Elastic Differential Cross Sections Research Articles

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.

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.

Measurement of the total cross section and rho -parameter from elastic scattering in pp collisions at sqrt{s}=13 TeV with the ATLAS detector

In a special run of the LHC with beta ^{star } = 2.5 km, proton–proton elastic-scattering events were recorded at sqrt{s} = 13 TeV with an integrated luminosity of 340~upmu {text {b}}^{-1} using the ALFA subdetector of ATLAS in 2016. The elastic cross section was measured differentially in the Mandelstam t variable in the range from -t = 2.5 cdot 10^{-4} GeV^{2} to -t = 0.46 GeV^{2} using 6.9 million elastic-scattering candidates. This paper presents measurements of the total cross section sigma _{text {tot}}, parameters of the nuclear slope, and the rho -parameter defined as the ratio of the real part to the imaginary part of the elastic-scattering amplitude in the limit t rightarrow 0. These parameters are determined from a fit to the differential elastic cross section using the optical theorem and different parameterizations of the t-dependence. The results for sigma _{text {tot}} and rho are σtot(pp→X)=104.7±1.1mb,ρ=0.098±0.011.\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \\sigma _{\ ext {tot}}(pp\\rightarrow X) = 104.7 \\pm 1.1 \\; \ ext{ mb },\\quad \\rho = 0.098 \\pm 0.011 . \\end{aligned}$$\\end{document}The uncertainty in sigma _{text {tot}} is dominated by the luminosity measurement, and in rho by imperfect knowledge of the detector alignment and by modelling of the nuclear amplitude.

Fresh look at experimental evidence for odderon exchange

Theory suggests that in high-energy elastic hadron+hadron scattering, t-channel exchange of a family of colourless crossing-odd states – the odderon – may generate differences between pp¯ and pp cross-sections in the neighbourhood of the diffractive minimum. Using a mathematical approach based on interpolation via continued fractions enhanced by statistical sampling, we develop robust comparisons between pp¯ elastic differential cross-sections measured at √s=1.96 TeV by the D0 Collaboration at the Tevatron and function-form-unbiased extrapolations to this energy of kindred pp measurements at √s/TeV=2.76,7,8,13 by the TOTEM Collaboration at the LHC and a combination of these data with earlier cross-section measurements at √s/GeV=23.5,30.7,44.7,52.8,62.5 made at the intersecting storage rings. Focusing on a domain that straddles the diffractive minimum in the pp¯ and pp cross-sections, we find that these two cross-sections differ at the (2.2−2.6)σ level; hence, supply evidence with this level of significance for the existence of the odderon. If combined with evidence obtained through different experiment-theory comparisons, whose significance is reported to lie in the range (3.4−4.6)σ, one arrives at a (4.0−5.2)σ signal for the odderon.

Theoretical study of low-energy electron collision with normal-pentane using R-matrix method

Low-energy electron collisions with normal-pentane (n-C5H12) that initiate the plasma to assist combustion are critical in understanding the underlying physics and chemistries. In the present work, we studied this collisional process using the R-matrix method at the static-exchange plus polarization and close-coupling model levels. The scattering calculation was performed by running the UKRmol+ code using the Quantemol Electron Collision interface to obtain elastic differential, momentum transfer, integral, and electronic excitation cross sections up to 20 eV and ionization cross sections up to 1000 eV. Our computed cross-section data are in better agreement with the available experimental results both regarding the magnitude and shape. We also demonstrated the importance of using a diffuse basis set in describing the scattering due to the Rydberg nature of the lowest unoccupied molecular orbitals of n-C5H12.

