Scattering Angle Distribution Research Articles

Measurement of the fractional radiation length of a pixel module for the CMS Phase-2 upgrade via the multiple scattering of positrons

High-luminosity particle collider experiments such as the ones planned at the High-Luminosity Large Hadron Collider require ever-greater vertexing precision of the tracking detectors, necessitating reductions in the material budget of the detectors. Traditionally, the fractional radiation length (x/X 0) of detectors is either estimated using known properties of the constituent materials, or measured in dedicated runs of the final detector. In this paper, we present a method of direct measurement of the material budget of a CMS prototype module designed for the Phase-2 upgrade of the CMS detector using a 40–65 MeV positron beam. A total of 630 million events were collected at the Paul Scherrer Institut PiE1 experimental area using a three-plane telescope consisting of the prototype module as the central plane, surrounded by two MALTA monolithic pixel detectors. Fractional radiation lengths were extracted from scattering angle distributions using the Highland approximation for multiple scattering. A statistical technique recovered runs suffering from trigger desynchronisation, and several corrections were introduced to compensate for local inefficiencies related to geometric and beam shape constraints. Two regions of the module were surveyed and yielded average x/X 0 values of (0.72 ± 0.05)% and (0.95 ± 0.09)%, which are compatible with empirical estimates for these regions computed from known material properties of 0.753% and 0.892%, respectively. Two types of higher-granularity maps of the fractional radiation length were produced, subdivided either into rectangular regions of uniform size, or polygonal-shaped regions of uniform material composition. The results bode well for the CMS Phase-2 upgrade modules, which will play a key role in the minimisation of the material of the upgraded detector.

Impact of Modeling Assumptions on Muon Scattering Images of Loaded Dry Storage Casks

Using cosmic muons allows for a noninvasive imaging approach to examine nuclear fuel in sealed dry storage casks. By assessing muons both before and after passing through the cask, one can infer details about the cask’s interior by analyzing scattering angle data. The effective scattering angles of muons depend on the characteristics of the interacting material, such as the atomic number (Z). This allows for the deduction of the material and geometric composition of the cask’s inventory. When employing simulations to forecast muon paths within the cask, it is essential to scrutinize the impact of modeling assumptions and simplifications on the scattering angle distribution. In this study, we examine the influence of modeling assumptions and simplifications on the effective scattering angle. Additionally, the significance of the number of particles used is shown. We evaluate four GEANT4 cask models of a CASTOR® V/19, each incorporating varying degrees of simplification, and analyze their impact on the projected muon scattering angle. These simplifications include both the simplification of individual geometric components of the cask and the complete exclusion of specific components. We assess and prioritize the various model simplifications in terms of their effect on the observed scattering angle. We recognize the importance of thoughtfully considering the degree of simplification used in the model to ensure accurate and reliable results for the scattering angle distribution.

The n-resolved single-electron capture in slow O6+–Ne collisions

Abstract A study of single-electron capture (SEC) in 18–240 keV O6+–Ne collisions has been conducted employing a combination of experimental and theoretical methodologies. Utilizing a reaction microscope, state-selective SEC cross sections and projectile scattering angle distributions were obtained. The translational energy spectra for SEC reveal the prevailing capture into n = 3 states of the projectile ion, with a minor contribution from n = 4 states. Notably, as the projectile’s energy increases, the relative contribution of SEC n = 4 states increases while that of SEC n = 3 states diminishes. Furthermore, we computed state-selective relative cross sections and angular differential cross sections employing the classical molecular Coulomb over-the-barrier model (MCBM) and the multichannel Landau–Zener (MCLZ) model. A discernible discrepancy between the state-selective cross sections from the two theoretical models is apparent for the considered impact energies. However, regarding the angular differential cross sections, an overall agreement was attained between the current experimental results and the theoretical results from the MCLZ model.

Automated potential energy surface development and comprehensive dynamics for the F + CH3NH2 reaction.

