Power-law Energy Dependence Research Articles

Cosmic-Ray Boron Flux Measured from 8.4 GeV/n to 3.8 TeV/n with the Calorimetric Electron Telescope on the International Space Station.

We present the measurement of the energy dependence of the boron flux in cosmic rays and its ratio to the carbon flux in an energy interval from 8.4 GeV/n to 3.8 TeV/n based on the data collected by the Calorimetric Electron Telescope (CALET) during ∼6.4 yr of operation on the International Space Station. An update of the energy spectrum of carbon is also presented with an increase in statistics over our previous measurement. The observed boron flux shows a spectral hardening at the same transition energy E_{0}∼200 GeV/n of the C spectrum, though B and C fluxes have different energy dependences. The spectral index of the B spectrum is found to be γ=-3.047±0.024 in the interval 25<E<200 GeV/n. The B spectrum hardens by Δγ_{B}=0.25±0.12, while the best fit value for the spectral variation of C is Δγ_{C}=0.19±0.03. The B/C flux ratio is compatible with a hardening of 0.09±0.05, though a single power-law energy dependence cannot be ruled out given the current statistical uncertainties. A break in the B/C ratio energy dependence would support the recent AMS-02 observations that secondary cosmic rays exhibit a stronger hardening than primary ones. We also perform a fit to the B/C ratio with a leaky-box model of the cosmic-ray propagation in the Galaxy in order to probe a possible residual value λ_{0} of the mean escape path length λ at high energy. We find that our B/C data are compatible with a nonzero value of λ_{0}, which can be interpreted as the column density of matter that cosmic rays cross within the acceleration region.

Disorder-induced Anderson-like localization for bidimensional thermoelectrics optimization

Disorder-induced Anderson-like localization for bidimensional thermoelectrics optimization

Cascades Damage in γ-Iron from Molecular Dynamics Simulations

The degradation of austenitic stainless steels under irradiation environment is a known problem for nuclear reactors, which starts from atoms displacement cascade. Here, molecular dynamics (MD) simulations have been used to investigate the formation of atomic displacement cascade in γ-iron for energies of the primary knock-on atom (PKA) up to 40 keV at 300 K. The number of Frenkel pairs increased sharply until a peak value was reached, which occurred at a time in the range of 0.1-2 ps. After that, a number of defects gradually decreased and became stabilized. Compared with α-iron, there was less defects in the stable stage, and more clustered defects were produced in γ-iron. Within the range of PKA energies, two regimes of power-law energy-dependence of the defect production were observed, which converge on 16.8 keV. The transition energy also marks the onset of the formation of large self-interstitial atom (SIA) clusters and vacancy clusters. Interstitial and vacancy clusters were in the form of Shockley, Frank dislocation loops and Stir-Rod dislocation loops.

Energy-dependent noncommutative quantum mechanics

We propose a model of dynamical noncommutative quantum mechanics in which the noncommutative strengths, describing the properties of the commutation relations of the coordinate and momenta, respectively, are arbitrary energy-dependent functions. The Schrödinger equation in the energy-dependent noncommutative algebra is derived for a two-dimensional system for an arbitrary potential. The resulting equation reduces in the small energy limit to the standard quantum mechanical one, while for large energies the effects of the noncommutativity become important. We investigate in detail three cases, in which the noncommutative strengths are determined by an independent energy scale, related to the vacuum quantum fluctuations, by the particle energy, and by a quantum operator representation, respectively. Specifically, in our study we assume an arbitrary power-law energy dependence of the noncommutative strength parameters, and of their algebra. In this case, in the quantum operator representation, the Schrö dinger equation can be formulated mathematically as a fractional differential equation. For all our three models we analyze the quantum evolution of the free particle, and of the harmonic oscillator, respectively. The general solutions of the noncommutative Schrödinger equation as well as the expressions of the energy levels are explicitly obtained.

Investigation of the thermoelectric response in conducting polymers doped by solid-state diffusion

Thermoelectric effect is a physical phenomenon which intricately relates the thermal energy of charge carriers to their charge transport. Understanding the mechanism of this interaction in different systems lies at the heart of inventing novel materials which can revolutionize thermoelectric power generation technology. Despite the recent surge of interest in organic thermoelectric materials, the community has had difficulties in formulating the charge transport mechanism in the presence of a significant degree of disorder. Here, we analyze the thermoelectric properties of various conducting polymers doped by solid-state diffusion of dopant molecules based on a transport model with a power law energy dependence of transport function. A fine control of the degree of doping via postdoping annealing provides an accurate empirical evidence of a strong energy dependence of the carrier mobility in the conducting polymers. A superior thermoelectric power factor of conducting polymers doped by solid-state diffusion to that of other doping methods can be attributed to a resulting higher intrinsic mobility and higher free carrier concentration.

