Fivefold Differential Cross Sections Research Articles

Electron impact single ionization of hydrogen molecule by twisted electron beam

In this communication, we present the results of the five-fold differential cross-section (5DCS) and triple differential cross-section (TDCS) for the (e, 2e) process on molecular hydrogen (H2) by the plane wave and the twisted electron beam impact. The formalism is developed within the first Born approximation using the plane wave and the twisted wave for the incident electron beam. We describe the plane wave, Heitler–London type wave function, Coulomb wave for the scattered electron, the H2 molecular state, and the ejected electron. We compare the angular profiles of the 5DCS and TDCS for the different values of orbital angular momentum (OAM) number m of the twisted electron beam with that of the plane wave beam. We also present the 5DCS for different molecular orientations and study the effect of m on the 5DCS. We further investigate the influence of the twisted electron beam on the (e,2e) process on the H2 molecule from the perspective of the ‘Young-type’ interference of the scattered waves, emanating from the two atomic centers of the H2 molecule. We also study the TDCS for macroscopic H2 target to explore the effect of opening angle (θ p) of the twisted electron beam on the TDCS. Our results clearly show the effect of the twisted electron’s OAM number (m) and the opening angle (θ p) on the 5DCS and TDCS of the molecular hydrogen.

Comprehensive measurements of cross sections and spin observables of the three-body break-up channel in deuteron-deuteron scattering at 65\xa0MeV/nucleon

Detailed measurements of five-fold differential cross sections and a rich set of vector and tensor analyzing powers of the ^{2}mathrm{H}({varvec{d}},dp){n} break-up process using polarized deuteron-beam energy of 65 MeV/nucleon with a liquid-deuterium target are presented. The experiment was conducted at the AGOR facility at KVI using the BINA 4pi -detection system. We discuss the analysis procedure including a thorough study of the systematic uncertainties. The results can be used to examine upcoming state-of-the-art calculations in the four-nucleon scattering domain, and will, thereby, provide further insights into the dynamics of three- and four-nucleon forces in few-nucleon systems. The results of coplanar configurations are compared with the results of recent theoretical calculations based on the Single-Scattering Approximation (SSA). Through these comparisons, the validity of SSA approximation is investigated in the Quasi-Free (QF) region.

Double ionization of helium by twisted electron beam

In this communication, we report our calculations of the five-fold differential cross-section (FDCS) for (e,3e) on the He atom using both the plane wave and the twisted incident electron beam. The formalism has been developed in the first Born approximation using the plane wave as well as the twisted electron wave for the incident electron. We describe plane wave, Le Sech, and 2 Coulomb wave with Gamow factor (2CG) respectively for the scattered, bound electrons of He atom and the ejected electrons. We compare the angular profile of the FDCS for different values of orbital angular momentum (OAM) (m) of the twisted electron with that of the plane wave. We present the angular profiles of the FDCS in the θ-variable and constant θ12 mode in the coplanar geometry. The effects of the opening angle (θp) of the twisted electron on the angular profile of the FDCS are also studied.

Molecular-frame (e,\xa02e) ionization dynamics of H2 at high impact-energy

We report a combined experimental and theoretical study on the electron-impact ionization dynamics of H2 at an impact-energy of 520 eV. The molecular-frame fivefold-differential cross sections were measured for electron emission in the plane perpendicular to the incoming projectile beam. An (e, 2e + ion) triple coincidence method was used covering projectile scattering angles of 6.5°, 10.0° and 20.0° and ejected energies of 20 eV and 30 eV. The experimental cross sections are compared with results from the multi-center distorted-wave (MCDW) as well as the molecular three-body distorted wave (M3DW) approaches. M3DW is in overall better agreement with the measured data in the binary lobes than MCDW, while the intensity of recoil lobes are underestimated by both theories. Furthermore, we examine the presence of two-center interference patterns by comparing the experimental cross section ratios between mutually perpendicular alignment angles of the molecular axis with that predicated by the interference model. Agreement with the interference model is found only for Bethe ridge kinematics, i.e. in the binary peak region and with the ejected electron momentum being roughly equal to the momentum transfer. Finally, we suggest a modified interference formula for the recoil peak which takes into account the backscattering of the ejected electron in the ionic potential.Graphical abstract

Revisit of (e,2e) & (e,3e) processes on atoms with twisted electron impact

SynopsisWe compute Triple Differential Cross Section (TDCS) and Five-fold Differential Cross Section (FDCS) for (e,2e) & (e,3e) processes on atoms respectively to investigate the effects of non zero angular momentum and the apex angle of the twisted electron. We observed that the differential coincidence cross sections largely depend on these parameters.

