Positron Backscattering Research Articles

Electron and positron backscattering from condensed targets

The backscattering process for electron and positron impinging on condensed targets is studied here. The calculation is performed for Li, Na, Al and Cu atoms in the 500–3000 eV energy range. The well known Vicanek and Urbassek theory is used to determine the backscattering coefficient for present solid atoms. To analyze the elastic scattering cross section, spherical complex optical potential formalism is used. Apart from the backscattering coefficient, momentum transfer cross section, range of penetration, and mean number of wide-angle collisions are also tabulated and compared to the available data. No previous work was found reporting the range of penetration for the atoms. Hence, we also report the electron backscattering coefficient and range of penetration for liquid water for which experimental and theoretical data are available for the range of penetration. The electron backscattering coefficient for liquid water is reported for the first time here.

Simulation of positron backscattering on Al, Cu, Ag and Au targets using GEANT4 code

In this paper, backscattering of 3 to 50‐keV positrons on Al, Cu, Ag and Au metallic targets has been systematically investigated using GEANT4 code. The dependence of positron backscattering coefficients on atomic number Z, target thickness, incident energy and angles has been discussed comprehensively. Besides, positron backscattering spectra for those metallic targets at different discrete scattering angles were also studied to provide theoretical basis of the most appropriate scattering angle selected for simulation parameters and specified applied measurement techniques. The impact of atomic number Z of targets on positron backscattering spectra was investigated as well. Simulation results are in reasonable agreement with previous experiment data and theoretical work. Copyright © 2016 John Wiley & Sons, Ltd.

Positron backscattering from solid targets: Modeling of scattering processes via various approaches

Monte Carlo simulation of 1–4keV positron backscattering from semi-infinite solid targets ranging from Be (z=4) to Au (z=79) with normal angle of incidence is here reported. In our study, the elastic and inelastic scattering cross sections are modeled by using various approaches based on either a classical or a quantum mechanical treatment. Calculations of positron backscattering coefficient are then reported for the solid targets of interest. The results obtained show a fairly good agreement with the data available in the literature. The dependence of the positron backscattering coefficient versus the atomic number of the solid target of interest has been investigated. In this respect, polynomial functions are proposed which does not require any recourse to Monte Carlo calculations.

Simulation of positron backscattering and implantation profiles using Geant4 code**Project supported by the National Natural Science Foundation of China (Grant Nos. 11175171 and 11105139).

For the proper interpretation of the experimental data produced in slow positron beam technique, the positron implantation properties are studied carefully using the latest Geant4 code. The simulated backscattering coefficients, the implantation profiles, and the median implantation depths for mono-energetic positrons with energy range from 1 keV to 50 keV normally incident on different crystals are reported. Compared with the previous experimental results, our simulation backscattering coefficients are in reasonable agreement, and we think that the accuracy may be related to the structures of the host materials in the Geant4 code. Based on the reasonable simulated backscattering coefficients, the adjustable parameters of the implantation profiles which are dependent on materials and implantation energies are obtained. The most important point is that we calculate the positron backscattering coefficients and median implantation depths in amorphous polymers for the first time and our simulations are in fairly good agreement with the previous experimental results.

The multi-scattering model for calculations of positron spatial distribution in the multilayer stacks, useful for conventional positron measurements

The spatial distribution of positrons emitted from radioactive isotopes into stacks or layered samples is a subject of the presented report. It was found that Monte Carlo (MC) simulations using GEANT4 code are not able to describe correctly the experimental data of the positron fractions in stacks. The mathematical model was proposed for calculations of the implantation profile or positron fractions in separated layers or foils being components of a stack. The model takes into account only two processes, i.e., the positron absorption and backscattering at interfaces. The mathematical formulas were applied in the computer program called LYS-1 (layers profile analysis). The theoretical predictions of the model were in the good agreement with the results of the MC simulations for the semi infinite sample. The experimental verifications of the model were performed on the symmetrical and non-symmetrical stacks of different foils. The good agreement between the experimental and calculated fractions of positrons in components of a stack was achieved. Also the experimental implantation profile obtained using the depth scanning of positron implantation technique is very well described by the theoretical profile obtained within the proposed model. The LYS-1 program allows us also to calculate the fraction of positrons which annihilate in the source, which can be useful in the positron spectroscopy.

