Angular Differential Cross Sections Research Articles

Dispersive optical-model potential parameters for neutron scattering on 197Au up to 200 MeV

In this study, dispersive optical model (DOM) potential parameters were derived for the 197Au target nucleus up to an incident neutron energy of 200 MeV. The procedure involved fitting the theoretical total cross sections σtot with the experimental ones and thereby determining the valid free potential parameters at the lowest value of χ2/M. The contribution of compound nuclei mechanism at low energies was also incorporated in the calculations. The theoretical results obtained using the derived potential were compared to the experimental data for both the angular differential cross-section and the elastic cross-section. While there was a good agreement with the experimental values for the total cross section, a satisfactory agreement was achieved for the angular cross section. The obtained potential is useful for describing the n+197Au scattering system and its outputs over an extensive energy spectrum.

State selective total and angular differential cross sections for positronium formation in [formula omitted]+[formula omitted] collisions

State-selective total and angular differential cross sections for positronium formation are presented in the collision of positron with helium atoms in their ground state by using the four-body formalism of the boundary-corrected continuum-intermediate-states approximation. The main purpose of the present study is to investigate the relative importance of intermediate ionization continuum states that has been incorporated with a suitable choice of distorting potential. In addition, the nine-dimensional integrals of the transition amplitude are analytically reduced to a one-dimensional real integral, which can be easily calculated numerically. The influence of the target static electron correlations on the capture probability is investigated using the different bound-state wave functions of He. The theoretical model for the calculation is fairly accurate and predicts a number of interesting features of the state-selective total and differential cross sections in the range of positron impact energy varies from 20 to 250eV. The total cross sections are highly peaked at an impact energy of 50 eV. The results are compared with those of other theories and the available experimental data. The present theoretical results and other measurements show satisfactory agreement in the wide energy range. Moreover, surface plots for the state-selective differential cross sections are also presented to illustrate the interesting feature of the positronium formation in this collision process.

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.

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.

Measurement of the polarisation of single top quarks and antiquarks produced in the t-channel at sqrt{s} = 13 TeV and bounds on the tWb dipole operator from the ATLAS experiment

A simultaneous measurement of the three components of the top-quark and top-antiquark polarisation vectors in t-channel single-top-quark production is presented. This analysis is based on data from proton–proton collisions at a centre-of-mass energy of 13 TeV corresponding to an integrated luminosity of 139 fb−1, collected with the ATLAS detector at the LHC. Selected events contain exactly one isolated electron or muon, large missing transverse momentum and exactly two jets, one being b-tagged. Stringent selection requirements are applied to discriminate t-channel single-top-quark events from the background contributions. The top-quark and top-antiquark polarisation vectors are measured from the distributions of the direction cosines of the charged-lepton momentum in the top-quark rest frame. The three components of the polarisation vector for the selected top-quark event sample are {P}_{x^{prime }} = 0.01 ± 0.18, {P}_{y^{prime }} = −0.029 ± 0.027, {P}_{z^{prime }} = 0.91 ± 0.10 and for the top-antiquark event sample they are {P}_{x^{prime }} = −0.02 ± 0.20, {P}_{y^{prime }} = −0.007 ± 0.051, {P}_{z^{prime }} = 0.79 ± 0.16. Normalised differential cross-sections corrected to a fiducial region at the stable-particle level are presented as a function of the charged-lepton angles for top-quark and top-antiquark events inclusively and separately. These measurements are in agreement with Standard Model predictions. The angular differential cross-sections are used to derive bounds on the complex Wilson coefficient of the dimension-six mathcal{O} tW operator in the framework of an effective field theory. The obtained bounds are CtW ∈ [−0.9, 1.4] and CitW ∈ [−0.8, 0.2], both at 95% confidence level.

