Fivefold Differential Cross Sections Research Articles

Photo double ionization of He by circular andlinear polarized single-photon absorption

We have measured absolute fully differential cross sections for photodouble ionization of helium by circularly and linearly polarized light20 eV above threshold. The data have been obtained by measuring incoincidence the momentum vector of the He2+ ion and one of theelectrons, covering 4π solid angle for all particles. We give anoverview over the momentum distribution in the three-body continuum andshow fivefold differential cross sections. We find a swirl in the electronmomentum space for double ionization by circularly polarized light. Thepresent data supersede earlier data from our group(V mergel et al 1998 Phys. Rev. Lett. 805301).

Angular distribution in (e, 3e) collisions on helium

A fivefold differential cross section for electron-impact double ionization of helium is calculated for high incident energy (1-5 keV). The calculation is based on the first and second Born approximation. The results obtained are in reasonably good agreement with the recent (e,3e) experimental data. Some typical situations are investigated in order to identify the mechanisms of double ionization.

Interference, post-collision interaction and exchange effects in angular distribution patterns of resonant photo double-ionization in neon for equal electron energies

Angle-resolved patterns of the fivefold-differential cross section in neon are calculated ab initio for the case of resonant photo double-ionization under the condition of equal energies of the ejected electrons. The patterns reveal the important role of direct and indirect processes as well as post-collision interaction (PCI), interference and exchange effects. Comparison with available experimental data shows that some of these effects are readily confirmed, but the angular range with dramatic PCI effects still awaits experimental verification.

A comparative experimental and theoretical investigation of the electron-impact double ionization of He in the keV regime

We determine, both experimentally and theoretically, the fully resolved fivefold differential cross section (5DCS) of double ionization of helium by 5.6 keV electron impact. Symmetric energy sharing between the two ejected electrons is investigated at the excess energy of 8 and 20 eV with 0.22 and 0.24 au momentum transfer, respectively. Absolute 5DCS are determined by normalizing the experimental data to the well established single-ionization cross sections. The calculation is performed by using the convergent close-coupling method for the interaction between the two slow ejected electrons, together with the first Born approximation for the interaction of the fast incident electron with the atom. Experimental and theoretical 5DCS tend to agree in shape but disagree in magnitude by factors of three and 14 for the 20 and 8 eV excess energies, respectively. The small momentum transfer invites absolute comparison of the present electron-impact double-ionization results with the corresponding double-photoionization experiment and theory. Theoretically, the momentum transfer is sufficiently close to zero to show the scaling between the two scattering processes. This smallness of the momentum transfer also makes the calculated 5DCS nearly invariant with respect to simultaneous inversion of the momenta of the two ejected electrons.

Fivefold differential cross section of fast(e,2e)ionization ofH2,D2, andT2by a Franck-Condon approach

The fivefold differential cross sections of the simple ionization of hydrogen, deuterium, and tritium diatomic molecules are determined by the use of one-center Coulomb continuum wave functions describing the slow ejected electron. Vertical transitions from the lowest vibrational state of the fundamental ${}^{1}{\ensuremath{\Sigma}}_{g}$ state of the target to the vibrational levels of the fundamental ${}^{2}{\ensuremath{\Sigma}}_{g}$ state of ${\mathrm{H}}_{2}^{+},$ ${\mathrm{D}}_{2}^{+},$ or ${\mathrm{T}}_{2}^{+}$ are considered. The results obtained for two different energy resolutions (1 and 3 eV) show that the difference between these three species should increase with a decrease of the energy resolution.

Model calculations for the two-fragment electro-disintegration of4He

Differential cross sections for the electro-disintegration process $e + {^4He} \longrightarrow {^3H}+ p + e'$ are calculated, using a model in which the final state interaction is included by means of a nucleon-nucleus (3+1) potential constructed via Marchenko inversion. The required bound-state wave functions are calculated within the integrodifferential equation approach (IDEA). In our model the important condition that the initial bound state and the final scattering state are orthogonal is fulfilled. The sensitivity of the cross section to the input $p{^3H}$ interaction in certain kinematical regions is investigated. The approach adopted could be useful in reactions involving few cluster systems where effective interactions are not well known and exact methods are presently unavailable. Although, our Plane-Wave Impulse Approximation results exhibit, similarly to other calculations, a dip in the five-fold differential cross-section around a missing momentum of $\sim 450 MeV/c$, it is argued that this is an artifact of the omission of re-scattering four-nucleon processes.

