Cross-section Fluctuations Research Articles

A Theory of Fluctuations in Nuclear Cross Sections

A Theory of Fluctuations in Nuclear Cross Sections

Crossover between the ballistic and diffusive regime of the spin-conductance and giant magnetoresistance in magnetic multilayered nanostructures

We analyze the interplay between disorder and band structure in current perpendicular to the planes giant magnetoresistance (GMR). We consider finite magnetic multilayers attached to pure crystalline leads, described by a tight-binding simple cubic two-band model $(s\ensuremath{-}d).$ Several models of disorder are considered, including random on-site potentials, lattice distortions, impurities, vacancies, and cross-section fluctuations. Magnetotransport properties are calculated in the zero-temperature zero-bias limit, within the Landauer-B\"uttiker formalism. Using a very efficient numerical scattering technique, we are able to perform simulations, over large length scales, and to investigate spin transport in the ballistic, diffusive, and localized regimes, as well as the crossover between them. The competition between disorder-induced mean-free-path reduction and disorder-induced spin asymmetry enhancement of the conductance highlights several different regimes of GMR.

EFFECTS OF FLUCTUATION OF FREE ELECTRONS ON PHOTOIONIZATION CROSS-SECTION NEAR THRESHOLD

Based on relativistic HFS self-consistent field average atomic model, the effect of the fluctuation of free electrons on the threshold of photoionization in local thermal equilibrium plasmas is studied by employing the principle of entropy in grand-canonical ensemble. Some results are discussed.

Photodissociation in quantum chaotic systems: Random-matrix theory of cross-section fluctuations

Using the random matrix description of open quantum chaotic systems we calculate in closed form the universal autocorrelation function and the probability distribution of the total photodissociation cross section in the regime of quantum chaos.

Aggregate fluctuations, financial constraints and risk sharing

Private information and costly state verification often result in credit rationing in models with smooth investment, affecting both loan size and total investment. The optimal contract is derived in a dynamic stochastic growth model with capital for two types of models: one with symmetric information and the other with asymmetric information and costly state verification. When all information is observed costlessly, the equilibrium optimal contract provides complete insurance to risk-averse savers against aggregate fluctuations. When information is asymmetric and there is costly state verification, the equilibrium optimal contract provides only partial insurance against aggregate shocks. The extent of insurance is measured by the marginal rate of transformation of consumption between borrowers and lenders which is closely linked to the user cost of capital. The deadweight monitoring costs create a wedge between a borrower's cost of capital and a lender's stochastic discount factor, with two results: (i) fluctuations in the user cost of capital provides a mechanism by which aggregate shocks can be␣propagated; (ii) the distribution of capital's share of output among borrowers, lenders, and monitoring costs varies even if capital's share is constant. Capital market frictions not only amplify aggregate fluctuations but also generate cross-sectional fluctuations that may not be observable in aggregate data.

Cross section fluctuations of a photon projectile in the generalized vector meson dominance model

We explain that the generalized vector meson dominance (GVMD) models successful in the theoretical description of photoproduction and electroproduction in high energy processes effectively implement color coherent phenomena expected in QCD. Within a model, which reproduces Bjorken scaling and nuclear shadowing for deep inelastic processes, we calculate ${P}_{\ensuremath{\gamma}}(\ensuremath{\sigma}{,Q}^{2}),$ the probability for a photon to interact with a target with the cross section \ensuremath{\sigma}. We find that within the GVMD model the virtual photon has two main components: the ``hard'' one with a small cross section of the order of ${1/Q}^{2}$ and the high probability and the ``soft'' one with a typical hadronic cross section with the probability suppressed by the factor of ${1/Q}^{2}.$ Thus the GVDM model produces ${P}_{\ensuremath{\gamma}}(\ensuremath{\sigma}{,Q}^{2})$ similar to that within the parton model and suggests the interplay between hard and soft QCD at ${Q}^{2}>1{\mathrm{GeV}}^{2}.$ We study the limit $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\sigma}}0$ and show that ${P}_{\ensuremath{\gamma}}(\ensuremath{\sigma}{,Q}^{2})\ensuremath{\propto}1/\ensuremath{\sigma}$ in both the GVMD model and QCD. Thus similarly to the parton model the GVMD model predicts the color transparency phenomenon. This is an indirect indication that Bjorken scaling, color transparency and shadowing in nuclei in DIS are closely related.