This work is an extensive investigation of the F + CH3NH2 reaction dynamics using a newly-developed potential energy surface (PES). The full-dimensional spin-orbit (SO) corrected (MRCI+Q/aug-cc-pwCVDZ) PES is developed by the Robosurfer program package and the ManyHF method is used in order to fix the Hartree-Fock (HF) convergence issues in the entrance channel. On the surface, retrieved by the fitting of the iteratively extended set of the ManyHF-CCSD(T)-F12a/triple-zeta-quality and SO-corrected energy points, quasi-classical trajectory (QCT) simulations are run. By analyzing the opacity functions and integral cross sections (ICSs) of six reaction channels, the dynamics of the two most reactive hydrogen-abstraction reactions resulting in HF + CH2NH2/CH3NH products are selected for a thorough examination. Despite the statistically and thermodynamically expected results, the kinetically preferred amino hydrogen-abstraction is the dominant mechanism at low collision energies. The initial attack angle and scattering angle distributions are investigated as well. The post-reaction energy distributions show that the collision energy mostly converts into the translational energy of the products, while the reaction energy excites the vibration of the products. The computed vibrationally resolved rotational distributions and vibrational state distributions of the HF product are compared to experimental data, and the theory and experiment are found to be in good agreement.

Vibrational mode-specificity in the dynamics of the OH- + CH3I multi-channel reaction.

We report a comprehensive characterization of the vibrational mode-specific dynamics of the OH- + CH3I reaction. Quasi-classical trajectory simulations are performed at four different collision energies on our previously-developed full-dimensional high-level abinitio potential energy surface in order to examine the impact of four different normal-mode excitations in the reactants. Considering the 11 possible pathways of OH- + CH3I, pronounced mode-specificity is observed in reactivity: In general, the excitations of the OH- stretching and CH stretching exert the greatest influence on the channels. For the SN2 and proton-abstraction products, the reactant initial attack angle and the product scattering angle distributions do not show major mode-specific features, except for SN2 at higher collision energies, where forward scattering is promoted by the CI stretching and CH stretching excitations. The post-reaction energy flow is also examined for SN2 and proton abstraction, and it is unveiled that the excess vibrational excitation energies rather transfer into the product vibrational energy because the translational and rotational energy distributions of the products do not represent significant mode-specificity. Moreover, in the course of proton abstraction, the surplus vibrational energy in the OH- reactant mostly remains in the H2O product owing to the prevailing dominance of the direct stripping mechanism.

Detailed quasiclassical dynamics of the F- + SiH3Cl multi-channel reaction.

We report a detailed quasiclassical trajectory study on the F- + SiH3Cl multi-channel reaction using a full-dimensional ab initio analytical potential energy surface. Reaction probabilities, cross sections, initial attack and scattering angle distributions as well as product relative translational, internal, vibrational, and rotational energy distributions are obtained in the collision energy range of 1-40 kcal mol-1 for the following channels: SiH3F + Cl-, SiH2Cl- + HF, SiH2F- + HCl, SiH2FCl + H-, SiH2 + FHCl-, and SiHFCl- + H2. All the channels are translationally cold indicating indirect mechanisms, except proton transfer (SiH2Cl- + HF), which shows mixed direct-indirect character. The angular distributions vary depending on collision energy and inversion/retention for SiH3F + Cl-. In the case of SiH2Cl- + HF front-side/back-side attack backward-forward/forward scattering preference is found at low/high collision energy. SiH2F- + HCl is formed with isotropic scattering and the preferred angle of attack is similar to the SiH3F + Cl- channel. SiH2FCl + H-/SiH2 + FHCl- favors back-side attack and isotropic/backward scattering, whereas SiHFCl- + H2 does not show significant angular preference.

Scattering direction sampling methods for polarized Monte Carlo simulation of oceanic lidar.

