Elastic Differential Cross Sections Research Articles

Elastic differential neutron-scattering cross section on even Neodymium isotopes

In this paper, we present an analytical formula for the neutron scattering cross section on even-even heavy nuclei, employing the rotational model and making certain assumptions, such as the use of the Yukawa potential shape for the neutron-nucleon interaction, the rigid rotor approximation, and the assumption of a uniformly distributed nuclear matter within the nucleus. Notably, a significant aspect of this study is the avoidance of any approximation of a central potential, in contrast to the commonly employed methods of expanding the potential based on the power of , utilizing the Legendre polynomial basis, or employing Fourier-Bessel analysis. Despite the simplicity of the chosen model (rigid rotor model and the two-parameter potential), our results yield satisfying and encouraging outcomes. This suggests the effectiveness of our approach in analyzing neutron scattering on even-even heavy nuclei. It is important to note that further investigations are warranted to deepen our understanding and refine the assumptions utilized in this study. Future research should explore the applicability of the proposed analytical formula to diverse nuclei and consider more complex models to expand our comprehension of neutron-nucleus interactions.

Differential and integral elastic cross sections for electrons and positrons collisions with carbon dioxide molecules

This study investigates the elastic scattering of electrons and positrons by carbon dioxide (CO2) molecules over a wide energy range from 1 eV to 1 KeV. We have computed differential and integral elastic cross-sections (DCS and ICS) using partial wave analysis and compared the theoretical results with available experimental data. Our findings show a strong correlation with experimental results, particularly at mid to high-energy ranges, validating the employed theoretical frameworks. Additionally, the Sherman function was examined to explore spin polarisation effects during scattering events. This research provides crucial insights for applications in atmospheric physics, materials science, and molecular scattering processes, demonstrating its direct relevance to real-world problems and paving the way for further investigation into particle-molecule interactions.

Extraction of Molecular-Frame Electron-Ion Differential Scattering Cross Sections Based on Elliptical Laser-Induced Electron Diffraction.

We extracted the molecular-frame elastic differential cross sections (MFDCSs) for electrons scattering from N_{2}^{+} based on elliptical laser-induced electron diffraction (ELIED), wherein the structural evolution is initialized by the same tunneling ionization and probed by incident angle-resolved laser-induced electron diffraction imaging. To establish ELIED, an intuitive interpretation of the ellipticity-dependent rescattering electron momentum distributions was first provided by analyzing the transverse momentum distribution. It was shown that the incident angle of the laser-induced returning electrons could be tuned within 20° by varying the ellipticity and handedness of the driving laser pulses. Accordingly, the incident angle-resolved DCSs of returning electrons for spherically symmetric targets (Xe^{+} and Ar^{+}) were successfully extracted as a proof-of-principle for ELIED. The MFDCSs for N_{2}^{+} were experimentally obtained at incident angles of 4° and 7°, which were well reproduced by the simulations. The ELIED approach is the only successful method so far for obtaining incident angle-resolved ionic MFDCS, which provides a new sensitive observable for the transient structure retrieval of N_{2}^{+}. Our results suggest that the ELIED has the potential to extract the structural tomographic information of polyatomic molecules with femtosecond and subangstrom spatiotemporal resolutions that can enable the visualization of the nuclear motions in complex chemical reactions as well as chiral recognition.

Scattering of e∓ in beryllium isonuclear series: cross sections and transport characteristics

The elastic scattering of electrons and positrons by beryllium atoms and its isonuclear ion states is described in this paper in terms of differential and various angle integrated cross sections. For this element, the critical minima in the elastic differential cross sections and the optimum spin polarization sites are found. These calculations are performed using the Dirac partial wave analysis (DPWA) and a projectile-target modified complex optical model potential. Further, the Monte Carlo method is used to calculate the transport characteristics of electrons in a mixture of inert gas (He, Ar) and beryllium vapor for electric field values E/N = 1-100 Td, taking into account inelastic collisions. We studied the effect of metal vapor concentration on drift velocity, average electron energy, diffusion and mobility coefficients. Finally, we investigated the effect of beryllium vapor on the electron energy distribution function in the inert gas. On comparing present work with existing theoretical calculation, a reasonable agreement is observed.

Oscillations in the elastic high energy amplitude

We discuss the oscillations in the elastic pp differential cross section seen in the TOTEM data at s=13\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{s}=13$$\\end{document} TeV on the top of the usual smooth behaviour.