Double Ionization of Helium by Fast Electron Impact

Double ionization of He by 3-keV electron impact is explored in a kinematically complete experiment. The 12-dimensional, 4-particle final-state momentum space is mapped for two slowly ejected electrons $({\mathbf{k}}_{b,c}<1.2\mathrm{a}.\mathrm{u}.)$, the ${\mathrm{He}}^{2+}$ ion $({\mathbf{k}}_{\mathrm{He}}<5\mathrm{a}.\mathrm{u}.)$ and the fast electron for all relative emission angles and energy partitions. Different reaction mechanisms are identified by examining the angular correlation between the slow electrons as a function of the momentum transfer. A fivefold differential cross section is presented for asymmetric energy sharing in coplanar geometry.

Electron angular distributions in double photoionization: Use of effective Sommerfeld parameters

We present calculations of the fivefold differential cross-section (FDCS) for double photoionization of helium at excess energies of 6 and 20 eV above threshold. Our results are obtained using for the final double-continuum state a product of three Coulomb wave functions, with the Sommerfeld parameters modified to describe the strength of interaction of any two particles affected by the third particle. Our calculations are compared with recent absolute measurements by Dorner et al. (Phys. Rev. A 57, 1074 (1998)), both in coplanar and non-coplanar geometries. Very good agreement is obtained for the shape of the angular distributions, and differences in the absolute magnitude exist in comparison with the standard choice of Sommerfeld parameters.

Triple differential cross section of electron impact ionisation of Na(3s, 3p, 3d)

The fivefold differential cross section (5DCS) of the ionisation by electron impact of atomic sodium is determined theoretically for its fundamental 3s(2 S) state and the excited 3p(2 P) and 3d(2 D) states by a procedure which employs in the transition matrix element of the first order Born approximation, the correlated double continuum (3C) wave function. This permits us to determine the statistical M-state population and the orientation and alignment tensors in (e,2e) detection. It is also shown that, the use of Gamow correlation term, in the independent particle (2C) model, reproduces, only in some situations, the shape of the angular distribution of the 5DCS obtained by the (3C) wave function.

Helicity Dependence of the Photon-Induced Three-Body Coulomb Fragmentation of Helium Investigated by Cold Target Recoil Ion Momentum Spectroscopy

The angular and energy dependence of circular dichroism in photo-double-ionization of helium at a photon energy of 99thinspeV is investigated. Using cold target recoil ion momentum spectroscopy the absolute fivefold differential cross section has been obtained by a coincident measurement of the vector momenta of one electron and the recoiling He{sup 2+} ion covering all relative azimuthal and polar angles. The experimental results are contrasted with numerical calculations using different helium ground state wave functions and forms of the dipole operator. {copyright} {ital 1998} {ital The American Physical Society}

Giant resonances in the26Mg(e,e′α0)22Nereaction

The fivefold differential cross section of the reaction ${}^{26}\mathrm{Mg}{(e,e}^{\ensuremath{'}}c)$ was measured for transferred momenta of 0.35 and $0.54{\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$ and emitted particle angles from $\ensuremath{-}10\ifmmode^\circ\else\textdegree\fi{}$ to 270\ifmmode^\circ\else\textdegree\fi{} with respect to the transferred-momentum direction. Angular correlation functions for the emitted ${\ensuremath{\alpha}}_{0}$ were obtained from the data. A model-independent analysis allowed us to obtain the $E0,$ $E1,$ and $E2$ multipole components of the ${}^{26}\mathrm{Mg}{(e,e}^{\ensuremath{'}}{\ensuremath{\alpha}}_{0}{)}^{22}\mathrm{Ne}$ cross section, between 14 and 26 MeV of excitation energy. The $E1$ component shows a bump around 16.5 MeV, associated with the ${T}_{l}$ isospin component of the giant dipole resonance. The evaluated strengths associated with the ${\ensuremath{\alpha}}_{0}$ decay channel, presented in percentage of the respective energy-weighted sum rules are 0.45(7)% for $E1,$ 1.4(3)% for $E2,$ and 0.2(1)% for $E0.$

(e,3e) electronic momentum spectroscopy: perspectives and advantages

Five-fold and four-fold differential cross sections for electron-impact double ionization of helium are calculated in new proposed experimental situations where the scattered electron and one of the ejected electrons have similar energies. It is shown that only this new electron momentum spectroscopy provides direct information about the electron - electron correlations in a target. Various models of the helium ground-state wavefunction are used to justify this statement.