Monte Carlo techniques have been widely applied in polarized light simulation. Based on different preconditions, there are two main types of sampling strategies for scattering direction: one is the scalar sampling method; the others are polarized sampling approaches, including the one- and two-point rejection methods. The polarized simulation of oceanic lidar involves a variety of mediums, and an efficient scattering sampling method is the basis for the coupling simulation of the atmosphere and ocean. To determine the optimal scattering sampling method for oceanic lidar simulation, we developed a polarized Monte Carlo model and simulated Mie scattering, Rayleigh scattering, and Petzold average-particle scattering experiments. This simulation model has been validated by comparison with Ramella-Roman's program [Opt. Express13, 4420 (2005)OPEXFF1094-408710.1364/OPEX.13.004420], with differences in reflectance and transmittance Stokes less than 1% in Mie scattering. The simulation results show these scattering sampling methods differ in runtime, scattering angle distributions, and reflectance and transmittance Stokes. Considering the current simulation accuracy of oceanic lidar, the differences in reflectance and transmittance Stokes are acceptable; thus, the runtime becomes the main evaluation factor. The one-point rejection method and scalar sampling method are preferable for the oceanic lidar polarized simulation. Under complex atmosphere-ocean coupling systems, scalar sampling methods may be a better choice since the calculation process of the sampling is independent of the incident Stokes vector.

Measuring the Migdal effect in semiconductors for dark matter detection

The Migdal effect has received much attention from the dark matter direct detection community, in particular due to its power in setting limits on sub-GeV particle dark matter. Currently, there is no experimental confirmation of the Migdal effect through nuclear scattering using Standard Model probes. In this work, we extend existing calculations of the Migdal effect to the case of neutron-nucleus scattering, with a particular focus on neutron scattering angle distributions in silicon. We identify kinematic regimes wherein the assumptions present in current calculations of the Migdal effect hold for neutron scattering, and demonstrate that these include viable neutron calibration schemes. We then apply this framework to propose an experimental strategy to measure the Migdal effect in cryogenic silicon detectors using an upgrade to the NEXUS facility at Fermilab.

Experimental study on material discrimination based on muon discrete energy

Cosmic-ray muon is a kind of charged particle with strong penetrating capability and sensitivity to high atomic number materials. In recent years, muongraphy emerged as a novel technique by using cosmic-ray muon to image unknown volume, and is widely applied to nuclear security, geosciences, archaeology and civil engineering. The effect of multiple Coulomb scattering between muons and materials with different atomic number is different, and the scattering angle is related to material <i>Z</i> and muon energy. If we can measure muon scattering angle and muon energy, we can identify the category of material interacted with muon. However, it is difficult to measure the energy of each muon in real time, most of the researches use the mean muon energy ~4 GeV to alternate each muon energy which causes image to blurred and material discrimination accuracy to decrease. This article introduces a method of using the discrete muon energy to fit the scattering angle distribution derived from continuous muon energy and estimate the weight of each discrete muon energy. Then measure the scattering angle of the material to be identified, histogram the scattering angle and couple it with the calibrated scattering angle distribution by discrete muon energy. The last step is to calculate the radiation length from the above equation. The radiation length is a characteristic quantity of the material, and used to identify materials in this method. We carry out the experiment on material’s discrimination based on the apparatus of cosmic-ray muon tomography made by China Institute of Atomic Energy. The system contains 6 layers, consisting of several drift tube detectors planted in two orthogonal coordinate for tracking muon trajectory. Five materials are selected to be distinguished in the experiment, they being C, Al, Fe, Pb, and W. The scattering angles formed by muons passing through these materials are measured respectively, and their radiation lengths are measured and identified in pairs. In order to evaluate material discrimination accuracy, we plot the ROC curve between each pair of materials. The result reveals that Al-Fe and Fe-Pb can be effectively identified at a 95% confidence level, under 1400 valid muon events. Considering that the difference in material density also influences discrimination accuracy, we simulate several other materials identified by Pb. It is concluded that this method can identify the materials with radiation length greater than 0.7 cm. Compared with the discrimination method of unknowing muon energy, this method improves the accuracy of Pb-W discrimination by 18.5%.

Development of a cold target recoil ion momentum spectrometer and a projectile charge state analyzer setup to study electron transfer processes in highly charged ion-atom/molecule collisions.