Pencil beam transport in a random medium using the Fermi transport equation

The effect of a random transport cross section on the transverse spreading of a pencil beam of charged particles is analysed using the Fermi approximation to the 3D transport equation, in conjunction with a Gaussian model of cross section fluctuations. Stochasticity is seen to enhance the spreading of the beam but ensemble averaged quantities such as the transverse spatial moments and the scalar flux appear not to be sensitive to the details of the underlying statistical model. Furthermore, only asymptotic solutions for the scalar flux are possible because of divergent behaviour that can be traced to an inconsistency between the assumption of forward peakedness of the angular flux. which underlies the Fermi approximation, and the spreading induced by the randomness of the material properties.

Neutron Cross-Section Probability Tables in TRIPOLI-3 Monte Carlo Transport Code

Neutron transport calculations need an accurate treatment of cross sections. Two methods (multigroup and pointwise) are usually used. A third one, the probability table (PT) method, has been developed to produce a set of cross-section libraries, well adapted to describe the neutron interaction in the unresolved resonance energy range. Its advantage is to present properly the neutron cross-section fluctuation within a given energy group, allowing correct calculation of the self-shielding effect. Also, this PT cross-section representation is suitable for simulation of neutron propagation by the Monte Carlo method. The implementation of PTs in the TRIPOLI-3 three-dimensional general Monte Carlo transport code, developed at Commissariat à l’Energie Atomique, and several validation calculations are presented. The PT method is proved to be valid not only in the unresolved resonance range but also in all the other energy ranges.

Distribution of backscattered intensity in the distorted Born approximation: Application to C-band SAR images of woodland

The intensity distribution in synthetic aperture radar (SAR) images of woodland is known to depend upon imaging conditions. Whilst phenomenological models can be used to match observed backscatter distributions, a physical model is needed to explain their origins. Images of woodland obtained during airborne SAR trials are analysed and shown to exhibit non-exponential intensity distributions. Expressions are derived for the moments of the intensity distribution using discrete scattering models based on the Born and distorted Born approximations. The predictions of the Born approximation are such that, at all but extremely high resolutions, the intensity statistics reflect only fluctuations in the number of discrete scatterers in resolution cells. In the distorted Born approximation it is revealed that, even at modest resolutions, fluctuations in both number and cross section of objects can influence intensity distributions. This is shown to be a direct consequence of the incorporation of attenuation effects in the distorted Born model. The theory is applied to scattering from a model woodland canopy and shown to yield intensity moments in close agreement with observations. The consequences of the model for other scattering situations are discussed.

Extended ensemble molecular dynamics method for constant strain rate uniaxial deformation of polymer systems

We describe a novel molecular dynamics (MD) method to simulate the uniaxial deformation of an amorphous polymer. This method is based on a rigorously defined statistical mechanics ensemble appropriate for describing an isothermal, displacement controlled, uniaxial stress mechanical test. The total number of particles is fixed and the normal stresses in the direction normal to the applied strain are constant, i.e., an NTLxσyyσzz ensemble. By using the Lagrangian of the extended system (i.e., including additional variables corresponding to the temperature and cross-sectional area fluctuations), we derive a set of equations of motion for the atomic coordinates and the additional variables appropriate to this ensemble. In order to avoid the short MD time step appropriate for the stiff covalent bonds along the polymer chains, we introduce bond length constraints. This is achieved using a variation of the commonly used SHAKE [J. P. Ryckaert, G. Ciccotti, and H. J. C. Berendsen, J. Comp. Phys. 23, 327 (1977)] algorithm. A numerical method for integrating the equations of motion with constraints via a modification of the velocity Verlet [W. C. Swope, H. C. Andersen, P. H. Berens, and K. R. Wilson, J. Chem. Phys. 76, 637 (1982)] algorithm is presented. We apply this new algorithm to the constant strain rate deformation of an amorphous polyethylene in a model containing several distinct polymer chains. To our knowledge, this is the first time that bond length constraints were applied to a macromolecular system together with an extended ensemble in which the simulation cell shape is allowed to fluctuate.

