Experimental Differential Cross Sections Research Articles

Determination of Nuclear Matter Radii by Means of Microscopic Optical Potentials: The Case of 78\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{78}$$\\end{document}Kr

In this work we use microscopic Nucleon–Nucleus Optical Potentials (OP) to analyze elastic scattering data for the differential cross section of the 78\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{78}$$\\end{document}Kr (p,p) 78\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{78}$$\\end{document}Kr reaction, with the goal of extracting the matter radius and estimating the neutron skin, quantities that are both needed to determine the slope parameter L of the nuclear symmetry energy. Our analysis is performed with the factorized version of the microscopic OP obtained in a previous series of papers within the Watson multiple scattering theory at the first order of the spectator expansion, which is based on the underlying nucleon–nucleon dynamics and is free from phenomenological inputs. Differently from our previous applications, the proton and neutron densities are described with a two-parameter Fermi (2pF) distribution, which makes the extraction of the matter radius easier and allows us to make a meaningful comparison with the original analysis, that was performed with the Glauber model. With standard minimization techniques we performed data analysis and extracted the matter radius and the neutron skin. Our analysis produces a matter radius of Rm(rms)=4.12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R_m^{\\mathrm{(rms)}} = 4.12$$\\end{document} fm, in good agreement with previous matter radii extracted from 76\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{76}$$\\end{document}Kr and 80\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{80}$$\\end{document}Kr, and a neutron skin of ΔRnp≃-0.1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta R_{np} \\simeq - 0.1$$\\end{document} fm, compatible with a previous analysis. Our factorized microscopic OP, supplied with 2pF densities, is a valuable tool to perform the analysis of the experimental differential cross section and extract information such as matter radius and neutron skin. Without any free parameters it provides a reasonably good description of the experimental differential cross section for scattering angles up to ≈\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\approx $$\\end{document} 40 degrees. Compared to the Glauber model our OP can be applied to a wider range of scattering angles and allows one to probe the nuclear systems in a more internal region.

Angular differential cross section measurement for 11B(p, α0)8Be reaction with proton energy of 2.5 MeV

This report presents experimental differential cross section measurements at α0-particles’ eight outgoing angles of 50°, 70°, 90°, 106°, 120°, 130°, 150°, and 160° from 11B(p, α0)8Be reaction induced by 2.5 MeV proton beam bombarding on a natural boron target. The proton beams were accelerated by the 5SDH-2 pelletron at the University of Science - Hanoi National University (HUS). A good agreement has been observed between the obtained results and those from the literature. The importance of the data in a widely angular range is evidenced for the precise determination of the total integrated cross section.

Predicting differential cross sections of electron scattering from N2 using DCMe method

The e + N2 scattering system is usually a typical testing model in electron scattering from molecule. The accurate resonant and the non-resonant differential cross sections (DCSs), integral cross sections (ICSs) and momentum transfer cross sections (MTCSs) of electron scattering from N2 molecule are studied using limited experimental DCSs and the difference converging method for electron scattering (DCMe) proposed in our previous work. The DCMe results well represent those known experimental data and obtain all unknown ones at given energies. It supplies a theoretical alternative to correctly predict the DCSs those may be experimentally unknown or hard to have quantum mechanically. This study shows that.

Electron impact electronic excitation of benzene: Theory and experiment.

We report experimental differential cross sections (DCSs) for electron impact excitation of bands I to V of benzene at incident energies of 10, 12.5, 15, and 20eV. They are compared to calculations using the Schwinger multichannel method while accounting for up to 437 open channels. For intermediate scattering angles, the calculations reveal that the most intense band (V) emerges from surprisingly similar contributions from all its underlying states (despite some preference for the dipole-allowed transitions). They further shed light on intricate multichannel couplings between the states of bands I to V and higher-lying Rydberg states. In turn, the measurements support a vibronic coupling mechanism for excitation of bands II and IV and also show an unexpected forward peak in the spin-forbidden transition accounting for band III. Overall, there is decent agreement between theory and experiment at intermediate angles and at lower energies and in terms of the relative DCSs of the five bands. Discrepancies between the present and previous experiment regarding bands IV and V draw attention to the need of additional experimental investigations. We also report measured DCSs for vibrational excitation of combined C-H stretching modes.