Integral measurements of plural and multiple scattering of electrons with energies between 10 and 100 keV for [formula omitted]: I. Thin and intermediate-thickness targets

Angle-integrated plural- and multiple-scattering distributions have been measured for electrons impinging with kinetic energies from 10 to 100 keV on targets with atomic numbers between those of C and Bi and mass thicknesses ranging from ≈5 to 300 μg/cm2. The thinnest targets, ≈5 to 20 μg/cm2, are not self-supporting and have been deposited on C backings with areal densities around 10 μg/cm2. The intermediate-thickness ones are made of a single element and have mass thicknesses of ≈100 to 300 μg/cm2. The electrons scattered at frontal angles are collected with a Faraday cup covering the polar angles below 12.0°. In addition, to supplement this information, an aluminium ring spanning a polar angle interval of 9.1° has been installed around the entrance of the Faraday cup and the charge deposited on it has also been recorded. The electrical current in the scattering chamber is measured as well so as to provide an accurate normalisation. Corrections for the fraction of impinging electrons backscattered by both the Faraday cup and the ring are applied to the data. The measurements are compared with the predictions of a Monte Carlo code that simulates each individual elastic collision. For targets made of a single element, the analytical Goudsmit–Saunderson and Lewis theories are tested as well. In all cases, the single-scattering angular differential cross sections, obtained by partial-wave solution of the Dirac equation in a self-consistent central potential, are taken from the ICRU Report 77. Good agreement is found within the uncertainties of the data. An analytical formula for the angular integration of the Goudsmit–Saunderson distribution is presented in an Appendix.

Collisions of proton or highly charged ion–atom in a strong magnetic field and dense quantum plasmas

Magneto inertial fusion driven by heavy ions beam (HIB) is a very attractive potential approach for the nuclear energy system. One of the key issues is to investigate the interaction process of the HIB-target considering the condition of plasma screening and strong magnetic field background. In this paper, the influence of the external magnetic field and the plasma screening was investigated by simplifying the process of beam bombarding into a two-body collision between the energetic ions and target atoms. The classical-trajectory Monte Carlo method was accommodated by modifying the Hamiltonian in the collision system, where the effects of plasma screening and the account for the strong magnetic field background were considered. The total cross sections of single electron ionization and charge transfer of the projectile (H+, He2+, Xe32+, Bi31+, U34+)–atom (H, He) collisions are computed. The results indicated that the magnetic field effect becomes more obvious in the low energy regime of the projectiles. With the increase in energy, the change of total cross sections and angular differential cross sections gradually disappears. In the dense quantum plasmas, plasma screening presents very different effects for protons and heavy ion projectiles. This work may pave the way for extending the study to other collision systems calculations.

Differential scattering in proton collisions with molecular hydrogen

The recently developed two-centre wave-packet convergent close-coupling approach to proton collisions with molecular hydrogen is applied to calculate various singly differential cross sections. The approach is based on an effective one-electron description of the {hbox {H}_2} target. The angular differential cross sections for elastic scattering, total excitation and electron capture are presented. Furthermore, we calculate the singly differential ionisation cross sections as functions of the ejected-electron energy and angle, as well as projectile scattering angle. Good agreement with available experimental data is observed, providing improvement over previous theoretical investigations into the singly differential cross section for ionisation. Specific mechanisms responsible for electron emission in particular kinematic regimes are identified. It is concluded that the effective one-electron WP-CCC method is capable of providing reasonably accurate results on singly differential cross sections for all included interconnected processes taking place in {hbox {p}}+{hbox {H}_2} collisions.Graphic abstract

Total, state-selective, and angular-differential cross sections for electron capture in He2++H collisions in warm dense plasmas

The total, state-selective, and angular-differential cross sections for He2++H collision system in warm dense plasmas are studied by using the two-center atomic orbital close-coupling method in the energy range 0.1–300 keV/u. The calculations are performed for plasma density and temperature ranges ne ∼1018 to ∼1021 cm−3, Te = 0.3 eV–1.2 eV, typical for the H- and He-rich white dwarfs. The plasma environments are described by a unified screened potential involving electron degeneracy, finite-temperature gradient, and exchange-correlation effects. The results for H++H cases with the same plasma parameters are also presented for comparison to elucidate the discrepancies of plasma screening effects on the electron capture dynamics for collision systems with different nuclear symmetries. Moreover, classical Debye screening results are also given for comparison to clarify the effects of quantum correlations in warm dense plasmas on the electron capture dynamics. The present work is expected to provide theoretical and data support for the astrophysical plasmas.