We report the development and performance of a cold target recoil ion momentum spectrometer (COLTRIMS) setup at TIFR, which is built to study various atomic and molecular processes involving the interaction of slow, highly charged ions from an electron cyclotron resonance based ion accelerator. We give a detailed description of the experimental setup, as well as report some initial results on the electron-capture process in collisions of Ar8+ ions with helium and carbon monoxide targets. Here, we present the longitudinal momentum transfer and the sub-shell resolved Q-value spectrum in the case of 2, 4, and 6 keV/u Ar8+ beams in collision with helium. A longitudinal momentum resolution of 0.27a.u. is achieved in the present system. We also report the state-selective scattering angle distributions for all the collision systems under investigation. We further discuss the fragmentation of the CO2+ molecular ions for different electron capture channels for the 5 keV/u Ar8+ beam. The combination of the COLTRIMS, along with the beam cleaner, the electrostatic deflectors, and the charge state analyzer, is shown to have certain advantages.

Effects of background noise on fit parameters of plasma scattering angle distributions.

The presence of noise in plasma particle measurements by scientific instruments causes inaccuracies in the determined plasma bulk parameters. This study demonstrates and evaluates the effects of noise in the determination of typical distribution functions describing the scattering angles of plasma particles passing through thin foils. First, we simulate measurements of plasma particles passing through a thin carbon foil, considering that their scattering angles follow kappa-like distribution functions, as being addressed in previous studies. We work with these specific distributions because we can produce them in the laboratory. We add Poisson-distributed background noise to the simulated data. We fit the simulated measurements and compare the fit parameters with the input parameters. As expected, we find that the discrepancy between the initial parameters and those derived from the fits increases with the relative increase of the noise. The misestimations exhibit characteristic trends as functions of the signal-to-noise ratio and the input parameters. Second, we examine the scattering angle distributions measured with a laboratory experiment of protons passing through a thin carbon foil for different signal-to-noise ratios. These measurements support the simulation results, although they exhibit a larger discrepancy than found in the simulations. Finally, we discuss how we can improve the accuracy of estimated distribution parameters in space and ground-based applications by excluding data-points from the tails of the distribution functions. Although our results exhibit the effects of noise in a specific type of distribution functions, we explain that this technique can be applied to and optimized for other specific data-sets.

Full-dimensional automated potential energy surface development and dynamics for the OH + C2H6 reaction.

We develop a full-dimensional analytical potential energy surface (PES) for the OH + C2H6 reaction using the Robosurfer program system, which automatically (1) selects geometries from quasi-classical trajectories, (2) performs ab initio computations using a coupled-cluster singles, doubles, and perturbative triples-F12/triple-zeta-quality composite method, (3) fits the energies utilizing the permutationally invariant monomial symmetrization approach, and (4) iteratively improves the PES via steps (1)-(3). Quasi-classical trajectory simulations on the new PES reveal that hydrogen abstraction leading to H2O + C2H5 dominates in the collision energy range of 10-50 kcal/mol. The abstraction cross sections increase and the dominant mechanism shifts from rebound (small impact parameters and backward scattering) to stripping (larger impact parameters and forward scattering) with increasing collision energy as opacity functions and scattering angle distributions indicate. The abstraction reaction clearly favors side-on OH attack over O-side and the least-preferred H-side approach, whereas C2H6 behaves like a spherical object with only slight C-C-perpendicular side-on preference. The collision energy efficiently flows into the relative translation of the products, whereas product internal energy distributions show only little collision energy dependence. H2O/C2H5 vibrational distributions slightly/significantly violate zero-point energy and are nearly independent of collision energy, whereas the rotational distributions clearly blue-shift as the collision energy increases.

Energy loss correction on multiple Coulomb scattering of muons simulated by Geant4

The scattering angle distribution of muons passing through an object is crucial reference data for the application of the accelerator muon scattering imaging. In this study, the scattering angle distribution of muons in the accelerator energy region was simulated using the Monte Carlo toolkit Geant4 and calculated using the Molière’s theory. The results show that a significant deviation occurs when Molière’s theory is used to calculate the scattering angle distribution of muons in the accelerator energy region. We demonstrated that the deviation is due to the energy loss. Therefore, an energy loss correction was introduced on Molière’s theory, after which the calculated results are in good agreement with the Geant4 simulation. Furthermore, the relative error caused by using Moliere’s theory with different energy losses was calculated for muons of different energies, which can help clarify the importance of energy loss for accelerator muon scattering imaging.