Asymptotic normalization coefficient for 6He+p→7Li from the proton transfer d(6He,7Li)n reaction

The main purpose of this work is to determine values of the asymptotic normalization coefficients for the virtual decays 6He+p[Formula: see text]Li(g.s.) and 6He+p[Formula: see text]Li(0.48[Formula: see text]MeV). For this purpose, the recently measured experimental differential cross-section of the proton transfer reaction d(6He,7Li)n has been analyzed. The modified distorted wave born approximation is used to determine the values of the asymptotic normalization coefficients. The peripheral character of this reaction has been tested. It has been shown that this reaction is peripheral. New values of the asymptotic normalization coefficients for the virtual decays 6He+p[Formula: see text]Li(g.s.) and 6He+p[Formula: see text]Li(0.48[Formula: see text]MeV) with their uncertainties have been obtained.

Dynamics of the Oxygen Atom Transfer Reaction between Carbon Dioxide and the Tantalum Cation.

The understanding of fundamental atomic-level processes often requires well-defined model systems. The oxygen atom transfer from CO2 to a transition metal cation in the gas phase presents such a model system. We investigate the reaction of Ta+ + CO2 for which the formation of TaO+ is highly efficient and attributed to multistate reactivity. Here, we study the atomistic dynamics of the oxygen atom transfer reaction by recording experimental energy and angle differential cross sections by crossed beam velocity map imaging supported by ab initio quantum chemical calculations. Product ion velocity distributions are dominated by signatures for indirect dynamics, despite the reaction being highly exothermic. Product kinetic energy distributions show little dependence on additional collision energy even with only four atoms involved, which hints at dynamical trapping behind a submerged barrier.

Measurement of differential cross sections for proton elastic scattering on natO at Ep= 4-6 MeV, suitable for EBS

In this study we present the experimental differential cross sections of natO(p,p0) elastic scattering, determined via the relative measurement technique, in the proton beam energy range Elab=4-6 MeV with a varying step (from 5-15 keV), at six backscattering detector angles between 120o and 170o (every 10o). A thin, self-supporting target manufactured in the lab was used in this experiment and the determination of its stoichiometry was carried out according to the currently existing evaluation, which has also been benchmarked recently. The measurements were performed using the Van de Graaff Tandem 5.5 MV Accelerator of N.C.S.R. “Demokritos” in Athens, Greece. The differential cross-section datasets obtained in the present work and already existing ones in literature for this extended proton beam energy range are shown and the observed peculiarities and discrepancies are discussed and analyzed.

Elastic scattering based on energy-dependent relativistic Love-Franey model at energies between 20 and 800 MeV* *Supported by the National Natural Science Foundation of China (12175072, 11722546, 12147106)

In order to investigate the elastic scattering, we fit scattering observables of the weighted fits (WF16) with the relativistic Love-Franey (RLF) model. The masses, cutoff parameters, and initial coupling strengths of RLF are assumed to be independent of energy. Because the energy boundary between low energy and high energy is around 200 MeV, the masses, cutoff parameters, and initial coupling strengths of RLF are obtained by fitting scattering observables of WF16 at an incident energy of 200 MeV. With the masses, cutoff parameters, and initial coupling strengths as the input, the energy-dependent RLF model is constructed over the laboratory energy range of 20 to 800 MeV within a unified fit. To examine the validity of this fit, we investigate p+ elastic scattering for various energies. Although the scattering observables of pp and pn of 200 MeV best fit the values of WF16, the RLF model of 200 MeV without the Pauli blocking (PB) corrections fails to describe the experimental differential cross sections, analyzing powers, and spinrotation functions. When the PB corrections are taken into account for various energies, the RLF model can well describe the experimental data of p+ elastic scattering.

