either a (sharp or smooth) cutoff can be introduced, or dimensional regularization can be applied. We show that these two methods yield different results after renormalization. Furthermore, if a cutoff is used, the NN phase shift data cannot be reproduced if the cutoff is taken to infinity. We also argue that the assumptions which allow the use of dimensional regularization in perturbative EFT calculations are violated in this problem. Another possibility is to introduce a regulator into the potential before iteration and then keep the cutoff parameter finite. We argue that this does not lead to a systematically-improvable NN interaction.

Pion-pion scattering at low energy

We present technical details of the evaluation of the elastic ππ scattering amplitude to two loops in chiral perturbation theory. In particular, we elaborate on the renormalization procedure at the two-loop order and on the evaluation of the relevant Feynman diagrams that can all be expressed in terms of elementary functions. For the sake of clarity, we discuss these matters both in the N- component φ 4 theory (in its symmetric phase) and in chiral perturbation theory. Estimates for the relevant low-energy constants of O( p 6) are presented. Threshold parameters and phase shifts are then calculated for two sets of O( p 4) coupling constants and compared with experiment. We comment on the extraction of threshold parameters from phase shift data.

ππ,Kπ, andπNpotential scattering and a prediction of a narrowσmeson resonance

Low energy scattering and bound state properties of the \pi N, \pi\pi and K\pi systems are studied as coupled channel problems using inversion potentials of phase shift data. In a first step we apply the potential model to explain recent measurements of pionic hydrogen shift and width. Secondly, predictions of the model for pionium lifetime and shift confirm a well known and widely used effective range expression. Thirdly, as extension of this confirmation, we predict an unexpected medium effect of the pionium lifetime which shortens by several orders of magnitude. The \sigma meson shows a narrow resonance structure as a function of the medium modified mass with the implication of being essentially energy independent. Similarly, we see this medium resonance effect realized for the K\pi system. To support our findings we present also results for the \rho meson and the \Delta(1232) resonance.