Determination of the29Si level density from 3 to 22 MeV

The level density of ${}^{29}$Si has been studied over an excitation energy range of 3 to 22 MeV. Three techniques were used to derive level density values from experimental data. In the region of resolved levels, results were obtained from level counting while neutron resonance data were used in the region of slightly overlapping levels near the neutron binding energy. At the highest excitation energies, characterized by strongly overlapping levels, Ericson theory was employed to deduce level densities by examining energy-dependent fluctuations in cross sections. Three reactions yielding the same compound nucleus, ${}^{29}$Si, were investigated. Partial cross sections from ${}^{28}$Si($n,p$), ${}^{28}$Si($n$,\ensuremath{\alpha}), and ${}^{27}$Al($d,n$)${}^{28}$Si reactions were measured with good experimental resolution and statistical accuracy. From these cross sections, level densities were extracted using the two independent methods proposed by Ericson. Reasonable agreement was found among level densities derived from the two Ericson methods. Values obtained are also fairly consistent with those of various predictions and theoretical models.

Relativistic theory of stopping for heavy ions.

We calculate the electronic stopping power and the corresponding straggling for ions of arbitrary charge number, penetrating matter at any relativistic energy. The stopping powers are calculated by a simple method. Its starting point is the deviation of the precise theory from first-order quantum perturbation. We show that this deviation can be expressed in terms of the transport cross section, ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{tr}}$, for scattering of a free electron by the ion. In the nonrelativistic case the deviation is precisely the Bloch correction to Bethe's formula; we look into the nonrelativistic case in order to clarify both some features of our method and a seeming paradox in Rutherford scattering. The corresponding relativistic correction is obtained from ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{tr}}$ for scattering of a Dirac electron in the ion potential. Here, the major practical advantage of the method shows up; we need not find the scattering distribution, but merely a single quantity, ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{tr}}$, determined by differences of successive phase shifts. For a point nucleus our results improve and extend those of Ahlen. Our final results, however, are based on atomic nuclei with standard radii. Thereby, the stopping is changed substantially already for moderate values of \ensuremath{\gamma}=(1-${\mathit{v}}^{2}$/${\mathit{c}}^{2}$${)}^{\mathrm{\ensuremath{-}}1/2}$. An asymptotic saturation in stopping is obtained. Because of finite nuclear size, recoil corrections remain negligible at all energies. The average square fluctuation in energy loss is calculated as a simple fluctuation cross section for a free electron. The fluctuation in the relativistic case is generally larger than that of the perturbation formula, by a factor of \ensuremath{\sim}2--3 for heavy ions. But the finite nuclear radius leads to a strong reduction at high energies and the elimination of the factor ${\ensuremath{\gamma}}^{2}$ belonging to point nuclei. \textcopyright{}1996 The American Physical Society.

Origin of large-amplitude random telegraph signal in silicon bipolar junction transistors after hot carrier degradation

The random telegraph signal (RTS) with a relative amplitude of up to 100% has been observed in the forward and reverse base current in polycrystalline emitter bipolar junction transistors after hot carrier degradation. The RTS is explained by modulations in the surface generation-recombination rate due to fluctuations in the capture cross section of two-state interface centers. Carrier trapping/emission on slow oxide traps and/or defect reconfiguration are assumed to be responsible for the cross-section fluctuations

Mass Dependence of Cross Section Fluctuation in Dissipative Reaction 19F+51V

Excitation functions for projectile-like fragments from 19F+51V reaction have been measured at 102.25 to 109.50 MeV in 250 keV steps. A TOF+(ΔE - E) telescope at θL = ∠1.7° is used to identify atomic number Z and mass number A of ejectiles simultaneously. Fluctuations of the dissipative cross section for a series of isotopes are observed. Their coherence energy widths are extracted by generalized statistical fluctuation analysis and the dependence on mass number and on N/Z values are observed for the first time.

Correlations and fluctuations in high-energy nuclear collisions.

