Bare Projectiles Research Articles

Zero-degree binary encounter electron production in 30 MeV bare O8+ in collisions with H2, He, Ne, Ar, Kr and Xe

Double differential cross-sections for the production of binary encounter electrons were measured for collisions of 30 MeV bare O8+ projectiles with H2, He, Ne, Ar, Kr and Xe targets at an electron ejection angle of θ = 0° with respect to the beam direction. Results were analyzed in terms of the impulse approximation (IA), in which target electrons in the projectile frame undergo 180° Rutherford scattering in the field of the bare projectile ion. Excellent agreement with the data was found for the H2 and He targets, while for the multi-electron targets good agreement was established only when target electrons whose velocities were lower than the projectile velocity were included in the calculation.

Binary encounter electron production at relativistic velocities

Relativistic binary-encounter electrons produced in very fast collisions of bare and H-like Ar with carbon foils are studied as a function of laboratory frame emission angle. It is found that the velocity of the binary-encounter peak is consistent with a relativistic billiard ball model. The cross section for binary-encounter electron production is not in good agreement with a simple Rutherford scattering model. It is also found that the ratio of H-like to bare projectile cross sections is 1 at 0 degrees and becomes less than 1 at large emission angles.

State-selective scaling for capture to the level n=4 by multicharged ions on light atoms.

We show that the selective-state electron-capture cross sections to the level {ital n}=4 by multicharged ions colliding with H and He targets satisfy scaling rules derived from the eikonal impulse approximation. Partial capture cross sections for different bare projectiles are plotted together, and they compare quite well with recent selective experiments.

Binary encounter electron emission in collisions of highly charged ions with helium gas targets

The energy and angular distribution of δ-electrons produced in collisions of bare argon projectiles with helium gas targets are reported. Double differential electron emission cross sections, d 2 σ dE e dΩ e , have been measured as a function of the electron emission energy, E e, and the polar electron emission angle, V e. The major interest was directed upon the angular dependence of the integrated single differential emission cross sections of the binary encounter (BE) electrons, dσ(Θ e ) dΩ e . The cross sections are compared with electron argon scattering data (calculated and tabulated in Phys. Rev. A 15 (1977) 2173 [1]) as well as experimental data derived from light ion impact on helium (ionic charge q≤9+). The theoretical results are calculated with the impulse approximation (IA) model developed by Lee et al. (Phys. Rev. A 41 (1990) 4816 [2]). Even for higher ionic charge states the measured BE electron emission cross sections are well described by the IA model and are found to scale quadratically with the ionic charge state, q 2, and the projectile energy, E p 2.

Angular distribution of delta electrons emitted in collisions of 1.0-MeV/u Fq+ (q=4,6,8,9) with molecular hydrogen.

The angular distribution, as well as the energy distribution of \ensuremath{\delta} electrons produced in collisions of 1.0-MeV/u ${\mathrm{F}}^{\mathit{q}+}$ (q=4,6,8,9) ions with molecular hydrogen, have been studied for laboratory observation angles (${\mathrm{\ensuremath{\theta}}}_{\mathit{L}}$) from 0\ifmmode^\circ\else\textdegree\fi{} to 70\ifmmode^\circ\else\textdegree\fi{} with respect to the beam direction. The measurements are in fair agreement with the impulse approximation calculations which use the quantal elastic electron-ion differential scattering cross sections folded with the Compton profile of the target electrons. We observe that the energy of the centroid of the binary-encounter-electron (BEE) peak is projectile charge state, q, and laboratory angle, ${\mathrm{\ensuremath{\theta}}}_{\mathit{L}}$, dependent. Moreover, at 0\ifmmode^\circ\else\textdegree\fi{}, an enhancement of the ratio of the observed double differential cross section for nonbare projectiles to that for the bare ion projectiles, \ensuremath{\sigma}(q+)/\ensuremath{\sigma}(9+), is observed, contrary to the ${\mathit{q}}^{2}$ scaling predicted by a first Born calculation for ionization. This ratio \ensuremath{\sigma}(q+)/\ensuremath{\sigma}(9+) decreases nonotonically with increasing ${\mathrm{\ensuremath{\theta}}}_{\mathit{L}}$, and becomes smaller than one for ${\mathrm{\ensuremath{\theta}}}_{\mathit{L}}$\ensuremath{\ge}30\ifmmode^\circ\else\textdegree\fi{}.

Influence of the projectile field on free target electrons.