A Theoretical Study of Scattering of e± by Tl Atom

This article incorporates details of our calculations of the observable quantities for the scattering of electrons and positrons from a post transition metal Thallium (Tl), in the energy range of 1 eV ≤ Ei ≤ 1 MeV, using the relativistic Dirac partial wave (phase-shift) analysis employing a complex optical-potential. Absolute differential, integrated elastic and inelastic, transport, total ionization, and total cross sections and a thorough study of the critical minima in the elastic differential cross sections along with the associated angular positions of the maximum polarization points in the Sherman function are provided to study the collision dynamics. The optical potential model incorporates the interactions of the incident electron and/or positron with both the nucleus and the bound electrons of the target atom. In-depth analyses of the spin asymmetry, which are sensitive to phases related interference effect, brought on by the various ingredients of the lepton-atom interaction, are also presented. The performance of the current approach to explain the observations, with the exception of the extremely low energy domain, is shown by a comparison of the previous experimental and theoretical results on this target atom.

Elastic and inelastic low-energy electron scattering from pyridine.

A comprehensive investigation of elastic and inelastic electron scattering from molecular pyridine is reported using the ab initio R-matrix method with the static exchange plus polarization and close-coupling approximations for incident energies up to 10eV. The two well-known low-lying 1 2B1 and 1 2A2 shape resonances as well as a 2 2B1 mixed-character resonance compare well with the theoretical and experimental results. We also detect five core-excited resonances (1 2A1, 1 2B2, 3 2B1, 2 2A2, and 4 2B1), which lie above the first electronic excitation threshold. The total elastic cross sections and momentum transfer cross sections agree reasonably with previous reference data. Comparisons of the differential elastic cross sections of pyridine with those measured for benzene, pyrazine, and pyrimidine show remarkable agreement at scattering angles above 40° but behave differently for forward scattering below 40° below 6eV, due to the dominant effect of the permanent dipole moment on the differential cross section in the low energy region with narrow scattering angles. Inelastic electronic excitation cross sections are presented, showing the influence of core-excited resonances below the ionization threshold for the first time.

Annihilation and nuclear elastic scattering of low-energy antiprotons

We perform a fitting procedure to differential elastic scattering cross section data of antiproton at intermediate energy on three different nuclei to evaluate parameters of a six-parameters Woods-Saxon optical potential. Then, with these values, we calculate the reaction cross sections at different momenta and evaluate the differential elastic cross sections for low-momenta antiproton ([Formula: see text]). We find that our analysis underestimates the reaction cross sections for data over the momentum-range 50 MeV/c to 1000 MeV/c. We predict measurable effect for antiprotons with momentum above 50 MeV/c at large angles ([Formula: see text]), in agreement with other recent results. Finally, we consider possible improvements to the model and the analysis.

Joint theoretical and experimental study on elastic electron scattering from a methane molecule

We report on a combined experimental and theoretical study of elastic differential cross section DCS (E, θ) from methane molecule in the intermediate energy range (50-300eV), with experimental results limited to an angle interval of 25 to 125 degrees. Theoretical results are acquired using two approximations: a simple sum of individual atomic cross sections and the other with molecular effect taken into the account. The experimental setup based on a crossed beam technique comprising of an electron gun, a single capillary gas needle, and a detection system with a channeltron was used to measure differential cross sections. The absolute scale for the cross sections is obtained by a relative-flow method using argon gas as a reference. The dependence of DCS on the energy of incident electrons has been considered in detail. The results are analysed and compared with available theoretical and experimental data.

Low Energy Positron Scattering by F and F2.

We have determined integral and differential elastic cross sections for positron scattering with atomic F and F2 molecules from 0.01 to 1000 eV with different theoretical approaches. Higher order polarizabilities were successively considered in the scattering potential, and we observed that the differential and integral cross sections converge only when the pure dipole second hyperpolarization level is taken into account, demonstrating the importance of the hyperpolarization effects on the low energy positron scattering dynamics. Ramsauer structures were found for both targets, and in the particular case of the F atom, the effect of its quadrupole moment proved to be relevant around the position of the Ramsauer minimum, which was determined together with the scattering length for each of the adopted polarization schemes. A relation of these quantities with the matching radius between the correlation and polarization interactions is also discussed. Agreement between the model potential and ab initio cross sections for the lowest level of target polarization is found for F2. Since there is no previous theoretical or experimental determination of cross sections for these targets, we compared the differential cross sections of F2 with experimental data available for N2 and O2 and found reasonable agreement.