Deuteron- α scattering: Separable versus nonseparable Faddeev approach

{\bf Background} Deuteron induced reactions are widely used to probe nuclear structure and astrophysical information. Those (d,p) reactions may be viewed as three-body reactions and described with Faddeev techniques. {\bf Purpose} Faddeev-AGS equations in momentum space have a long tradition of utilizing separable interactions in order to arrive at sets of coupled integral equations in one variable. However, it needs to be demonstrated that observables calculated based on separable interactions agree exactly with those based on nonseparable forces. {\bf Methods} Momentum space AGS equations are solved with separable and nonseparable forces as coupled integral equations. {\bf Results} Deuteron-alpha scattering is calculated via momentum space AGS equations using the CD-Bonn neutron-proton force and a Woods-Saxon type neutron(proton)-$^4$He force, for which the Pauli-forbidden S-wave bound state is projected out. Elastic as well as breakup observables are calculated and compared to results in which the interactions in the two-body sub-systems are represented by separable interactions derived in the Ernst-Shakin-Thaler (EST) framework. {\bf Conclusions} We find that the calculations based on the separable representation of the interactions and the original interactions give results that are in excellent agreement. Specifically, integrated cross sections and angular distributions for elastic scattering agree within $\approx$ 1\%, which is well below typical experimental errors. In addition, the five-fold differential cross sections corresponding to breakup of the deuteron agree extremely well.

Double ionization of helium by proton impact: from intermediate to high momentum transfer

Fil: Ambrosio, Marcelo Jose. Kansas State University; Estados Unidos. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Oficina de Coordinacion Administrativa Ciudad Universitaria. Instituto de Astronomia y Fisica del Espacio. - Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Astronomia y Fisica del Espacio; Argentina

Double ionization of neon by electron impact: use of correlated wave functions*

A model including correlation both in the initial state and in the final state is applied to the case of the double ionization of neon. The results of our model are compared to the available experimental data performed at high incident energy. Fully (fivefold) differential cross sections (FDCS) have been studied by applying the first Born approximation. Four ion states of Ne++, which are not resolved in the experiments, have been included in our calculation.

Asymmetric electron energy sharing in electron-impact double ionization of helium

We present the fully fivefold differential cross sections (FDCSs) for ($e,\phantom{\rule{0.16em}{0ex}}3e$) processes in helium within the first Born approximation. The calculation is performed for a coplanar geometry in which the incident electron is fast ($\ensuremath{\sim}6$ keV), the momentum transfer is small (0.24 a.u.), and for an asymmetric energy sharing between both slow ejected electrons at excess energy of 20 eV. Two cases have been considered: ${E}_{1}=15$ eV, ${E}_{2}=5$ eV and ${E}_{1}=8$ eV, ${E}_{2}=12$ eV. While waiting for new theoretical and experimental results for confrontations, in particular for asymmetric energy sharing, our results clearly demonstrate that, for the same incident energy, the same momentum transfer and the same excess energy, the ($e,\phantom{\rule{0.16em}{0ex}}3e$) process in helium with asymmetric energy sharing between ejected electrons is more likely than the case with symmetric energy sharing. The two- and three-dimensional representation of the FDCSs covering all possible values of the angle of ejections are presented and discussed. The theoretical cross sections are calculated by using a compact-kernel-integral-equation approach associated with the Jacobi matrix method to calculate a three-body wave function and which leads to a full convergence in terms of the basis size.