Design, simulation and performance of a slow positron beam with secondary electron tagging for positron annihilation lifetime spectroscopy

A positron annihilation lifetime spectrometer using a magnetically guided continuous positron beam and the signal from secondary electrons (SE) emitted from the sample is presented. The positron and secondary electrons trajectories as well as the physics of SE were simulated using GEANT4 program. A special attention was paid to the consequences of positron backscattering, in particular on the shape of the lifetime spectrum. A very good agreement was obtained between simulation and measurements concerning the time resolution (~300–400ps FWHM) for the studied range of incident positron energies. Due to the complex shape of the resolution function, the present design of the spectrometer is not suited to study of short lifetimes, but can be used for depth profiling porosimetry of materials with Ps formation with the an excellent peak to background ratio of ~105.

Development of a spin-polarised positron beam

The development stages of a system for variable-energy spin-polarised positron beam spectroscopy are described. Methods for achieving maximum practical beam polarisation include a Na-22 source configuration with a low-Z backing to reduce positron backscattering, and positioning a 250μm beryllium foil in front of the source to absorb the slower and decelerate the faster beta positrons, the latter suffering significantly less depolarisation during moderation than the former. To switch the direction of spin polarisation of electrons in the target sample the direction of the positron guiding field was reversed, and strong rare earth magnets were placed behind the sample. Systematic problems associated with low beam intensity and electronic drifts are discussed. Results for single-crystal iron compare well with those expected from theory, but suggest a beam/target polarisation of ∼ 5% of that expected. Prospects for future beam development and application are outlined.

Stochastic equations in the invariant imbedding formulation of particle transport

Invariant imbedding theory is an alternative formulation of particle transport theory. Although stochastic foundations of invariant imbedding have been known from the beginnings, the method itself has so far exclusively been used for calculating first moments, i.e. expectations. The present paper attempts to set up a probability balance equation in the invariant imbedding approach from which equations for the first and second order densities are derived. It is shown that only the equations for the first order densities are non-linear, while subsequent order densities obey linear equations. This is expected to considerably simplify solution to those problems which involve second order density calculations where invariant imbedding techniques may be profitably used. Examples of such quantities are the variance or correlations between particles detected at two different energies or angles or the higher moments of the emitted multiplicity distribution such as the variance from a target bombarded by incident particles. One possible area of application of our equations is non-destructive estimation of fissile material by the active neutron assay technique. Another area is the study of particle cascade development in sputtering and positron backscattering from surfaces. The approach is illustrated by a simple forward–backward scattering model for these two problems.

Depth profiling of aluminium metal using slow positron beam

Slow positron beam Doppler-broadening technique was used to study depth profiling of aluminium metals sample. The variation of the line-shape parameters with incident positron energy was studied. Also, the depth profile of the S parameter was investigated. The positron implantation profile and backscattering fraction for aluminium sample was studied theoretically using data obtained empirically by Monte Carlo simulation. Results obtained revealed that aluminium metal has high S parameter in the surface and near surface regions and low S parameter in the bulk. The value of the S parameter decreased from the surface region reached a minimum at S = 0.292 and started to increase. While the W parameter increased and reached a value of 0.199 and started to decrease. The calculated positron implantation profile decreased with increase in the energy of the incident positrons but the implantation profile depth increased with an increase in the energy of the incident positrons. The results further revealed that the backscattering fraction increased with increase in the energy of the incident positrons. Keywords : Material, positron annihilation, structure and vacancy Nigerian Journal of Physics Vol. 18 (1) 2006: pp. 19-24

Dependence of electron and positron backscattering coefficients on Al film thickness

The backscattering coefficient of 1–4 keV electron and positron beams normally incident impinging on Al thin film targets is stochastically modeled within a Monte Carlo frame work. The aim of the present paper is to study the behavior of the backscattering coefficient as a function of the Al film thickness. To the authors’ knowledge, no theoretical or experimental work on the dependence of the positron backscattering coefficient on film thickness targets has been reported so far. It is found that the backscattering coefficient for both electron and positron beams presents different behaviors when the Al film thickness belongs to the nano-scale. Beyond this scale, the behavior becomes qualitatively similar.

