Escape of photoelectrons and Compton‐scattered photons from an HPGe detector

The response function of a planar HPGe detector due to escape of photoelectrons and Compton‐scattered photons was studied for a point source with 59.5 keV energy. It was shown that both mechanisms, in addition to Ge x‐ray escape, leading to partial deposition of energy, could be observed in the same experiment. A Monte Carlo program was used to investigate these components of the response function. The results indicate that although the escape of scattered photons and Ge x‐rays are of the same magnitude, the escape of photoelectrons plays a more important role in the efficiency of a detector. Copyright © 2003 John Wiley & Sons, Ltd.     

Escape of photons and electrons from an HPGe detector at 81 keV

Escape of Ge K x‐rays, Compton‐scattered incident radiation and photoelectrons from an HPGe detector was investigated for 81 keV incident photons. All three escape mechanisms were observed in the same experiment. Experimental escape fractions were compared with the results from Monte Carlo simulations. Good agreement was obtained for the escape of photons. However, the simulations underestimated the escape of photoelectrons. Copyright © 2005 John Wiley & Sons, Ltd.     

An estimation of EDXRF spectrometer properties,based on a two‐layer composite Si‐Ge detector

A mathematical model for the two‐layer composite Si‐Ge energy dispersive X‐ray detector is proposed, based on analyses of radiation and electron transport in the detector, and a mathematical model of an energy dispersive X‐ray fluorescent spectrometer with the detector is considered. The Monte Carlo method is applied to calculate probabilities of photon detection in different parts of the detector's response function. The composite detector with the time anti‐coincidence scheme is proposed; its first layer is Si detector, and the second layer is Ge detector. It is shown that this composite detector has some advantages, such as reduced Ge photo escape peaks intensities and efficiency of detection of high energy photons similar to efficiency of Ge detector. Applying the X‐ray detector for the energy dispersive X‐ray fluorescent spectrometer provides for a lower background level. Copyright © 2012 John Wiley & Sons, Ltd.     

Components of detector response function: Monte Carlo simulations and experiment

Components of the response function of an HPGe detector for 32 keV incident photons (Ba Kα x‐rays) were studied using a Monte Carlo program. Physical mechanisms and the role of incident photons, detector x‐rays, photoelectrons and Compton recoil and Auger electrons for each component were investigated. The position, intensity and shape of the components, particularly of the photoelectrons, were studied in detail. Two distinct components for photoelectron escape were identified by considering the fate of photoelectrons, Ge x‐rays and Auger electrons produced in the same interaction. In contrast to the often‐cited shelflike structure, it was found that both components have a slope. The contribution of recoil electrons to the spectrum for single, double and multiple Compton scattering followed by photoelectric absorption of the scattered photon was investigated. The results of the Monte Carlo simulations are presented along with the measured Ba x‐ray spectrum. Copyright © 2006 John Wiley & Sons, Ltd.     

Absorbed dose calculations for macromolecular crystals: improvements to RADDOSE

Radiation damage is an unwelcome and unavoidable aspect of macromolecular crystallography. In order to quantify the extent of X‐ray‐induced changes, knowledge of the dose (absorbed energy per unit mass) is necessary since it is the obvious metric against which to plot variables such as diffraction intensity loss and B factors. Significant improvements to the program RADDOSE for accurately calculating the dose absorbed by macromolecular crystals are presented here. Specifically, the probability of energy loss through the escape of fluorescent photons from de‐excitation of an atom following photoelectric absorption is now included. For lighter elements, both the probability of fluorescence and of its subsequent escape from the crystal are negligible, but for heavier atoms the chance of fluorescence becomes significant (e.g. 30% as opposed to Auger electron decay from a K‐shell excited iron atom), and this has the effect of reducing the absorbed dose. The effects of this phenomenon on dose calculations are presented for examples of crystals of an iron‐containing protein, 2‐selenomethionine proteins, a uranium derivatised protein, and for a nucleic acid sample. For instance, the inclusion of fluorescent escape results in up to a 27% decrease in the calculated absorbed dose for a typical selenomethionine protein crystal irradiated at the selenium K‐edge.     