Measurement, evaluation and benchmarking of differential cross sections for proton elastic scattering on natO in the energy range E = 4–6 MeV, suitable for EBS

In this study we present the experimental differential cross sections of the natO(p,p0) elastic scattering, determined via the relative measurement technique, in the proton beam energy range Elab = 4–6 MeV with a varying step (from 5 to 15 keV), at six backscattering detector angles between 120° and 170° (every 10°). A thin, self-supporting target manufactured was used in this experiment and the determination of its stoichiometry was carried out according to the currently existing evaluation at lower energy, which has also been benchmarked recently. The measurements were performed using the Van de Graaff Tandem 5.5 MV Accelerator of N.C.S.R. “Demokritos” in Athens, Greece. Theoretical calculations leading to the extension of the existing evaluation up to Ep,lab ∼ 6 MeV have also been performed and the obtained results seem to reproduce well not only the differential cross-section datasets obtained in the present work, but also already existing ones in literature for this extended proton beam energy range. The observed peculiarities and discrepancies are discussed and analyzed, while the theoretical differential cross sections are validated via an accurate benchmarking experiment carried out at RUBION, Ruhr University Bochum, using a thick Bi2O3 target.

Study of6,8He+p elastic scattering using the BHF formalism with three-body forces

In the present work, we have analyzed the elastic scattering data of6He+p at 25.6, 38.6, 40.9, and 71 MeV/A and8He+p at 15.6, 25.6, 32.5, 66, and 72 MeV/A, using the microscopic local optical potential calculated within the framework of the Brueckner–Hartree–Fock (BHF) formalism. The calculation requires mainly two inputs: (1) the nucleon–nucleon (NN) interaction and (2) the nucleon distributions in target nuclei. In the present work, realistic internucleon (NN) potential from Argonne v18 (AV18) and the Urbana IX (UVIX) model of three-body forces with several nucleon density distributions are used for generating the nucleon–nucleus optical potential. We have used the exact method for calculating both the direct and the exchange parts of the spin–orbit potential. We confirm the earlier results that the spin–orbit potential for these neutron-rich nuclei is diffused and extended. Our results show that the different density distributions reproduce rather well the experimental differential cross sections for both isotopes, while the phenomenological density with a two-neutron halo gives satisfactory results for6He-p analyzing power data. None of the densities used for8He can reproduce the experimentally analyzed power data. Our analysis reveals that the calculated microscopic optical potentials, with and without three-body forces using the BHF approach, provide satisfactory agreement with the elastic scattering data for6,8He+p.

Low-energy deuteron–alpha elastic scattering in cluster effective field theory

In this paper, we study the low-energy $$d{-}\alpha $$ elastic scattering within the two-body cluster effective field theory (EFT) framework. The importance of the $$d(\alpha ,\alpha ) d$$ scattering in the $$^6 \text {Li} $$ production reaction leads us to study this system in an effective way. In the beginning, the scattering amplitudes of each channel are written in a cluster EFT with two-body formalism. Using the effective range expansion analysis for the elastic scattering phase shift of S, P and D partial waves, the unknown EFT low-energy coupling constants are determined and the leading and next-to-leading orders EFT results for the phase shift in each channel are presented. To verify the accuracy of the results, we compare experimental phase shift and differential cross section data with obtained results. The accuracy of the EFT results and consistency with the experimental data indicate that the EFT is an effective approach for describing low-energy systems.

Cross sections for elastic electron scattering by benzene at low and intermediate energies

We present experimental and theoretical differential cross sections for elastic electron scattering from benzene. The present experimental results are obtained at incident electron energies ranging from 1 to 50 eV and for scattering angles from ${10}^{\ensuremath{\circ}}$ to ${130}^{\ensuremath{\circ}}$. The experimental measurements are compared to available results from 1 to 10 eV and to theoretical results from 10 to 50 eV, both based on the Schwinger multichannel (SMC) method. Different electron scattering calculations are carried out by employing varied basis sets and multichannel coupling schemes. This allows us to (i) obtain relatively converged cross sections with respect to the inclusion of Rydberg excited states, (ii) observe significant variations in the forward scattering as a function of the multichannel coupling scheme, and (iii) explore possible effects stemming from states lying above the ionization threshold. Overall, the agreement between experiments and models is found to be very good to excellent. The remaining discrepancies point out areas in which the SMC method should be improved.