Performance analysis of the intense slow-positron beam at the NC State University PULSTAR reactor

An intense positron beam, for application in nanophase characterization, is now under construction at the 1 MW PULSTAR nuclear reactor at North Carolina State University (NCSU). A tungsten converter/moderator is used, allowing positrons to be emitted from the surface with energies of a few electron volts. These slow positrons will be extracted from the moderator and formed into a beam by electrostatic lenses and then injected into a solenoidal magnetic field for transport to one of three experimental stations, via a beam switch. To optimize the performance of the beam and to predict the slow-positron intensity, a series of simulations were performed. A specialized Monte-Carlo routine was integrated into the charged-particle transport calculations to allow accounting for the probabilities of positron re-emission and backscattering from multiple-bank moderator/converter configurations. The results indicate that either a two-bank or a four-bank tungsten moderator/converter system is preferred for the final beam design. The predicted slow-positron beam intensities range from nearly 7×10 8 to 9×10 8e +/s for the two-bank and the four-bank systems, respectively.

Implantation profile of Na22 continuous energy spectrum positrons in silicon

The implantation profile of positrons emitted from a continuous energy spectrum source of Na22 in close proximity to a silicon target is modeled. The primary motivation is the use of positron lifetime spectroscopy to characterize layers of defects such as those created by ion irradiation, usually deemed accessible only to techniques which utilize slow positrons. The model combines the Makhov profile, used with considerable success to describe the profile of low energy (<30keV) monoenergetic positrons, with the well-established, universal β-decay energy spectrum. The success of this approach is verified by measuring the fractions of positrons absorbed in thinned silicon samples. This verification utilizes lifetime measurements performed on silicon in a bilayer sandwich configuration with copper as a backing. The model accounts for the uncertainty in the positron backscattering at the silicon∕copper interface. An optimal fit of the model to the experimental data requires that the parameter defining the mean depth of the Makhov profile (usually denoted r) is energy dependent. An example of application is provided in the form of a positron lifetime measurement of defects in silicon introduced by 1.5MeV proton irradiation. Excellent agreement is found between the lifetime data and those obtained using a slow positron technique.

Positron backscattering from an Al target: analytical calculation and Monte Carlo simulation

AbstractPositron backscattering coefficients are analytically calculated and numerically simulated for an Al target in the positron energy range 0.50–4 keV and for incident angles between 0° and 80° . The differential elastic scattering cross section has been obtained using the Bentabet and Bouarissa approximation (Phys. Lett. 2006; A 355: 390). Both the analytical and simulated results show good agreement with the experiment and previous theoretical work. Copyright © 2007 John Wiley & Sons, Ltd.

Monte Carlo simulations of positrons transmission and backscattering probabilities in nickel

Monte Carlo simulations for positron backscattering from the semi-infinite nickel with normal angle of incidence and the transmission through nickel foils of isotropically implanted positrons from a 22Na β + source is reported. The elastic scattering cross section, have been obtained from Rutherford differential cross section where the numerical coefficient in the atomic screening parameter and spin-relativistic correction factor is taken to be variable. Inelastic scattering model was employed to simulate the energy loss using Gryzinski’s semi-empirical expression and Liljequist and Gryzinski models to calculate the total inelastic scattering cross section. The simulated results and the available experimental data are found to be in reasonable agreement.

Positron and electron backscattering from elemental solids in the 1–10 keV energyrange

Electron and positron backscattering coefficients are analytically calculated for a number ofselected atomic targets in the energy range 1–10 keV and for incident angles between0° and 80°. The dependence of the backscattering coefficient on the material, on the projectileprimary energy and on the incidence angle has been examined and discussed. Our resultsare found to be in better agreement with experiment than earlier Monte Carlo simulations.