粒子在二维开放型四分之一圆形微腔中的逃逸研究

利用半经典理论对粒子在开放型四分之一圆形微腔中的逃逸过程进行了研究,推导出了逃逸几率密度的计算公式.我们研究了一簇从四分之一圆形微腔的左下方的入口出射、并从该微腔右边界逃逸的粒子轨迹.对于粒子的每一条逃逸轨迹,记录下它的传播时间和逃逸的位置.结果发现逃逸时间图随着逃逸点的位置的变化曲线呈现出振荡结构.随着碰撞次数的增加,逃逸点的位置越靠近该腔的右顶端.对一系列的探测点,找到从源点出发到达探测点的轨迹,然后应用半经典理论来构造波函数,进而给出逃逸几率密度的计算公式.研究结果标明,逃逸几率密度与探测平面上逃逸点的位置、粒子的动量、初始出射角及与微腔的碰撞次数有关.为了更清楚的看出量子力学和经典力学之间的联系,我们对体系的半经典波函数进行傅里叶变换,给出了粒子的路径长度谱.路径长度谱的每个峰值对应于一条粒子逃逸轨迹的长度.本文的研究对理解量子力学和经典力学之间的联系以及研究粒子在微腔中的的逃逸和输运过程有一定的参考价值.     

粒子在二维开放型四分之一圆形微腔中的逃逸研究

利用半经典理论对粒子在开放型四分之一圆形微腔中的逃逸过程进行了研究,推导出了逃逸几率密度的计算公式。我们研究了一簇从四分之一圆形微腔的左下方的入口出射、并从该微腔右边界逃逸的粒子轨迹。对于粒子的每一条逃逸轨迹,记录下它的传播时间和逃逸的位置。结果发现逃逸时间图随着逃逸点的位置的变化曲线呈现出振荡结构。随着碰撞次数的增加,逃逸点的位置越靠近该腔的右顶端。对一系列的探测点,找到从源点出发到达探测点的轨迹,然后应用半经典理论来构造波函数,进而给出逃逸几率密度的计算公式。研究结果标明,逃逸几率密度与探测平面上逃逸点的位置、粒子的动量、初始出射角及与微腔的碰撞次数有关。为了更清楚的看出量子力学和经典力学之间的联系,我们对体系的半经典波函数进行傅里叶变换,给出了粒子的路径长度谱。路径长度谱的每个峰值对应于一条粒子逃逸轨迹的长度。本文的研究对理解量子力学和经典力学之间的联系以及研究粒子在微腔中的的逃逸和输运过程可以提供一定的参考价值。     

Photoelectron,Compton and characteristic x‐ray escape from an HPGe Detector in the range 8–52 keV

Escape of photoelectrons, Compton‐scattered photons and Ge x‐rays from an HPGe detector was studied as a function of energy in the range 8–52 keV. A variable‐energy source producing Cu, Rb, Mo, Ag, Ba, and Tb x‐rays was used. All three mechanisms for energy loss were observed in the same experiment for Ba and Tb, while only x‐ray and photoelectron escapes were evident in the spectra for Ag, Mo, Rb, and Cu. Spectral features and possible mechanisms for partial energy deposition were investigated. A Monte Carlo program was used to simulate the relevant interactions, and to estimate the escape probabilities. Copyright © 2004 John Wiley & Sons, Ltd.     

Application of a pnCCD in X‐ray diffraction: a three‐dimensional X‐ray detector

The first application of a pnCCD detector for X‐ray scattering experiments using white synchrotron radiation at BESSY II is presented. A Cd arachidate multilayer was investigated in reflection geometry within the energy range 7 keV < E < 35 keV. At fixed angle of incidence the two‐dimensional diffraction pattern containing several multilayer Bragg peaks and respective diffuse‐resonant Bragg sheets were observed. Since every pixel of the detector is able to determine the energy of every incoming photon with a resolution ΔE/E? 10^?2, a three‐dimensional dataset is finally obtained. In order to achieve this energy resolution the detector was operated in the so‐called single‐photon‐counting mode. A full dataset was evaluated taking into account all photons recorded within 10⁵ detector frames at a readout rate of 200 Hz. By representing the data in reciprocal‐space coordinates, it becomes obvious that this experiment with the pnCCD detector provides the same information as that obtained by combining a large number of monochromatic scattering experiments using conventional area detectors.     