Signatures of target e-e correlations in the angular distribution of (e,3e) differential cross sections for the ionization of helium by fast electrons.

The effect of target {ital e}-{ital e} correlations on the angular distribution of fivefold differential cross section for the double ionization of helium by fast electrons has been studied. The helium ground-state wave functions due to Byron and Joachain [Phys. Rev. {bold 146}, 1 (1966)], Silverman, Platas, and Matsen [J. Chem. Phys. {bold 32}, 1402 (1960)], and Tweed and Langlois [J. Phys. B {bold 20}, 5213 (1987)] have been employed. The calculation has been done in the first-order Born approximation with the two ejected electrons being described by a product of two Coulomb waves. The correlations in the final state have been accounted for by suitable effective charges and the Gamow correlation factor. Kinematics corresponding to or close to the Bethe ridge and with small momentum transfer and low ejected electron energies has been chosen. When one (energetic of the two) of the electrons is ejected along the momentum transfer direction, the angular distribution of the other for angles in the range 180{degree}{plus_minus}60{degree} with respect to the first is found to bear clear signatures of {ital e}-{ital e} correlations in the ground-state wave function. {copyright} {ital 1996 The American Physical Society.}

Role of final state correlations in electron and positron impact ionization of H and He

Single ionization of H and double ionization of He are investigated using a multiple scattering approach and a correlated final state wavefunction, which satisfies the correct asymptotic condition for the electron and positron impact ionization of atoms. Analyses presented here show the influence of the Coulomb correlations in the final state on the three- and fivefold differential cross sections. Situations are discussed in which consideration of every pair of electron-electron and/or electron-positron correlation in the final state becomes important for physically satisfactory results.

On the mechanisms of (e, 3e) collisions with fast projectiles

The contributions of the so-called shake-off and two step mechanisms to the fivefold differential cross section of the double ionization of helium are studied and compared to recent theoretical results. A simple qualitative model for the estimation of the contribution of both mechanisms is proposed for experimentators. The predictions reproduce qualitatively the results of more elaborate theoretical calculations.

Structures in the cross section of double ionization of helium by the impact of fast electrons

The authors investigate the fivefold differential double-ionization cross section of helium by the impact of fast electrons. They consider the case where little momentum is transferred to the target so that a Born-type approximation in the projectile-target potential can be employed. Collision geometries are provided at which maxima and minima arise in the cross section and the associated ionization mechanisms are identified. Necessary kinematical conditions for the Bethe ridge in double ionization are worked out which provide a possibility for the measurement of the momentum profile of the initially bound state.

Structures in the cross section of double ionisation of helium by the impact of fast charged particles

In this work the five-fold differential double-ionisation cross section of helium by the impact of fast charged particles has been investigated. The case is considered in which little momentum is transferred to the target so that a Born-type approximation in the projectile-target potential can be employed. A scaling formula for the cross section has been derived which relates cross sections resulting from the impact of projectiles of different masses and charges. Further, collision geometries have been found for which maxima and minima arise in the cross section and the associated ionisation mechanisms have been identified. Necessary kinematical conditions for the Bethe ridge in double ionisation have been worked out

Double ionization mechanisms frome, (3?1)e and (e, 3e) experiments

Illustrative examples of energy and angular distributions from thee, (3–1)e and (e, 3e) double ionization processes in argon and krypton, at ∼ 5.5 keV impact energy are presented. The relevance of the resulting four-fold and five-fold differential cross sections to the identification of the double ionization mechanism is emphasized.

Electron-impact double ionization of argon studied by double and triple coincidence techniques: The first (e,3e) experiment.

Angular correlations between the three outgoing electrons in the double ionization of argon by electron impact have been measured for the first time. Double and triple coincidence techniques are used to determine simultaneously all final electron energies and angles, and provide fourfold and fivefold differential cross sections, respectively. The angular distributions are consistent with a two-step model for the double ionization mechanism. The present results clearly show the feasibility and potentiality of (e,3e) experiments.

A theory for relativistic (e, 2e) reactions

The five-fold differential cross section for the (e, 2e) reaction is derived using a relativistic plane-wave Born approximation. It is shown that (e, 2e) reactions with electron impact energies of a few MeV should provide a sensitive test of the wavefunctions of the inner shells of heavy elements. Calculations are presented for the K shells of gold and thorium using relativistic and non-relativistic Hartree-Fock theories. These show that relativistic effects are significant in the bound-state wavefunctions of heavy elements, and that they can be measured in a measurement of the differential cross section.