Anisotropic Electron Tail Generation during Tearing Mode Magnetic Reconnection.

The first experimental evidence of anisotropic electron energization during magnetic reconnection that favors a direction perpendicular to the guide magnetic field in a toroidal, magnetically confined plasma is reported in this Letter. Magnetic reconnection plays an important role in particle heating, energization, and transport in space and laboratory plasmas. In toroidal devices like the Madison Symmetric Torus, discrete magnetic reconnection events release large amounts of energy from the equilibrium magnetic field. Fast x-ray measurements imply a non-Maxwellian, anisotropic energetic electron tail is formed at the time of reconnection. The tail is well described by a power-law energy dependence. The expected bremsstrahlung from an electron distribution with an anisotropic energetic tail (v_{⊥}>v_{∥}) spatially localized in the core region is consistent with x-ray emission measurements. A turbulent process related to tearing fluctuations is the most likely cause for the energetic electron tail formation.

Linear response of a one-dimensional conductor coupled to a dynamical impurity with a Fermi edge singularity

I study the dynamical correlations that a quantum impurity induces in the Fermi sea to which it is coupled. I consider a quantum transport set-up in which the impurity can be realised in a double quantum dot. The same Hamiltonian describes tunnelling states in metallic glasses, and can be mapped onto the Ohmic spin-boson model. It exhibits a Fermi edge singularity, i.e. many fermion correlations result in an impurity decay rate with a non-trivial power law energy dependence. I show that there is a simple relation between temporal impurity correlations on the one hand, and the linear response of the Fermi sea to external perturbations on the other. This results in a power law singularity in the space and time dependence of the non-local polarisability of the Fermi sea, which can be detected in transport experiments.

Electron-electron correlations in a dynamical impurity system with a Fermi edge singularity

We study spatial correlations in the ground state of a one-dimensional electron gas coupled to a dynamic quantum impurity. The system displays a nontrivial many-body effect known as the Fermi edge singularity: transitions between discrete internal states of the impurity have a power-law dependence on the internal energies of the impurity states. We present compact formulas for the static current-current correlator and the pair-correlation function. These reveal that spatial correlations induced by the impurity decay slowly (as the third inverse power of distance) and have a power-law energy dependence, characteristic of the Fermi edge singularity.

Modelling of optical emissions enhanced by the HF pumping of the ionospheric F-region

Abstract. Strong enhancement of the optical emissions with excitation threshold from 1.96 eV (630.0 nm from O(1D)) up to 18.75 eV (427.8 nm from N2+(1NG)) have been observed during experiments of the ionosphere modification by high power HF radio waves. Analysis of the optical emission ratios showed clearly that a significant part of the ionospheric electrons have to be accelerated to energies above 30 eV and more in the region where the HF radio wave effectively interacts with the ionospheric plasma. The Monte-Carlo model of electron transport and the optical emission model were used to study the dependence of the optical emission intensity on the acceleration electron parameters. We obtained the following results from analysis of the enhanced intensities of the four optical emissions (630.0, 557.7, 844.6 and 427.8 nm) observed in the EISCAT heating experiment on 10 March 2002. The 630.0 emission with an excitation threshold of 1.96 eV is formed predominately by the thermal electrons, where the accelerated electrons play a minor role in the excitation of this emission. In order to explain the experimentally observed intensity ratios, the accelerated electrons must gain energies of more than 60 eV. For accelerated electrons with a power law energy dependence, the efficiency of the optical emission excitation depends on the exponent defining the shape of the electron spectra. However, an agreement with the observed emission intensities is achieved for exponent values not less than zero. Moreover, increasing the exponent to higher values does not affect the emission intensity ratios.

On the spectrum of Z-pinch plasma neutrons

Generation of neutrons from Z-pinch discharges in a deuterated gas medium has been studied. It is shown that a power-law energy dependence of the number of high-energy deuterons in Z-pinch plasma explains the observed broadening of the neutron spectrum in these systems. It is established that, at an average ion energy below 3 keV in Z-pinch plasma, neutrons are mostly generated due to the interaction of high-energy (∼100-keV) deuterons with the main plasma components.