Resonant tunneling of deuteron-triton fusion in strong high-frequency electromagnetic fields

We investigate deuteron-triton (DT) fusion in the presence of linearly polarized strong electromagnetic fields in high-frequency limit, in which a complex spherical square-well potential is exploited to describe the nuclear potential. Within the framework of the Kramers-Henneberger (KH) transformation, we have calculated the total and angular differential fusion cross sections by investigating the asymptotical phase shifts of the Coulomb wavefunctions. With introducing a dimensionless quantity of $n_d$ representing the ratio of the particle quiver oscillation amplitude to the radius of nuclear potential, we find that, even though the tunneling probability of passing through the Coulomb repulsive potential keeps almost identical to that in the absence of electromagnetic fields, the peak of total fusion sections shows an apparent shift from the well known value of 110 keV to 78 keV for $n_d=0.01$. The angular differential cross sections also show some resonance peaks that shift from zero inclination angle to $\pi/2$ with increasing the parameter $n_d$. The corresponding astrophysical $S$-factors are found to be enhanced by several times in amplitudes. With the help of Wentzel-Kramers-Brillouin (WKB) approximate wavefunctions, the shape-resonance tunneling mechanism of the above findings are uncovered and some implications are discussed.

Non-dipole anisotropy parameters in the photoionization of Kr in the region of deep inner shell excitations

The photoelectron angular distribution (PAD) of the Kr 4p1/2 and 4p3/2 fine structure states was measured with linearly polarized synchrotron radiation in the vicinity of the resonant excitations of the 3p subshell. Experimental dipole and non-dipole anisotropy parameters were determined from the measured angular differential cross sections. In order to interpret our experimental results we have used a theoretical model going beyond the dipole approximation considering the quadrupole and octupole terms for the direct photoionization. We have taken into account several autoionization channels relevant for the studied photon energy range. The photon energy dependence of the measured anisotropy parameters puts in evidence the importance of the channel interactions. Moreover, unexpectedly large non-dipole contribution have been observed.

Tau longitudinal and transverse polarizations from visible kinematics in (anti-)neutrino nucleus scattering

Since the ντ(ν¯τ)AZ→τ∓X reaction is notoriously difficult to be directly measured, the information on the dynamics of this nuclear process should be extracted from the analysis of the energy and angular distributions of the tau decay visible products. These distributions depend, in addition to d2σ/(dEτdcos⁡θτ), on the components of the tau-polarization vector. We give, for the first time, the general expression for the outgoing hadron (pion or rho meson) energy and angular differential cross section for the sequential ντAZ→τ−(π−ντ,ρ−ντ)X and ν¯τAZ→τ+(π+ν¯τ,ρ+ν¯τ)X reactions. Though all possible nuclear reaction mechanisms contribute to the distribution, it may be possible to isolate/enhance one of them by implementing appropriate selection criteria. For the case of the quasi-elastic reaction off oxygen and neutrino energies below 6 GeV, we show that the pion distributions are quite sensitive to the details of the tau-polarization components. We find significant differences between the full calculation, where the longitudinal and transverse components of the tau polarization vector vary with the energy and the scattering angle of the produced tau, and the simplified scheme in which the polarizations are set to one and zero, being the latter their respective asymptotic values reached in the high energy regime. In addition to its potential impact on neutrino oscillation analyses, this result can be used to further test different nuclear models, since these observables provide complementary information to that obtained by means of the inclusive nuclear weak charged-current differential cross section. We also study the effects on the cross section of the W4 and W5 nuclear structure functions, which contributions are proportional to the charged lepton mass, and therefore difficult to constrain in muon and electron neutrino experiments.