Electron scattering cross sectional data for precursors used in plasma-assisted deposition

In this study, a comprehensive electron scattering analysis is performed on the precursors AlF3 and AlCl3 used in the plasma-assisted deposition technique. We used the R-matrix and spherical complex optical potential formalisms to calculate the integral elastic cross sections for electron energies between 0.1 and 5000 eV. At low energies, we computed differential and integral elastic cross sections and excitation cross sections using the R-matrix method. We have also reported the ionization cross section using the complex scattering potential-ionization contribution method and the binary-encounter-Bethe method. Our computed results show overall good agreement with the available data in the literature.

Elastic cross section data for precursor molecules used in low-temperature plasmas: Sn(CH3)4 and Ga(CH3)3

Tetramethyltin [Sn(CH3)4] and trimethylgallium [Ga(CH3)3] are important source molecules of Sn and Ga atoms which are used in manufacturing techniques involving low-temperature plasmas. Accurate numerical modeling of plasma environments requires a comprehensive set of electron scattering cross sections by these precursor molecules. Here, we report the elastic integral, differential, and momentum transfer cross sections for electron collisions with Sn(CH3)4 and Ga(CH3)3 for energies ranging from 0 to 30 eV. Our calculations were carried out with the Schwinger multichannel method implemented with pseudopotentials and considered two levels of approximation in our calculations, namely static-exchange and static-exchange plus polarization. We identified three shape resonances for Sn(CH3)4 and one clear low-lying resonance for Ga(CH3)3. The low-energy behavior of the s-wave cross section and eigenphase was investigated and, for both molecules, we found evidence of a Ramsauer–Townsend (RT) minimum and a virtual state. Our results indicate that negative differential conductivity would occur in a gas composed of Sn(CH3)4. On the other hand, this effect would be suppressed in a gas of Ga(CH3)3 due to an overlap between the position of the RT minimum and the shape resonance in the momentum-transfer cross section.

Prospects for thermalization of microwave-shielded ultracold molecules

Toward more efficient schemes for achieving deeply degenerate molecular Fermi gases, we study anisotropic thermalization in dilute gases of microwave shielded polar molecular fermions. For collision energies above the threshold regime, we find that thermalization is suppressed due to a strong preference for forward scattering and a reduction in total cross section with energy, significantly reducing the efficiency of evaporative cooling. We perform close-coupling calculations on the effective potential energy surface derived by Deng [] to obtain accurate two-body elastic differential cross sections across a range of collision energies. We use Gaussian process regression to obtain a global representation of the differential cross section over a wide range of collision angles and energies. The route to equilibrium is then analyzed with cross-dimensional rethermalization experiments, quantified by a measure of collisional efficiency toward achieving thermalization. Published by the American Physical Society 2024

Results on elastic cross sections in proton–proton collisions at [formula omitted] GeV with the STAR detector at RHIC

We report results on an elastic cross section measurement in proton–proton collisions at a center-of-mass energy s=510 GeV, obtained with the Roman Pot setup of the STAR experiment at the Relativistic Heavy Ion Collider (RHIC). The elastic differential cross section is measured in the four-momentum transfer squared range 0.23≤−t≤0.67 GeV2. This is the only measurement of the proton-proton elastic cross section in this t range for collision energies above the Intersecting Storage Rings (ISR) and below the Large Hadron Collider (LHC) colliders. We find that a constant slope B does not fit the data in the aforementioned t range, and we obtain a much better fit using a second-order polynomial for B(t). This is the first measurement below the LHC energies for which the non-constant behavior B(t) is observed. The t dependence of B is also determined using six subintervals of t in the STAR measured t range, and is in good agreement with the phenomenological models. The measured elastic differential cross section dσ/dt agrees well with the results obtained at s=540 GeV for proton–antiproton collisions by the UA4 experiment. We also determine that the integrated elastic cross section within the STAR t-range is σelfid=462.1±0.9(stat.)±1.1(syst.)±11.6(scale)μb.

Simple Lévy α-Stable Model Analysis of Elastic pp and pp¯ Low-|t| Data from SPS to LHC Energies

A simple Lévy α-stable (SL) model is used to describe the data on elastic pp and pp¯ scattering at low-|t| from SPS energies up to LHC energies. The SL model is demonstrated to describe the data with a strong non-exponential feature in a statistically acceptable manner. The energy dependence of the parameters of the model is determined and analyzed. The Lévy α parameter of the model has an energy-independent value of 1.959 ± 0.002 following from the strong non-exponential behavior of the data. We strengthen the conclusion that the discrepancy between TOTEM and ATLAS elastic pp differential cross section measurements arises only in the normalization and not in the shape of the distribution of the data as a function of t. We find that the slope parameter has different values for pp and pp¯ elastic scattering at LHC energies. This may be the effect of the odderon exchange or the jump in the energy dependence of the slope parameter in the energy interval 3 GeV ≲s≲ 4 GeV.