On some probabilistic functions of radiative transfer theory

We derive analytic formulae expressing the mean number of scatterings for escaping and thermalized photons and the probabilities of eventual escape and eventual thermalization, in terms of the direct escape probability of line photons. Specializations of these formulae give well known relations. A comparison with Finn's numerical results shown good agreement.     

类锂铝复合机制产生X光激光的等离子体状态

本文从速率方程出发,讨论了类锂铝复合等离子体的激发态结构,衰减常数,反转率和小信号增益等表征介质增益特性的物理量以及它们随电子温度,电子密度和光子逃逸几率的变化。找到了进行类锂铝离子通过复合机制产生X光激光设计应创造的等离子体状态目标区域。还讨论了这些物理量随原子序数变化的定标律。     

Application of an ePix100 detector for coherent scattering using a hard X‐ray free‐electron laser

A prototype ePix100 detector was used in small‐angle scattering geometry to capture speckle patterns from a static sample using the Linac Coherent Light Source (LCLS) hard X‐ray free‐electron laser at 8.34 keV. The average number of detected photons per pixel per pulse was varied over three orders of magnitude from about 23 down to 0.01 to test the detector performance. At high average photon count rates, the speckle contrast was evaluated by analyzing the probability distribution of the pixel counts at a constant scattering vector for single frames. For very low average photon counts of less than 0.2 per pixel, the `droplet algorithm' was first applied to the patterns for correcting the effect of charge sharing, and then the pixel count statistics of multiple frames were analyzed collectively to extract the speckle contrast. Results obtained using both methods agree within the uncertainty intervals, providing strong experimental evidence for the validity of the statistical analysis. More importantly it confirms the suitability of the ePix100 detector for X‐ray coherent scattering experiments, especially at very low count rates with performances surpassing those of previously available LCLS detectors.     

Photon escape probabilities for stark-broadened lyman series lines

A simple formula is derived for the escape probability of photons in optically thick resonance lines of hydrogenic ions. The result is valid whenever quasi-static Stark broadening predominates in the line wings, a condition that is satisfied in most laser-produced plasmas. In contrast to impact (Lorentzian) broadening, Stark broadening tends to decrease the probability of photon escape as the plasma density increases.     

Optimal Kα XRF detection geometry of arsenic in skin using an extended fundamental parameter method

The fundamental parameter (FP) method was extended to account for the geometrical details of experimental x‐ray fluorescence (XRF) detection. In the traditional FP method the primary fluorescence photons have parallel pathways towards the detector. In the new approach the primary fluorescence photons can travel in any direction which allows them to reach the detector if not absorbed or scattered. The derived XRF signal equation explicitly depends on the length of the collimator in front of the detector, the detector size, position and orientation. An algorithm which numerically calculates the XRF signal for any set of parameters was developed and implemented for the K_α XRF signal of arsenic in skin. Optimal positions and orientations of the detector and collimator ensemble which maximize the XRF signal were found. Results and limitations of the method were also discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

Performance of the micro‐PIC gaseous area detector in small‐angle X‐ray scattering experiments

The application of a two‐dimensional photon‐counting detector based on a micro‐pixel gas chamber (µ‐PIC) to high‐resolution small‐angle X‐ray scattering (SAXS), and its performance, are reported. The µ‐PIC is a micro‐pattern gaseous detector fabricated by printed circuit board technology. This article describes the performance of the µ‐PIC in SAXS experiments at SPring‐8. A dynamic range of >10⁵ was obtained for X‐ray scattering from a polystyrene sphere solution. A maximum counting rate of up to 5 MHz was observed with good linearity and without saturation. For a diffraction pattern of collagen, weak peaks were observed in the high‐angle region in one accumulation of photons.     

The probability of orbital angular momentum states of single photons with Z-tilt corrected residual aberration in a slant path turbulent atmosphere

With Rytov approximation and Kolmogorov spectrum model of index-of-refraction fluctuation, we study the effects of turbulence aberration on the orbital angular momentum of single photons in atmospheric communication channel. A theoretical model of measurement probabilities of orbital angular momentum states for single photons propagation under the Zernike tilt corrected slant path turbulent atmosphere channel is established. Our research shows that tilt-corrected residual aberration not only damage the initial OAM, but also induce new OAM. With the increasing of D/ρ₀, the number of the initial OAM photons will go down while the effective number of new OAM ascends. Meanwhile, the receiving probability of initial OAM photons declines, as the turbulence shifts from weak to strong. For Zernike tilt-corrected residual aberration, the receiving probability of initial OAM photons declines as the diameter of detector increases. The effect of Zernike tilt-corrected residual aberration on OAM of the photons is more larger than the effect of Zernike tilt turbulent aberration.     