The spectral distribution of loosely bound target electrons emitted in collisions with fast bare projectiles is described in terms of electron capture to the projectile continuum. Comparison with experimental data on electron ejection from He by 1--5-MeV/amu H[sup +], C[sup 6+], O[sup 8+], and F[sup 9+] impact into forward directions shows that the impulse approximation for rearrangement is able to describe the shape of the energy distribution not only at the cusp, but also in the binary-encounter region and beyond. The results of the post form of the impulse approximation are discussed in relation to the first-order Born approximation, the continuum distorted-wave theory, the fully peaked prior impulse approximation, and in particular the recently presented distorted-wave strong-potential Born approximation.

Radiative electron capture in relativistic atomic collisions.

Radiative electron capture (REC) from a low-Z target atom into a bare high-Z projectile is described in the impulse approximation for the momentum distribution of the captured electron in the initial target state. Otherwise the treatment is rigorous by using exact relativistic Coulomb wave functions for the bound and continuum projectile states. As an application of the computer program, photon spectra and differential cross sections have been calculated for 295-MeV/u ${\mathrm{U}}^{92+}$+N collisions. The angular distributions for K-shell REC as well as for L-shell REC show pronounced deviations from ${\mathrm{sin}}^{2}$\ensuremath{\theta}. Cross sections for radiative recombination with capture into the K shell and into the L subshells are presented for projectile charges between 20 and 100 and for energies between 100 MeV/u and 2 GeV/u.

Electron capture to the continuum in collisions of bare projectiles with Ne targets

The authors have investigated the cusp resulting from electron capture to the continuum of 1.25-5 MeV amu-1 fully stripped hydrogen and oxygen as a function of the collision energy and the detector angular resolution theta 0. It is revealed that the characteristic cusp shape parameters depend strongly on the experimental resolution. The experimental data are compared with the second-order Born theory and the impulse approximation. Both theories confirm the theta 0 dependence of the shape parameters and give a reasonable description of the cusp asymmetry. However, theory tends to overestimate the absolute cross sections, in particular in the case of oxygen.

Cross Sections for Electron Capture in Relativistic Atomic Collisions

Cross sections for the capture of electrons from single-electron targets into bare projectiles moving at relativistic velocities are calculated using the relativistic eikonal approximation. The calculations are performed for projectile energies between 0.2 and l04 GeV/u and for projectile-target combinations that presumably are of interest for future experiments, namely Au and U colliding with C, Al, Cu, Ag, Au, and U and vice versa. State-to-state cross sections are given for initial and final 1s1/2, 2s1/2, 2p1/2 and 2p3/2 states.

Relativistic third-order Oppenheimer-Brinkman-Kramers cross sections for electron capture

A relativistic form of the third-order Oppenheimer-Brinkman-Kramers (OBK) approximation, evaluated to leading order in the fine-structure constant alpha , is used to calculate cross sections for s-state to s-state electron capture from a target atom to a bare projectile ion. These calculated cross sections are somewhat smaller than those obtained with the second-order OBK approximation. Reasonably satisfactory agreement is found with the available experimental data. It is emphasized that the OBK approximation must be evaluated with the inclusion of only the leading order terms in alpha for satisfactory results to be obtained. It is shown that certain terms logarithmic in the Lorentz factor gamma , which occur in the scattering amplitude at ultra-high relativistic energies, are of higher order in alpha .

Impact parameter dependence of classical capture probability from any initial state by fast bare projectiles

A model for calculating the impact parameter dependence of the single electron capture probability in fast collisions of highly charged ions and atoms is proposed. It is based on concepts suggested by Bohr and Lindhard in their classical electron capture model. In the authors' model the target atom electrons have the spatial distribution of a 'frozen' wavefunction. Using hydrogenic wavefunctions an analytic expression for the impact parameter dependence of the single electron capture probability for any target subshell is derived. Introducing this impact parameter dependence extends the applicability of the model beyond single electron capture to multielectron charge-transfer processes. The present calculations are applied to two-electron systems using the independent electron approximation.

The continuum distorted wave-eikonal initial state model for single electron capture in ion-atom collisions

Close analytical transition matrix elements are obtained for single electron capture from an arbitrary initial state of an atomic target to an arbitrary final state of a bare projectile by using the continuum distorted wave-eikonal initial state approximation. As an application, theoretical total cross sections for capture into 2s and 2p states of the projectile for impact of protons on H and He targets are computed. These results are compared with existing experimental data as well as with other theoretical calculations.

Electron capture and target ionization in collisions of bare projectile ions incident on helium.