Elastic and inelastic cross-sections for 12C + CO2 and 13C + CO2 scattering at superthermal energies

ABSTRACT We report elastic and inelastic cross-sections for fast superthermal 12C(3P) and 13C(3P) atoms scattering on 12CO2. The cross-sections were computed using quantum-mechanical rotationally close-coupling formalism with the electronic interaction described by a newly constructed potential energy surface correlating to the lowest energy asymptote of the complex. State-to-state rotational cross-sections, differential cross-sections, and derived transport properties of interest for energy relaxation are also reported. The computed elastic differential cross-sections are found to be strongly anisotropic, show significant energy dependence, and differ by up to 2 percent between the two isotopes of carbon.

Stereodynamical control of cold HD + D2 collisions.

We report full-dimensional quantum calculations of stereodynamic control of HD(v = 1, j = 2) + D2 collisions that has been probed experimentally by Perreault et al. using the Stark-induced adiabatic Raman passage (SARP) technique. Computations were performed on two highly accurate full-dimensional H4 potential energy surfaces. It is found that for both potential surfaces, rotational quenching of HD from with concurrent rotational excitation of D2 from is the dominant transition with cross sections four times larger than that of elastically scattered D2 for the same quenching transition in HD. This process was not considered in the original analysis of the SARP experiments that probed ΔjHD = -2 transitions in HD(vHD = 1, jHD = 2) + D2 collisions. Cross sections are characterized by an l = 3 resonance for ortho-D2(jD2 = 0) collisions, while both l = 1 and l = 3 resonances are observed for the para-D2(jD2 = 1) partner. While our results are in excellent agreement with prior measurements of elastic and inelastic differential cross sections, the agreement is less satisfactory with the SARP experiments, in particular for the transition for which the theoretical calculations indicate that D2 rotational excitation channel is the dominant inelastic process.

Pikoe: A computer program for distorted-wave impulse approximation calculation for proton induced nucleon knockout reactions

pikoe, Proton-Induced KnockOut reaction calculation for Exclusive processes, is a Fortran 90 program that calculates triple- and quadruple-differential cross sections, vector analyzing powers, and momentum distributions of reaction residues, for proton-induced nucleon knockout reactions in normal and inverse kinematics. The distorted-wave impulse approximation with the factorization approximation to the nucleon-nucleon transition matrix is adopted, and the distorted waves of the incoming proton and the outgoing two nucleons are calculated quantum mechanically. Kinematics of the reaction particles are treated in a relativistic manner, which gives the proper asymptotics of the three-body scattering wave in the plane-wave limit. Program summaryProgram Title: pikoeCPC Library link to program files:https://doi.org/10.17632/m594h58kck.1Licensing provisions: MITProgramming language: Fortran 90Supplementary material: See https://www.rcnp.osaka-u.ac.jp/~kazuyuki/pikoe/index.phpNature of problem: Calculation of triple- and quadruple-differential cross sections, vector analyzing powers, and momentum distributions of reaction residues, for nucleon knockout reactions with proton beams/targets in normal/inverse kinematics.Solution method: Numerov method for solving single-channel second-order differential equations; multi dimensional integration with the Gauss-Legendre quadrature rule.Additional comments including restrictions and unusual features: The global optical potential by Koning and Deraloche [1] for nucleons at energies from 1 keV to 200 MeV, for (near-)spherical nuclei with mass number between 24 and 209, is implemented in the program. Tables of nucleon-nucleon (NN) elastic differential cross sections and NN transition amplitudes calculated with the NN effective interaction by Franey and Love [2] are provided as external files for pikoe (included in the package). Users are encouraged to prepare tables for the optical potentials and the cross sections of the elementary process according to the reaction system of interest by themselves. With external files thus prepared, pikoe can be applied to various kinds of knockout processes such as α or deuteron knockout by proton, α-induced knockout reactions, etc. Calculation of spin observables, the vector analyzing power in fact, however, is restricted to nucleon-induced nucleon knockout processes with the coplanar kinematics.