Determination of Asymptotic Normalization Coefficients by Analytic Continuation of Differential Cross Sections

A method is discussed for determining the asymptotic normalization coefficients (ANC) using the analytic continuation of experimental differential cross sections for nuclear transfer reactions to the pole point of the reaction amplitude with respect to the variable costheta, where theta is the scattering angle. Within the framework of this method, using experimental data on the differential cross section for the reaction {}^{12}textrm{C}(0^{+};0textrm{ MeV})(d,p){}^{13}textrm{C}(1/2^{+};3.09textrm{ MeV}) the ANC for the channel {}^{13}textrm{C}(1/2^{+};3.09textrm{ MeV})to{}^{12}textrm{C}(0^{+};0textrm{ MeV})+n was determined. When determining the ANC, the corrections caused by the Coulomb interaction in the initial, final and intermediate states of the reaction were taken into account. It is shown that these corrections significantly affect the extracted ANC value.

Primary rainbow and Airy minima in 12C + 12C elastic scattering with families of non-monotonic potentials*

The experimental differential cross section of the 12C + 12C elastic scattering over a wide laboratory energy scale 25 ⩽ E lab ⩽ 360 MeV are analyzed within the framework of the optical model (OM) using non-monotonic (NM) nucleus–nucleus potential. The real parts of the NM potentials are derived from the energy density functional (EDF) formalism with the sudden approximation embodying the Pauli exclusion principle and the imaginary parts are taken as phenomenology. The diffractive and the refractive scattering with Airy structures in the whole angular region of the 12C + 12C elastic scattering in the above mentioned energy range are found profoundly successful in OM with the NM nucleus–nucleus potentials in five of different potential families. All the families at lower energies converge at 240 MeV to the unique potential family starting with the EDF potential. This, in conjunction with our recent findings for the 16O + 16O system in Islam et al (2021 J. Phys. G 48 075109), not only verifies the Goldberg criterion for elimination of discrete potential ambiguities for NM potentials, but also establishes that this leads uniquely to the EDF family. The 90° excitation function is also successfully reproduced with extension using NM potentials. The near- and far-side (N/F) decomposition of total elastic scattering amplitude has also been studied using our NM potentials.

Positron scattering from pyrazine

The present paper provides a joint experimental and theoretical study of positron scattering from pyrazine. Experimental data were measured employing a low-energy positron beamline, and covered an energy range from 1 to 79 eV. Cross sections were measured for total scattering, total elastic scattering, positronium formation, direct ionization, and the sum of the total discrete electronic-state excitation processes. In addition, measured total electronic excitation cross sections for the individual ${1}^{1}{B}_{3u},$ ${1}^{1}{B}_{2u},$ ${1}^{1}{B}_{1u},$ and ${2}^{1}{B}_{2u}$ states are also reported. Finally, experimental elastic differential cross sections (DCSs), here in the energy range $1--20$ eV, are also presented. Results from two theoretical approaches are given: the R-matrix approach and the independent atom method with screening corrected additivity rule and interference terms. Where a comparison between our experimental and theoretical results could be made, the level of accord varied from being quite good to marginal depending on the actual scattering process under consideration. Last, a comparison between the present elastic DCS results and those from our earlier study on positron scattering from pyrimidine [Palihawadana et al., Phys. Rev. A 88, 012717 (2013)] showed a somewhat unexpected level of agreement.