Applications of invariant embedding: positron backscattering from surfaces

An effective invariant-embedding technique is developed for the detailed description of charged-particle backscattering from solids, with example calculations concentrating on quasielastic positron backscattering. The invariant-embedding formalism considered incorporates elastic and inelastic interactions, as well as particle annihilation effects, and allows a very efficient numerical scheme (based upon a recurrence in the number of elastic collisions) for accurate and fast evaluation of various distributions of backscattered particles, including those resolved at once in numerous variables. Not invoking drastic simplifications characteristic for existing analytical-based approaches and easily handling realistic collision cross-sections, the calculation scheme allows to test the accuracy of simulation programs and – within its (albeit more narrow) range of validity – offers significant advantages compared to those as regards accuracy, computing speed, and resolution. Capabilities of the approach are illustrated by calculation results pertaining to elastic and inelastic positron backscattering for various targets and energies in the keV range. Distributions in (dependences on) numerous variables (incidence and/or emission directions, numbers of elastic and/or inelastic collisions, path length, energy, target atomic number) and their combinations are exemplified, and their nontrivial features are briefly discussed.

Monte Carlo simulation of kilovolt positron penetration and backscattering probabilities in solids

Monte Carlo simulations of the backscattering probabilities, mean penetration depths and implantation profiles of positrons for elemental solids are reported as a function of atomic number 4⩽ Z⩽82 and incident energies from 5 to 70 keV. It is demonstrated that backscattering probability and mean penetration depth values can be estimated reliably by using a simple Monte Carlo code for different incident energies and angles. The simulation results are in general in good agreement with other simulations and experiments.

Positron transmission into Kapton: The effective mass absorption coefficient of relevance to positron lifetime experiments

The penetration of positrons from a Na22 source into Kapton foils sandwiched between different backscattering materials (Al, Cu, and Pt) has been studied for the geometry characteristic of positron annihilation techniques. Kapton has served as absorber and each of the selected metals as detector. The method, based on measuring the positron lifetimes, makes use of the difference in values of the fractions of positrons annihilating inside and outside the bulk matrix of the detector. A model on positron transmission and backscattering into 2π solid angle was constructed for the purpose. A correction term was added to the classical exponential form of the transmitted intensity, for absorber thickness z smaller than a critical thickness zc above which the transmitted intensity function falls exponentially. Numerical analysis of the data based on the model function has revealed the existence of two effective mass absorption coefficients pertaining, respectively, to the regions below and above zc. The coefficient αs+ for z<zc of relevance to positron lifetime experiments was found to be considerably smaller (by a factor 3) than the coefficient αl+ extracted by exponential regression measurements for sufficiently large absorber thicknesses. The need for new data on the coefficient for backscattering into 2π solid angle led to measuring the latter for the three used metals, yielding in the end the result αs+=14.12 cm2 g−1. The observed gap between αs+ and αl+ is qualitatively discussed.

Backscattering of slow positrons from semi-infinite aluminum

Monte Carlo simulation for 1–10 keV positron backscattering from semi-infinite aluminum with normal angle of incidence is reported. The elastic scattering cross sections have been obtained from the modified Rutherford differential cross section where the numerical coefficient in the atomic screening parameter is taken to be variable. To model inelastic scattering, we have investigated for the first time the effects of continuous slowing down through collisions with conduction electrons. Attention has also been paid to effects of changing the angle of incidence. Our simulated results and the available experimental data are found to be in reasonable agreement, and show that the energy dependence of the backscattered fractions can be fitted with a simple function: B(E)=0.0187997 ln E+0.102644. This suggests that both the transport model and the scattering cross sections used in the present work are reliable.

Positron backscattering in polymer/metal systems

Positron backscattering was observed at interfaces of polymer/metal using positron annihilation lifetime spectroscopy in the Teflon and Mylar films and poly (MMA-co-nBMA) acrylic coatings on tungsten (W) and molybdenum (Mo) substrates. Aluminum (Al) used as a comparison substrate did not have significant backscattering. Major changes were observed in the third, I3, and fourth, I4, intensity components of thin layers of Teflon and Mylar films on W and Mo substrates compared to Al. The average value of positron backscattering was estimated at 39% and 32% for W and Mo, respectively, with a 22Na source. A model was presented for calculation of the backscattering coefficient (B) in the polymer/metal systems and compared with experimental results.