MASAP: A package for atomic scattering amplitude in solids

We present the MsSpec Atomic Scattering Amplitude Package (MASAP), composed of a computation program and a graphical interface to generate atomic scattering amplitude (ASA) of an atom, either isolated or embedded in an environment, at any chosen energy of the impinging electron up to ≈15 KeV. The ASA is calculated using an effective, complex optical potential which provides damping effects in the scattering process in a fully relativistic framework. Optionally, scalar relativistic and non-relativistic approximations are also available to assess their applicability to a given problem. In order to describe electron propagation in solids we suggest to replace ASA's based on Plane Waves (PW) scattering with effective ASA's based on curved Spherical Waves (SW) using truncated-overlapped potentials of the Muffin-Tin (MT) type constructed according to the Mattheiss prescription. The graphical user interface generates not only ASA data files providing atomic Differential Cross Sections (DCS) but also files of related quantities such as total Cross Section (CS), both elastic and inelastic, atomic tl-matrices and phase shifts. We found in general that the imaginary part of the optical potential enhances the calculated elastic DCSs in the forward direction compared to the same potential without the imaginary part, a feature related to the optical theorem, but gives rise to a lower intensity at all other directions as expected due to the damping effect of the complex part of the potential. We show calculated differential and transport Cross Sections for aluminum and gold atoms both in isolation and in crystals with the Face-Centered-Cubic (FCC) structure. Program summaryProgram Title: MASAPCPC Library link to program files:https://doi.org/10.17632/gtxp3mn5hs.1Licensing provisions: Apache 2.0Programming language: FORTRAN 77, Python3External routines:•SciPy (https://www.scipy.org)•Atomic Simulation Environment (https://wiki.fysik.dtu.dk/ase/)•h5py (https://www.h5py.org)•wxPython (https://www.wxpython.org)Nature of problem: Calculation of atomic scattering amplitudes of scattered electrons by an embedded atom in a solid including damping and relativistic effects. Comparison between ASA's in an isolated atomic system and a solid. Introduction of an effective ASA for electrons propagating in a solid derived from Multiple Scattering Theory.Solution method: Potential scattering theory. Muffin-tin approximation. Superposition of atomic electron densities obtained by self-consistent Dirac-Fock atomic calculations. Hedin-Lundqvist potential as an optical potential. Fully relativistic theory, with scalar-relativistic and non-relativistic approximations for comparison.Additional comments including restrictions and unusual features: Even though the program can perform calculations at impinging electron energies up to ≈15 Kev, DCS calculations are recommended in the range 50 : ≈1500 eV both in the case of isolated atoms and atoms embedded in solids, since this interval is more suitable for studying the details of the atomic potentials in their environment.In the case of solids, at energies lower than ≈50 eV, the details of the electronic structure might be important, whereas in the case of isolated atoms this range might suffer from the neglect of the polarization potential and coupling to available inelastic channels. In this respect an option to add an empirical form of a polarization potential to investigate its effects is available to the interested user.

Probing the Elastic Scattering Differential Cross Section for Al + p at Backward Angles in a Low Energy Regime

We report on the absolute differential cross section for proton elastic scattering on aluminum in the energy range of 0.8 MeV to 2.1 MeV. In the literature we have found previously published data that follow similar trends but are not consistent with one another. The present measurements also fall within that range, moreover, covering angular regions where there were no reported data, improving databases such as IBANDL. Different methods for the optical model calculations are shown where angular distributions at backward angles are in good agreement, allowing one to fix the optical potential parameters. The calculation results, as well as their data fit, differ significantly as one would expect for the energy range covered in this work, where the nuclear part of the interaction contribution is almost zero. Our data, as well as previous reports, suggest an increase with higher energies for the value of the elastic cross section at backward angles. Further work is required from both experimental and theoretical fronts.

Physics with intact protons at the LHC: from the odderon discovery to the sensitivity to beyond standard model physics

We describe the discovery of the colorless C-odd gluonic compound, the odderon, by the D0 and TOTEM Collaborations by comparing elastic differential cross sections measured in pp and pp¯ interactions at high energies. We also discuss the reach on quartic anomalous couplings and the sensitivity to axion like particle production by using the LHC as a γγ collider and detecting the intact protons at high luminosity.