Elastic and absorption electron collisions with acetaldehyde

We report a theoretical–experimental investigation on elastic electron scattering by acetaldehyde (CH $$_3$$ CHO) in the 0.5–800 eV energy range. Theoretically, the Pade approximation and the single-center partial-wave expansion method were applied to solve the Lippmann–Schwinger scattering equation, whereas a molecular complex optical potential was used to describe the electron–molecule interaction. Calculations in the independent-atom framework were also performed. Angular distributions of the elastically scattered electrons were measured in the 10 $$^{\circ }$$ –130 $$^{\circ }$$ and 30–800 eV ranges using a crossed beams geometry. Absolute values of differential cross sections were derived by the relative flow technique. In addition, integral and momentum transfer cross sections were obtained from the experimental and theoretical differential cross sections via a numerical integration procedure. Comparison between our results and previous experimental and theoretical calculations is made.

Fully relativistic study on electron impact elastic scattering from Nq+ (q = 1–3), Na+, Arq+ (q = 1–3, 7–8), and Xeq+ (q = 2–6, 8)

AbstractA study is presented on the elastic scattering of electrons from Nq+ (q = 1–3), Na+, Arq+ (q = 1–3, 7–8), Xeq+ (q = 2–6, 8) to understand the available experimental differential cross section results. A model potential approach has been utilized to describe the scattering process. The model potential includes the static, exchange, polarization and absorption potentials. The static potentialis obtained through the charge density calculated by obtaining ionic wave functions using multi‐configuration Dirac‐Fock (MCDF) approximation. Thereafter, the static potential is added to the suitable exchange, polarisation and absorption potentials to construct the spherically averaged complex optical potential. Using the obtained potential in the Dirac equations,these are solved with the partial wave phase shift analysis method and the differential cross sections are calculated. Results for different ions exhibit prominent interference structures in the energy versus cross section curves and show good agreement on comparison with the experimental results available in the selected energy ranges.

A dynamical (e,2e) investigation into the ionization of pyrazine

We report an experimental and theoretical investigation into the dynamics of electron-impact ionization of the unresolved outermost molecular orbitals (6ag + 1b1g) of pyrazine (C4N2H4). Experimental triple differential cross sections (TDCS) are compared with cross sections calculated within a molecular 3-body distorted wave (M3DW) framework. The M3DW theory was able to reproduce the qualitative scattering behaviour in the binary region, but failed to describe the absolute intensity of the TDCS and the recoil scattering behaviour. Momentum profiles were used to identify possible sources where the M3DW may mask the quantum character of the ionized orbitals in describing the ionization dynamics.

Nature of potential families from elastic 16O + 16O rainbow scattering* *Dedicated to the loving memories of F Bary Malik for inspiring us to use NM potentials; and Devika Basak, who was not only the loving wife of our group leader (AKB), but a source of extraordinary care, affection and inspiration for all his students and colleagues, sadly leaving us

The experimental differential cross-sections of 16O + 16O elastic scattering in the energy range 75 MeV ⩽ E lab ⩽ 1120 MeV are analysed using families of non-monotonic (NM) shallow nucleus–nucleus potential in the framework of the optical model. The experimental data is reproduced successfully using six families of NM potentials. It is found that all families converge at 350 MeV. The clear indication of the convergence of the potential families at 350 MeV conforms to the Goldberg criterion concerning the removal of discrete ambiguities even for the shallow NM potential. The study further suggests that the energy of convergence heralds the occurrence of the primary rainbow at that incident energy.

Production of high-energy neutrons by interaction of a deuteron beam with matter

Experimental double differential cross section data for neutrons in the high-energy region are still scarce because of the difficulty of producing high-energy neutrons. The present work studies the possibility of producing high-energy neutrons by interaction of a deuteron beam with matter. The Geant4 toolkit is used to simulate the interaction between a deuteron beam and matter. An analytical method is also developed to calculate the neutron yields produced in the interaction of the deuteron beam with matter. The input cross section data are not only taken from the TEDNL-2017 library but are also calculated by the isospin-dependent quantum molecular dynamics model. It is shown that it is possible to produce high-energy neutrons by interaction of a deuteron beam with matter. If one wishes to produce high-energy neutrons, a low-Z target and a small emission angle may be considered. A thin target is a good choice if one wishes to produce neutrons with a smaller energy peak width.