Prediction of Muon Energy using Deep Neural Network with Multiple Coulomb Scattering Data

This study is based on the determination of muon beam energies using multiple Coulomb scattering data in artificial neural networks. Muon particles were scattered off a 50-layer lead object by using the G4beamline simulation program which is based on Geant4. Before working with deep neural networks, average scattering angle distributions in terms of the number of crossed layers were analyzed with the fitting method using the well-known formula for multiple Coulomb scattering to estimate muon beam energies. Subsequently, average scattering angles over the number of crossed layers from 1 to 10 were used in deep neural network structures to estimate the muon beam energy. It has been observed that deep neural networks significantly improve the resolutions compared to the ones obtained with the fitting method.

Direct dynamics simulation of the thermal O(3P) + dimethylamine reaction in the triplet surface. I. Rate constant and product branching

AbstractIn order to provide atomistic details for the mechanism of the collisional dynamics of O(3P) and dimethylamine (DMA) in the triplet electronic surface, direct dynamics simulations are reported herein. The simulations are performed at the U‐HSE06/aug‐cc‐pVDZ level of theory. The results are reported for the relative collision energy of 7.8 kcal/mol. For the vibrational and rotational excitations, following temperature regimes have been considered: 200 and 10 K, respectively. Simulations reveal that the reaction can lead to two product channels in the considered energy regime: (1) 2OH + 2CH3NHCH2 and (2) 2OH + 2CH3NCH3. The computed reaction cross section for pathways 1 and 2 are as follows: 17.89 0.20 Å2 and 3.28 0.03 Å2, whereas the computed microcanonical reaction rate constants for pathways 1 and 2 are as follows: (4.21 0.05)*10−10 and (7.72 0.07)*10−11 cm3/(molecule sec). Both pathways follow direct and indirect H abstraction processes. Among the direct pathways, stripping and rebound mechanisms have been observed, whereas the indirect pathway involves formation of a post‐reaction complex having lifetime ~0.4–0.5 ps. The velocity scattering angle distribution for the reaction is dominated by scattering in the sideways (60–120 ) and backward (120–180 ) directions with some contribution from the scattering in the forward direction (0–60 ).

State-selective single-electron capture in intermediate-energy C4+ + He collisions

A combined experimental and theoretical study on single capture in 15--$50\phantom{\rule{0.28em}{0ex}}\mathrm{keV}/\mathrm{u}\phantom{\rule{0.16em}{0ex}}{\mathrm{C}}^{4+} +$ He collisions was performed. State-selective single-electron capture cross sections and projectile scattering angle distributions were obtained by using a reaction microscope. A comparison of the state-selective cross sections with theoretical calculations based on the two-active-electron semiclassical atomic-orbital close-coupling method showed an excellent agreement for the considered impact energies. For the angular differential cross sections, an overall agreement was also obtained between the present experimental and theoretical results. Simulations performed using an extended Fraunhofer-type diffraction model suggest that the undulatory structures observed at small scattering angles for capture to ${\mathrm{C}}^{3+}(1{s}^{2}2s$) and ${\mathrm{C}}^{3+}(1{s}^{2}2{p}_{0}$) can be interpreted as the diffraction pattern of the incident projectile de Broglie wave confined by an aperture defined as the region around the target where the considered capture process is likely. The strong competition between single-electron capture to ${\mathrm{C}}^{3+}(1{s}^{2}2{p}_{0}$) and ${\mathrm{C}}^{3+}(1{s}^{2}2{p}_{1}$) is also discussed to interpret the differences observed between their respective differential cross sections.

Direct dynamics in a proton transfer reaction of isomer product competition. Insight into the suppressed formation of the isoformyl cation.