O18 -induced single-nucleon transfer reactions on Ca40 at 15.3A MeV within a multichannel analysis

Background: Nucleon transfer reactions are selective tools for nuclear physics investigations. The theoretical and computational limits affecting in the past their data analysis could be nowadays surmounted thanks to the advent of methods with refined approximations and constraints, even when heavy-ion collisions are considered. Purpose: Modern microscopic calculations of heavy-ion-induced transfer reactions combined with precise experimental data offer the chance for accurately testing different reaction models as well as the nuclear structure description of the involved nuclear states. Method: Single proton and neutron transfer reactions were measured with the MAGNEX magnetic spectrometer for the O18+Ca40 system at 15.3A MeV. Excitation energy spectra and angular differential cross section distributions were extracted. The experimental results are compared with theoretical calculations performed in distorted wave and coupled channel Born approximation. The use of a coupled channel equivalent polarization potential to effectively describe the coupling effects affecting the initial state interaction is also considered. Spectroscopic amplitudes derived from a large-scale shell model with appropriate interactions adapted for the involved nuclei are employed. Results: Our theoretical calculations are in good agreement with experimental data, without the need for any scaling factor, validating the adopted reaction and nuclear structure parameters. Moreover, under the present experimental conditions, a weak dependence of the obtained results on the choice of the reaction models was observed. Conclusions: The good agreement between experimental and theoretical results validates the reliability of the parameter sets entering the calculations. They are extracted from or tested in complementary analyses of other reaction channels under the same experimental conditions. Such a multichannel approach represents the best option to pursue a solid, comprehensive, and model-independent description of the single-nucleon transfer reactions. The successful description of the present one-nucleon transfer data is also propaedeutic to the accurate assessment, under the same theoretical description, of higher-order transfer processes, like the sequential nucleon transfer mechanisms which are in competition with the direct charge exchange reactions.Received 14 September 2021Accepted 16 November 2021DOI:https://doi.org/10.1103/PhysRevC.104.064609©2021 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasLow & intermediate energy heavy-ion reactionsModels & methods for nuclear reactionsTransfer reactionsTechniquesOptical, coupled-channel & distorted wave modelsNuclear Physics

Differential study of proton-helium collisions at intermediate energies: Elastic scattering, excitation, and electron capture

In a series of papers we present a comprehensive investigation of the four-body proton-helium differential scattering problem using the two-center wave-packet convergent close-coupling approach in the intermediate energy region where coupling between various channels is important. The approach uses correlated two-electron wave functions for the helium target. For comparison, a recently developed method that reduces the target to an effective single-electron system is also used. In this paper we present calculations of angular differential cross sections for elastic-scattering, target excitation, and electron-capture processes. The results of the two-electron and effective single-electron methods exhibit a good level of agreement. They also agree well with available experimental data. It is concluded that both versions of the wave-packet convergent close-coupling approach are capable of providing a realistic differential picture of all interdependent and interconnected binary processes taking place in proton-helium collisions at intermediate energies.

Quantum reactive scattering calculations for the cold and ultracold Li + LiNa → Li2 + Na reaction.

A first-principles based quantum dynamics study of the Li + LiNa(v = 0, j = 0) → Li2(v', j') + Na reaction is reported for collision energies spanning the ultracold (1 nK) to cold (1 K) regimes. A full-dimensional ab initio potential energy surface for the ground electronic state of Li2Na is utilized that includes an accurate treatment of the long-range interactions. The Li + LiNa reaction is barrierless and exoergic and exhibits a deep attractive potential well that supports complex formation. Thus, significant reactivity occurs even for collision temperatures approaching absolute zero. The reactive scattering calculations are based on a numerically exact time-independent quantum dynamics methodology in hyperspherical coordinates. Total and rotationally resolved rate coefficients are reported at 56 collision energies and include all contributing partial waves. Several shape resonances are observed in many of the rotationally resolved rate coefficients and a small resonance feature is also reported in the total rate coefficient near 50 mK. Of particular interest, the angular distributions or differential cross sections are reported as a function of both the collision energy and scattering angle. Unique quantum fingerprints (bumps, channels, and ripples) are observed in the angular distributions for each product rotational state due to quantum interference and shape resonance contributions. The Li + LiNa reaction is under active experimental investigation so that these intriguing features could be verified experimentally when sufficient product state resolution becomes feasible for collision energies below 1 K.