Angular distributions in the double ionization of DNA bases by electron impact

Ab initio calculations of the five-fold differential cross sections for electron-impact double ionization of thymine, cytosine, adenine and guanine are performed in the first Born approximation for an incident energy close to 5500 eV. The wavefunctions of the DNA bases are constructed using the multi-center wave functions from the Gaussian 03 program. These multi-center wave functions are converted into single-center expansions of Slater-type functions. For the final state, the two ejected electrons are described by two Coulomb wave functions. The electron–electron repulsion between the two ejected electrons is also taken into account. Mechanisms of the double ionization are discussed for each case and the best choices of the kinematical parameters are determined for next experiments.

Double Ionization DNA bases by electron impact

Synopsis(e,3e) fivefold differential cross sections for the DNA bases are studied. The molecular wave functions are obtained by the multicenter wave functions from the Gaussain 03 program. To describe the correlations between ejected electron in the exit channel, we use the Ward-Macek method. The first order mechanisms involving the reaction are identified.

On the relativistic electron impact K-shell (e, (3-1)e) differential cross sections for atoms

In this paper, we present the results of our calculation of four-fold differential cross section (4DCS) for the K-shell electron impact double ionization (DI) on various atoms in the relativistic energy regime. The 4DCS is computed from the five-fold differential cross sections (5DCS) by integrating 5DCS over either the angles of one of the ejected electrons or the scattered electron (this process is referred as an (e, (3-1)e) process). Hence, it requires, possibly feasible double coincidence techniques to supplement our findings experimentally instead of the difficult triple coincidence technique, which is required for the complete description of the DI process. The angular profile of 5DCS is scanned with the angles of one of the ejected electrons for both the (e, (3-1)e) cases. A dominant peak in the momentum transfer direction is found when the scattered and one of the ejected electrons are detected in coincidence. The effects of nucleus (Z), energies of the ejected electrons, and the scattering angle on the 4DCS have been discussed. The angular correlation of the ejected electrons has also been discussed when only the ejected electrons are detected. We consider the spin aspects by scanning the singlet and triplet contributions in the angular profile of 4DCS. We also find that the interference term of the longitudinal and transverse interaction is responsible for the strengthening of the secondary peak. We observe a clear manifestation of the effect of nucleus on the spin asymmetry for behavior targets.

Measurement of the 12C(e,e′p)11B two-body breakup reaction at high missing momentum

The five-fold differential cross section for the 12CB reaction was determined over a missing momentum range of 200–400 , in a kinematics regime with and . A comparison of the results with previous lower missing momentum data and with theoretical models are presented. The extracted distorted momentum distribution is shown to be consistent with previous data and extends the range of available data up to 400 . The theoretical calculations are from two very different approaches, one mean field and the other short range correlated; yet for this system the two approaches show striking agreement with the data and each other up to a missing momentum value of 325 . For larger momenta, the calculations diverge which is likely due to the factorization approximation used in the short range approach.

On the spin interplay of the ejected electrons in the relativistic electron impact K-shell double ionization of atoms

A detailed analysis on the spin aspects of the ejected electrons is presented for the electron impact K-shell double ionization of Ca, Mo and Xe atoms. The five-fold differential cross sections have been seperated in terms of singlet–singlet and singlet–triplet transitions during the double ionization of the K-shell electrons of atoms. This type of study has led us to unravel the interesting spin interplay of the ejected electrons and their higher degree of dependence with their kinematical arrangements in the continuum state. Various geometrical arrangements are identified wherein the important relative contributions of the singlet and triplet terms are found. The singlet contribution for the back-to-back emission of the ejected electrons is found to be smaller for the Ca atom, however, on the other hand, it becomes the dominating term for the Xe atom and is isotropic in nature. We also observe that the parallel spin orientation of the ejected electrons is more favourable for the perpendicular emission of the ejected electrons (i.e., when θ1 = θq and θ2 = θq − 90°) and it remains the dominant term regardless of the energy sharing ratio of the ejected electrons. All of the singlet and triplet transitions depend on the emission direction of the ejected electrons as well as on their energies.