Cosmic-Ray Electron Flux Measured by the PAMELA Experiment between 1 and 625 GeV

Precision measurements of the electron component in the cosmic radiation provide important information about the origin and propagation of cosmic rays in the Galaxy. Here we present new results regarding negatively charged electrons between 1 and 625 GeV performed by the satellite-borne experiment PAMELA. This is the first time that cosmic-ray e⁻ have been identified above 50 GeV. The electron spectrum can be described with a single power-law energy dependence with spectral index -3.18 ± 0.05 above the energy region influenced by the solar wind (> 30 GeV). No significant spectral features are observed and the data can be interpreted in terms of conventional diffusive propagation models. However, the data are also consistent with models including new cosmic-ray sources that could explain the rise in the positron fraction.

Superfluid to Bose-Glass Transition in a 1D Weakly Interacting Bose Gas

We study the one-dimensional Bose gas in spatially correlated disorder at zero temperature, using an extended density-phase Bogoliubov method. We analyze, in particular, the decay of the one-body density matrix and the behavior of the Bogoliubov excitations across the phase boundary. We observe that the transition to the Bose-glass phase is marked by a power-law divergence of the density of states at low energy. A measure of the localization length displays a power-law energy dependence in both regions, with the exponent equal to -1 at the boundary. We draw the phase diagram of the superfluid-insulator transition in the limit of small interaction strength.

Two years of observations of the X-ray pulsar SMC X-1 with the ART-P telescope onboard the Granat observatory

We present the observations of the pulsar SMC X-1 with the ART-P telescope onboard the Granat observatory. We investigate the variability of the flux from the source on time scales of several tens of days. The intensity variation of the pulsar are shown to be consistent with the presence of a periodicity in the system with a characteristic time scale of ∼61 days. The precession of an inclined accretion disk, as indirectly confirmed by the absence of low-state pulsations, may be responsible for the observed variability. The spectrum of the source is well described by a power-law energy dependence of the photon flux density with a slope of ∼1.5 and an exponential cutoff at energies above ∼14–18 keV. We estimated the inclinations between the planes of the orbit and the accretion disk and the magnetic field of the neutron star.

Investigation of the dynamical susceptibility of Ce0.7Th0.3RhSb by inelastic neutron scattering

Following the observation that the specific heat of Ce0.7Th0.3RhSb shows non-Fermi liquid behavior, we have investigated the inelastic neutron scattering from this compound over the temperature range 10–100K, using the HET spectrometer at ISIS. We have found that the spectral function of Ce0.7Th0.3RhSb displays a power law dependence of energy, i.e. S(ω)∼ω−α, with α=0.33. The dynamical susceptibility obtained from the inelastic scattering spectra displays E/T scaling behavior as in other compounds showing non-Fermi liquid behavior. With increasing energy transfer above 10meV, Ce0.7Th0.3RhSb shows a more localized behavior with two broad crystalline electric field transitions around 20 and 30meV.

Accelerated cometary ions observed downstream of the comet Halley bow shock

Fluxes of energetic ions with energies exceeding 100 keV were observed upstream of the bow shock of comet Halley by the Tünde instrument which was on board the VEGA 1 spacecraft. Downstream of the shock, ion fluxes in the energy range 100 to 800 keV were observed. Cometary ions, such as O+, newly picked up by the solar wind have energies of about 15 keV in the solar wind frame of reference; hence the measured ion fluxes indicate that acceleration processes must have been operating near comet Halley. The measured ion fluxes were transformed into distribution functions in the solar wind frame using a variety of assumptions concerning the energy dependence of the distribution function and the identity of the ion species. The derived distribution function upstream of the shock falls off steeply with energy between 100 and 150 keV, with an effective temperature of about 7 keV or spectral index about −15. The distribution function increases with decreasing cometocentric distance, on average, reaching a maximum at the bow shock. Downstream of the shock, the spectra can be represented in two ways: (1) one population with a single spectral index based on a power law energy dependence or (2) two exponential function populations with different effective temperatures. In the latter case a soft component exists with an effective temperature of about 30 keV for energies less than about 250 keV and a harder component exists for higher energies with an effective temperature of about 100 keV. Downstream of the shock, the ion fluxes decrease with decreasing cometocentric distance. The measured distribution functions are compared with those obtained by similar instruments on Giotto and the International Cometary Explorer as well as with the predictions of several theoretical models that employ different acceleration mechanisms.