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.

Three-body breakup of 6He and its halo structure

The Borromean halo nucleus 6He has been studied by a kinematically complete measurement of Coulomb and nuclear breakup into α + 2n on Pb and C targets at 70 MeV/nucleon. Fully quantum-mechanical four-body breakup calculations reproduce the energy and angular differential cross sections below Erel∼1 MeV for both targets. The model used here reproduces the 6He ground-state properties as well as α-n and n-n scattering data and predicts an average opening angle 〈θnn〉 of 68∘ between the two halo neutrons. However, the model underestimates the breakup cross sections for higher Erel, indicating a possible contribution from the inelastic breakup. Alternatively, we examine the empirically modified calculations that reproduce the energy-differential cross sections for a wide range of scattering angles for both targets. The extracted B(E1) peaks at Erel∼1.4 MeV and amounts to 1.6(2) e2fm2 for Erel ≤ 20 MeV, resulting 〈θnn〉 = 56−10+9 degrees. In either interpretation, the current results show evidence of the dineutron spatial correlation in 6He.

Electron-capture cross sections from atoms to hydrogen-like projectiles

State-selective total and projectile angular-differential cross sections for single-electron transfer to the ground state from atoms in collisions with hydrogen-like projectiles are calculated by means of the four-body distorted wave approximation in the energy range from 25 to 2500 keV amu−1. In the initial channel, the effect of the dynamic electron–electron correlation is explicitly taken into account through the complete perturbation potentials. Distortion in the initial channel due to the Coulomb continuum states of the target and the active electron in the field of the residual projectile ion is included. The quantum-mechanical prior and post transition amplitudes for single-electron capture for symmetric and asymmetric collisions are then derived in terms of three-dimensional real integrals. The role of dynamic inter-electron correlation on the cross sections as a function of the impact energy is examined. Only for He+–He collisions, the projectile angular-differential cross sections for ground state capture are calculated at different impact energies. We investigate the effect of the total cross section as well as the projectile angular-differential cross sections to the choice of different ground state wavefunction of the projectile in the final state. It is observed that although the shape of the differential cross section does not change significantly for these functions, there is a significant change of the differential cross sections due to the choice of the target description. The differential cross section reveals pronounced minima and maxima in the projectile scattering angles as the projectile energy decreases. The observed structure demonstrates the analogy of atomic de Broglie’s matter-wave scattering and Fraunhofer-type diffraction. Finally the validity of our results is assessed by comparison with available experimental data.

Singly differential cross sections for direct scattering, electron capture, and ionization in proton-hydrogen collisions

We use the two-center wave-packet convergent close-coupling approach to calculate singly differential cross sections for direct scattering, electron capture, and ionization in proton-hydrogen collisions at intermediate energies. The distinct feature of the approach is that it gives a complete differential picture of all the interconnected processes at once, subject to the unitary principle. Results obtained for the angular differential cross sections of elastic scattering, excitation, and electron capture, as well as the ionization cross sections differential in the ejected-electron angle, and in the ejected-electron energy agree well with available experimental data. It is concluded that the two-center wave-packet convergent close-coupling approach is capable of providing a realistic differential picture of all collision processes taking place in proton-hydrogen collisions.

Evidence for target outer-shell excitation mediated by electron correlation in single-electron-capture collisions of slow He2+ ions with Ar atoms

We have performed kinematically complete experiments on single-electron capture in slow ${\mathrm{He}}^{2+}$-Ar collisions. Besides the pure capture to the ${\mathrm{He}}^{+}(n=2)$ level, capture into the deep ${\mathrm{He}}^{+}(n=1)$ state with simultaneous excitation of another target electron is also observed. In contrast to the pure capture, the total cross section for this two-electron transition decreases with increasing collision energy, and its angular-differential cross section exhibits a much slighter slope. We take these observations as evidence for electron capture mediated by electron-electron interactions.