Nucleon correlations in the target and projectile nuclei are shown to reduce significantly the fluctuations in multiple nucleon-nucleon collisions, total multiplicity and transverse energy in relativistic heavy-ion collisions, in particular for heavy projectile and target. The interplay between cross-section fluctuations, from color transparency and opacity, and nuclear correlations is calculated and found to be able to account for large fluctuations in transverse energy spectra. Numerical implementation of correlations and cross-section fluctuations in Monte-Carlo codes is discussed.

Hadron-nucleon total cross section fluctuations from hadron-nucleus total cross sections.

The extent to which information about fluctuations in hadron-nucleon total cross sections in the frozen approximation can be extracted from very high energy hadron-nucleus total cross section measurements for a range of heavy nuclei is discussed. The corrections to the predictions of Glauber theory due to these fluctuations are calculated for several models for the distribution functions, and differences of the order of 50 mb are found for heavy nuclei. The generating function for the moments of the hadron-nucleon cross section distributions can be approximately determined from the derivatives of the hadron-nucleus total cross sections with respect to the nuclear geometric cross section. The argument of the generating function, however, is limited to the maximum value of a dimensionless thickness function obtained at zero impact parameter for the heaviest nuclear targets: about 1.8 for pions and 3.0 for nucleons.

Fluctuations of cross sections seen in cosmic ray data?

We argue that the unexpected nonexponential behavior of some cosmic ray data is just a manifestation of cross section fluctuations discussed recently in the literature and observed in nuclear collisions and in diffraction dissociation experiments on accelerators.

Fluctuations in absorption spectra and final product state distributions following photodissociation processes

We present a quantum mechanical wave packet study for the unimolecular dissociation of a triatomic molecule into an atom and a diatom. The 3D potential energy surface used in the dynamics calculations is that of the B̃ state of water corresponding to the second absorption band. Both OH stretching coordinates and the bending angle are included. What is not taken into account is the strong nonadiabatic coupling to the lower-lying à and X̃ states which in reality drastically shortens the lifetime in the B̃ state. For this reason the present study is not a realistic account of the dissociation dynamics of water in the 122 nm band. It is, however, a representational investigation of a unimolecular reaction evolving on a realistic potential energy surface without barrier. The main focus is the resonance structure of the absorption spectrum and the final rotational state distributions of the OH fragment. The total absorption spectrum as well as the partial dissociation cross sections for individual rotational states of OH show drastic fluctuations caused by overlapping resonances. The widths of the individual resonances increase, on average, with the excess energy which has the consequence that the cross sections become gradually smoother. Although the low-energy part of the spectrum is rather irregular, it shows ‘‘clumps’’ of resonances with an uniform spacing of ∼0.1 eV. They are discussed in the context of IVR and a particular unstable periodic orbit. In accordance with the fluctuations in the partial dissociation cross sections as functions of the excess energy the final rotational state distributions show pronounced, randomlike fluctuations which are extremely sensitive on the energy. The average is given by the statistical limit (PST), in which all levels are populated with equal probability. With increasing excess energy the distributions more and more exhibit dynamical features which are reminiscent of direct dissociation like rainbows and associated interferences. Classical trajectories for small excess energies are chaotic, as tested by means of the rotational excitation function, but become gradually more regular with increasing energy. Our wave packet calculations hence demonstrate how the transition from the chaotic to the regular regime shows up in a fully quantum mechanical treatment. The results of the present investigation are in qualitative accord with recent measurements for the unimolecular dissociation of NO2.

Single diffractive hadron-nucleus interactions within the dual parton model

Single diffractive hadron-nucleus interactions are studied within the framework of the dual parton model. Introducing a diffractive component into the Monte-Carlo event generator DTUNUC we investigate particle production and the dependence of the diffractive cross section on the atomic number of the target nucleus. A comparison of the numerical results with recent experimental data is presented. We furthermore introduce hadronic cross section fluctuations and discuss their influence on diffractive proton-nucleus cross sections.

Radar cross-section fluctuation modelling of a tumblingdisc

It is shown that the radar cross-section (RCS) of a light disc falling freely in the atmosphere can be realistically modelled as an amplitude- and width-modulated pulse train. Good agreement is demonstrated between our experimental measurements and the theoretical model.