Monte-Carlo calculations of Ge detector escape-peak efficiencies

The authors present calculated first and second escape peak efficiencies for a variety of n-type coaxial Ge detectors using the Monte Carlo method. The results are given for right-circular cylindrical geometries of size ranging from 3-cm diameter * 3-cm thick to 8-cm diameter * 8-cm thick. For completeness, the intrinsic interaction and photopeak efficiencies for energies ranging from 20 keV to 20 MeV are listed. The calculations have been tested against experimental measurement and found to be in agreement to within the quoted errors (typically 10%). It is found that the ratio of the second escape peak efficiency to the first escape peak efficiency, R, is approximately independent of energy for small detector volumes but has a weak power law energy dependence for large volumes. It is shown that R also varies as an inverse power law of the active volume. >

Bremsstrahlung X ray spectra of JUpiter and Saturn: Predictions for future planetary spacecraft

Calculations of X ray spectra due to bremsstrahlung from precipitating auroral electrons at Jupiter and Saturn are presented. The model assumes that a field‐aligned potential drop accelerates a primary beam of electrons into the atmosphere where a population of secondary electrons having a power law energy dependence is generated. The spectrum at Jupiter is normalized to the soft X ray observations of Metzger et al. (1983) at the low‐energy end and constrained at the high‐energy end by UV auroral energy requirements. The spectrum at Saturn is constructed by analogy to the Jovian case allowing for variation of the beam energy, energy flux, and scale size of the Saturnian aurora. The results indicate that a significant flux of X rays is emanating from both planets which may serve as a basis for conducting planetary X ray astronomy as a part of future spacecraft missions to the planets.

Ion beam analysis of thin films

The theory of optical absorption due to transitions between a valence band and a hydrogen-like local level associated with a conduction band is modified to permit an arbitrary power-law dependence of energy on the magnitude of the wave-vector of carriers in the valence band. The observed absorption for photon energies below 1.6 eV in the ferromagnetic semiconductor CdCr2Se4 is discussed in terms of a combination of two types of terms. The first type of absorption is due to transitions to a local level from a band with two branches, in each of which there is an energy region with a width of 0.28 eV or more beginning 0.10–0.16 eV from the band edge, in which the energy measured from some origin near but not necessarily equal to the band-edge is approximately proportional to (wave-vector)(13). The second type of absorption has a dependence on photon energy ħω of the form (ħω − E3)2, where E3 is a threshold energy probably connected with indirect transitions between bands as suggested by Sakai, Sugano and Okabe. After constraints on parameters appearing in the theory are imposed by use of results of these authors and of Shepherd, it is found that curves of Harbeke and Lehmann on optical absorption in CdCr2Se4 at 4.2, 78, 130 and 298 K in the photon-energy range 1.14–1.42 eV can be fitted to a mean accuracy of 3%, using an average of 3.75 adjustable parameters for each curve. The strength of the indirect band-to-band absorption does not have the temperature dependence expected for phonon-assisted indirect band-to-band transitions, but can be described by a term independent of temperature plus another term proportional to the square of the deviation of the magnetization from saturation. The fitting of the absorption curves requires that the ratio of the widths of the two branches of the bands varies from about 1.6 at low temperatures to 1.35 at 298 K and that the total width of the bands involved is less than 1 eV.

An acquisition, storage, display and processing system for electron energy-loss spectra

An electronic recording system is described which can be used in conjunction with a transmission electron microscope fitted with an electron spectrometer. The system is based on a Texas Instruments 990/4 microcomputer and TI 733 data terminal. The minicomputer is programmed from a cassette tape which contains the software necessary for acquiring spectral data, displaying the spectra on a cathode ray tube and simple data processing. The latter includes performing a least-squares fit to a power-law energy dependence, which is used for stripping the background contribution from inner shell losses for quantitative microanalysis of light elements.

RelativisticN−None-boson-exchange potentials with asymptotic power-law energy dependence

We update the relativistic version of the generalized one-boson-exchange potentials on the basis of the recent accumulation of experimental data. We introduce into the vector-meson potentials a damping factor decreasing with energy as well as an enhancing factor in the scalar-meson potential increasing with energy in accord with the asymptotic power-law energy dependence of the potentials required in high-energy physics. With these factors we obtain a markedly improved fit to all phase parameters. Thus, with 11 adjusted parameters we obtain a satisfactory description of the $N\ensuremath{-}N$ interaction for the 0-515 MeV energy range.NUCLEAR STRUCTURE Relativistic one-boson-exchange potentials with asymptotic power-law energy dependence. Theoretical fits to phase shifts and observables.