Three-body-continuum Coulomb problem using a compact-kernel-integral-equation approach

We present an approach associated with the Jacobi matrix method to calculate a three-body wave function that describes the double continuum of an atomic two-electron system. In this approach, a symmetrized product of two Coulomb waves is used to describe the asymptotic wave function, while a smooth cutoff function is introduced to the dielectronic potential that enters its integral part in order to have a compact kernel of the corresponding Lippmann-Schwinger-type equation to be solved. As an application, the integral equation for the (${e}^{\ensuremath{-}},\phantom{\rule{4pt}{0ex}}{e}^{\ensuremath{-}},\phantom{\rule{4pt}{0ex}}{\mathrm{He}}^{2+}$) system is solved numerically; the fully fivefold differential cross sections (FDCSs) for ($e,3e$) processes in helium are presented within the first-order Born approximation. The calculation is performed for a coplanar geometry in which the incident electron is fast ($\ensuremath{\sim}6$ keV) and for a symmetric energy sharing between both slow ejected electrons at excess energy of 20 eV. The experimental and theoretical FDCSs agree satisfactorily both in shape and in magnitude. Full convergence in terms of the basis size is reached and presented.

K-shell (e, 3e) processes with transversely spin-polarized relativistic electrons

An ab-initio calculation of five fold differential cross section (FDCS) and transverse spin asymmetry in FDCS for the K-shell double ionization of atoms by transversely polarized incident electron is proposed.

Theoretical estimate of fivefold differential cross sections and spin asymmetry forK-shell(e,3e)processes with transversely-spin-polarized relativistic electrons

Ab initio first-order Born calculations of the fivefold differential cross section (FDCS) and transverse spin asymmetry in FDCS for the $K$-shell double ionization of atoms by transversely polarized incident electron are reported. The FDCS and transverse spin asymmetry in FDCS are found to be sensitive to atomic number $Z$, ejection angle, and energy-sharing ratio of the ejected electrons. FDCS is decomposed into longitudinal and transverse contributions and their effects on the angular profile of FDCS such as shifting in the binary peak are reported. Hitherto, all $(e,3e)$ experiments have been performed in the nonrelativistic energy regime without consideration of spin polarization. We hope that the present calculation of FDCS and spin asymmetry in FDCS may induce quantum mechanically complete $(e,3e)$ experiments in the relativistic energy regime wherein spin-dependent interaction becomes prominent.

Polarization observables inπ0ηphotoproduction on the proton

For $\pi^0\eta$-photoproduction on the nucleon formal expressions are developed for the five-fold differential cross section and the recoil polarization including beam and target polarizations. The polarization observables are described by various beam, target and beam-target asymmetries for polarized photons and/or polarized nucleons. They are given as bilinear hermitean forms in the reaction matrix elements divided by the unpolarized cross section. Numerical results for the linear and circular beam asymmetries for $\gamma p\to\pi^0\eta p$ are obtained within an isobar model and are compared with existing data. Predictions are also given for the target asymmetry $T_{11}$, and the beam-target asymmetries $T^c_{10}$ and $T^c_{11}$ for circularly polarized photons.

Molecular orientation effect on the differential cross sections for the electron-impact double ionization of oriented water molecules

Double ionization of isolated water molecules fixed in space is here investigated in a theoretical approach based on the first Born approximation. Secondary electron angular distributions are reported for particular (e,3e) kinematical conditions and compared in terms of shape and magnitude. Strong dependence of the fivefold differential cross sections on the molecular target orientation is clearly observed in (e,3-1e) as well as (e,3e) channels. Furthermore, for the major part of the kinematics considered, we identified the different mechanisms involved in the double ionization of water molecule, namely, the direct shake-off process as well as the two-step1 process. They are both discussed and analyzed with respect to the molecular target orientation.

Double ionization of two-electron systems

We address various issues related to the double ionization by electron impact of two-electron systems. The emphasis will be put on the theoretical description of high incident energy (e,3e) processes, for which the first Born approximation should be suitable. In the case of helium, absolute experimental data for fivefold differential cross sections are available in coplanar geometry. We will review and discuss the divergencies existing between the results obtained with different theoretical models, and those appearing when compared to the experiments in particular with respect to the absolute scale. We will then discuss some results obtained in a recently proposed out of plane geometry.