Proton transfer between HOCO+ and CO produces the formyl cation HCO+ and isoformyl cation HOC+ isomers initiating multiple astrochemical reaction networks. Here, the direct chemical dynamics simulations are performed to uncover the underlying atomistic dynamics of the above reaction. The simulations reproduce the measured product energy and scattering angle distributions and reveal that the reaction proceeds predominantly through a direct stripping mechanism which results in the prominent forward scattering observed in experiments. The reaction dynamics show propensity for the HCO+ product even at a collision energy larger than the threshold for HOC+ formation. This is a consequence of the larger opacity and impact parameter range for HCO+. In accordance with the revealed direct mechanistic feature, the reaction can be controlled by orienting the reactants into a reactive H-C orientation that also favors HCO+ formation. Considering the lack of equilibrated reactant complexes and the on the fly migration of the proton, the CO2-catalyzed isomerization is assumed to have insignificant impact on the isomer ratios. This work provides insights of dynamical effects besides energetics into the interesting finding of strongly suppressed formation of the metastable isoformyl cation for related proton transfer reactions in the measurements.

Molecular dynamics study on scattering characteristics of nitrogen molecules from platinum surface by molecular beam method

Rarefied gas flow has received wide attention due to the booming of micro/nano-electromechanical systems and aerospace engineering. Under such rarefied conditions, the frequency of intermolecular collisions is sharply reduced, so the impacts of interactions between gas molecules and the wall surface on flow states become non-negligible. Owing to the complexity of theoretical research and the poor reproducibility of experimentation, molecular dynamics simulation has developed into an effective method to study the interplay between gases and solid surfaces. In this study, molecular dynamics simulations on the scattering process of nitrogen molecules from a platinum surface are conducted in a three-dimensional system. The dependences of scattering angle distributions and momentum/energy variations on the incident velocity, angles, and surface roughness are obtained. The results of this paper are not only an attempt to reveal the mechanisms of gas–surface interactions but can also be used as necessary reference data for the development of appropriate gas–surface interaction models.

Dynamics Studies of O2 Collision on Pt(111) Using a Global Potential Energy Surface

The dynamics of O2 collision on Pt(111) has been studied by molecular dynamics simulations using a global potential energy surface (PES), which was developed by fitting ∼4800 plane-wave density functional theory points using the permutation invariant polynomial-neural network method. The simulations were performed for the normal and off-normal incidences at a wide range of incident energies and surface temperatures. A generalized Langevin oscillator model was used to incorporate the molecule–surface coupling that plays an important role in this collision process. The trapping probability, final energy distribution, scattering angle distributions of scattered molecules, and the energy transfer to surface distribution were determined and analyzed. The PES shows an activated path to the chemisorption states, as the trapping probability directly increases with incident energy (larger than 0.1 eV) to reach a maximum and then decreases at high incident energy. The trapping probability obviously reduces by raising surface temperature at low incident energy because the initial kinetic energy of molecule is more likely to be dissipated into surface motions than molecular internal ro-vibrational modes. Additional parallel momentum of off-normal incidence leads to a strong suppression of the trapping probability, caused by the energetic corrugation of the lateral barrier heights. The scattering angular distributions are found to be quasispecular and the final translational energy slightly increases with scattering angle deviating significantly from the hard-cube model, indicating the nonconservation of parallel momentum during the collision on the corrugate PES.

Noncollinear Ordering of the Orbital Magnetic Moments in Magnetite.

The magnitude of the orbital magnetic moment and its role as a trigger of the Verwey transition in the prototypical Mott insulator, magnetite, remain contentious. Using 1s2p resonant inelastic x-ray scattering angle distribution (RIXS-AD), we prove the existence of noncollinear orbital magnetic ordering and infer the presence of dynamical distortion creating a polaronic precursor for the metal to insulator transition. These conclusions are based on a subtle angular shift of the RIXS-AD spectral intensity as a function of the magnetic field orientation. Theoretical simulations show that these results are only consistent with noncollinear magnetic orbital ordering. To further support these claims we perform Fe K-edge x-ray magnetic circular dichroism in order to quantify the Fe average orbital magnetic moment.