The influence of frequency redistribution on the transfer of gyroresonant photons in the atmospheres of compact stars: Monte-Carlo analysis

We numerically model the frequency redistribution of gyroresonant photons in a plane-parallel semi-infinite plasma atmosphere of a compact star by means of the Monte-Carlo method. We calculate the mean frequency shift and the mean number of scatterings for photons leaving the atmosphere as functions of the optical depth at emission, plasma temperature, and magnetic field strength. The probability of the escape of cyclotron-radiation photons from the atmosphere as a function of their optical depth at birth is calculated. The influence of the frequency redistribution effects on the spectrum of emergent radiation is studied.     

Escape of Particles from an Open Square-Shaped Cavity

The escape of particles in an open square-shaped cavity has been examined. We consider a family of trajectories launched from the left bottom lead of the square cavity and escaped from the right boundary. For each escaping trajectories, we record the propagation time and the detector position. We find that the escape time graph exhibits a regular sawtooth structure. For a set of detector points, we search for the classical trajectories from the source point to the detector points. Then we use semiclassical theory to construct the wave function at different given points. The calculation results suggest that the escape probability density depends on the detector position and the momentum of the particle sensitively. The Fourier transform of the semiclassical wave function gives the path length spectrum. Each peak in the path length spectrum corresponds to the length of one escape trajectory of the particle. We hope that our results will be useful in understanding the escape and transport process of particles inside a microcavity.     

A versatile Monte Carlo package for computation of efficiencies of Si(Li), SDD and Ge detectors

Currently, most detector efficiency calculations for X‐ray detectors assume that the source is a point source on the axis of symmetry of the detector, but this is not always accurate. We have devised a Monte Carlo program to simulate photon transport in Si(Li), SDD and planar Ge detectors that natively handles finite, tilted and off‐axis sources. Although electron transport is not handled at this stage, photon transport is completely handled, including absorption from filters and multiple scattering in the detector crystal. The K escape peak is handled for both silicon and germanium detectors, and the L escape peak is also handled for germanium detectors. Our efficiency results compare very well with previous work when idealized systems are simulated, and the effect of a non‐idealized system is presented. Escape peak intensity ratios are given for both silicon detectors (K peak only) and germanium detectors (K and L peaks), and the results for the K escape peaks agree well with previous work. Results are presented for a recent annular detector system, which is a good example of systems that are poorly handled under previous efficiency calculations. Copyright © 2010 John Wiley & Sons, Ltd.     

The High Energy X-ray telescope (HE) onboard the Insight-HXMT astronomy satellite

The Insight-Hard X-ray Modulation Telescope(Insight-HXMT) is a broadband X-ray and γ-ray(1-3000 ke V) astronomy satellite. One of its three main telescopes is the High Energy X-ray telescope(HE). The main detector plane of HE comprises 18 Na I(Tl)/Cs I(Na) phoswich detectors, where Na I(Tl) is used as the primary detector to measure ~ 20-250 ke V photons incident from the field of view(FOV) defined by collimators, and Cs I(Na) is used as the active shielding detector to Na I(Tl) by pulse shape discrimination. Additionally, Cs I(Na) is used as an omnidirectional γ-ray monitor. The HE collimators have a diverse FOV,i.e. 1.1°×5.7°(15 units), 5.7°×5.7°(2 units), and blocked(1 unit). Therefore, the combined FOV of HE is approximately5.7°×5.7°. Each HE detector has a diameter of 190 mm resulting in a total geometrical area of approximately 5100 cm2, and the energy resolution is ~15% at 60 ke V. For each recorded X-ray event by HE, the timing accuracy is less than 10 μs and the deadtime is less than 10 μs. HE is used for observing spectra and temporal variability of X-ray sources in the 20-250 ke V band either by pointing observations for known sources or scanning observations to unveil new sources. Additionally, HE is used for monitoring the γ-ray burst in 0.2-3 Me V band. This paper not only presents the design and performance of HE instruments but also reports results of the on-ground calibration experiments.