A multi-channel U-Matrix model of hadron interaction at high energy

The present phenomenological study investigates a multi-channel model of high-energy hadron interactions by considering a full parton configurations space and the U-matrix unitarisation scheme of the elastic amplitude, comparing it to the two-channel model, and examining the consequences of up-to-date high-energy collider data on the best fits to various hadronic observables in pp and poverline{p} collisions. The findings of this study reveal that the data are well-fitted with the multi-channel model and that the difference compared to the two-channel one is negligible. Of particular significance is the observation that the U-matrix unitarisation is likely incompatible with uncorrelated pomeron exchange, as suggested by the equivalence between the U-matrix multi-channel and eikonal two-channel descriptions. Based on our best fit, predictions for the ρ parameter, the double diffractive cross-section, and the elastic differential cross-section are provided. We shed light on the effect of taking into account a multi-channel model on present and future cosmic ray data.

Low-Energy Electron and Positron Scattering by para-Difluorobenzene.

The Schwinger multichannel method is employed in calculations of the elastic integral and differential cross sections for collisions of low-energy electrons and positrons with para-difluorobenzene (1,4-C6H4F2). The present calculations involving electron scattering have been performed using both static-exchange and static-exchange plus polarization levels of approximation. Our results indicate the presence of three resonances of π*-character in the low-energy region and a fourth resonance, of σ*-character, at higher energy levels. With respect to the positron scattering, the calculations were conducted using the static plus polarization approximation at three different polarization levels. The present calculated electron and positron cross sections show a reasonable agreement with the total cross sections measured by Makochekanwa et al. (J. Phys. B, 2004, 37, 1841). It is also important to highlight that our computed integral cross section for electron scattering indicates the presence of a Ramsauer-Townsend minimum, while the integral cross section for positron scattering indicates the presence of a virtual state.

Strong Dark Matter Self-interactions Diversify Halo Populations within and surrounding the Milky Way

We perform a high-resolution cosmological zoom-in simulation of a Milky Way (MW)–like system, which includes a realistic Large Magellanic Cloud analog, using a large differential elastic dark matter self-interaction cross section that reaches ≈100 cm2 g−1 at relative velocities of ≈10 km s−1, motivated by the diverse and orbitally dependent central densities of dwarf galaxies within and surrounding the MW. We explore the effects of dark matter self-interactions on satellite, splashback, and isolated halos through their abundance, central densities, maximum circular velocities, orbital parameters, and correlations between these variables. We use an effective constant cross section model to analytically predict the stages of our simulated halos’ gravothermal evolution, demonstrating that deviations from the collisionless – relation can be used to select deeply core-collapsed halos, where is a halo’s maximum circular velocity, and is the radius at which it occurs. We predict that a sizable fraction (≈20%) of subhalos with masses down to ≈108 M ⊙ is deeply core collapsed in our SIDM model. Core-collapsed systems form ≈10% of the isolated halo population down to the same mass; these isolated, core-collapsed halos would host faint dwarf field galaxies with extremely steep central density profiles. Finally, most halos with masses above ≈109 M ⊙ are core-forming in our simulation. Our study thus demonstrates how self-interactions diversify halo populations in an environmentally dependent fashion within and surrounding MW-mass hosts, providing a compelling avenue to address the diverse dark matter distributions of observed dwarf galaxies.

Integral measurements of plural and multiple scattering of electrons with energies between [formula omitted] and [formula omitted] keV for [formula omitted]:II. Thick targets

Angle-integrated multiple-scattering distributions are provided for electrons with energies between 10 and 100 keV hitting Al, Cu, Sn, and Au foils. The present results differ from those published in part I (Barros et al., 2023) because the targets have ≈10 times larger mass thicknesses of the order of ≈1.5 to 5 mg/cm2. It is then possible to follow, by increasing the beam energy, the behaviour around the point of punch-through of the electrons (when a small fraction begins to cross the target, between ≈30 to 60 keV depending on the material and thickness) up to 100 keV, where absorption in the target itself is small. The measurements were performed together with those of part I employing the same setup. The electrons have been collected with a Faraday cup, accepting the most frontal scattering angles, and a ring, that surrounds the entrance of the cup, still covering rather forward deflections. The normalisation is provided by measuring the current in the chamber, which close-up completely the remaining solid angle, and the electrons stopped within the target, which is also electrically connected to the chamber. The same corrections for the electrons backscattered by the Faraday cup and the ring found in part I are applied. The measurements, all referring to homogeneous targets, are compared with the predictions of the Goudsmit–Saunderson and Lewis analytical approaches and to the PENELOPE-2018 Monte Carlo code to take into account, as far as possible, the effect of the energy loss. In all cases, the elastic differential cross sections are those of the ICRU Report 77, ensuing from a partial-wave solution of the Dirac equation in a self-consistent isolated-atom central potential. While the analytical calculations do not work, in general, for the thick targets, good agreement is found between simulations and measurements.