Absolute cross sections for the processes of single capture, transfer ionization, and single and double ionization were measured for ${\mathrm{C}}^{6+}$, ${\mathrm{N}}^{7+}$, ${\mathrm{O}}^{8+}$, and ${\mathrm{F}}^{9+}$ projectiles incident on a helium target in the projectile velocity range of 0.25--2.0 MeV/amu. The cross sections were determined by measuring projectile-ion final charge states in coincidence with target recoil-ion final charge states. The single-capture and transfer-ionization cross sections were corrected for ionization from impurity charge states in the beam and for double-collision processes in the target gas cell. These corrections, which are necessary for the relative as well as the absolute cross sections, were found to be as large as 50% of the cross section. The measured cross sections are compared to the multistate, coupled-channel calculations of Shingal and Lin using an independent-electron model.

Single electron capture by high velocity bare and one-electron projectiles in collisions with molecular hydrogen

Total cross-sections for single electron capture by 0.5–2.4 /amu bare and hydrogen-like F and O projectiles on molecular hydrogen have been measured. The measured cross sections are compared with empirical scaling rules and are found to scale as E −4.82 and q 3.75.

Mechanisms of double excitation in ion-atom collisions at high velocities.

Double-excitation cross sections of helium atoms by bare heavy-ion projectiles at high energies are calculated within the one-center atomic-orbital expansion method including the electron-electron interaction between correlated helium wave functions. The resulting excitation cross sections to 2${\mathit{s}}^{2}$ $^{1}$${\mathit{S}}^{\mathit{e}}$, 2${\mathit{p}}^{2}$ $^{1}$${\mathit{D}}^{\mathit{e}}$, 2s2p $^{1}$${\mathit{P}}^{\mathit{o}}$, and 2${\mathit{p}}^{2}$ $^{1}$${\mathit{S}}^{\mathit{e}}$ states are analyzed. We conclude that double excitations at high energies by low-${\mathit{Z}}_{\mathit{p}}$ projectiles are dominated by a first-order process in which the two-electron transition proceeds through one electron-projectile interaction in conjunction with shakeup or rearrangement due to electron-electron interactions. For high-${\mathit{Z}}_{\mathit{p}}$ projectiles at a given velocity, on the other hand, the excitation is dominated by a second-order process in which the transition proceeds through two successive electron-projectile interactions.

Recoil-ion-projectile-ion-cusp-electron triple-coincidence measurements for 1-MeV/u bare and one-electron O and C projectiles on Ne.

We have measured in coincidence the projectile-ion charge state, the target-recoil-ion charge state, and the energy of a free electron (cusp electron) emerging from the same collision with a velocity close to the beam velocity, for 1-MeV/u bare and one-electron oxygen and carbon projectiles colliding with neon targets. The most probable recoil-ion charge state of recoil ions not associated with cusp electrons is 1. Most cusp electrons accompany a projectile that does not change charge, and the most probable recoil-ion charge state in this case lies between 2 and 3. The recoil-ion charge-state distribution associated with a cusp electron and bound-state capture by the projectile is shifted towards even higher charge states. Cusp-electron production in conjunction with electron loss by the projectile is not associated with such a large shift. The probability of cusp-electron production given the production of a recoil ion increases with increasing recoil-ion charge state for projectiles that do not change charge and for projectiles that capture an electron, and decreases with increasing recoil-ion charge state for projectiles that lose an electron in the collision.

Contributions of different mechanisms for electron capture at relattvistic impact energies

Electron capture by impact of bare projectiles on different targets at high relativistic collision energies is studied. Contributions to total cross sections, of experimental interest, given by various radiative and nonradiative intermediate mechanisms are analysed. The nonradiative reactions are represented by two center-distorted wave models.

The Landau-Zener model for electron capture by highly charged ions in collisions with atomic hydrogen

The two-state Landau-Zener model with rotational and degenerate Stark-effect coupling has been formulated to yield cross sections Q n m for populating Rydberg substates ¦ n m > of the one electron projectile ion P ( Z − 1)+ the transfer reaction P z+ + H(1s) → P (Z − 1)+( n m + H + , where P Z+ represents a bare projectile ion. Total cross sections agree well with experiment and more elaborate calculations but the l-distributions exhibit some discrepancies at high velocities.

Impulse approximation for cusp electron production from target K and L shells.

The forward peak resulting from electron capture to the continuum of bare projectiles is investigated within the impulse approximation in both its prior and post form. It is found that the asymmetry of the peak as well as the peak intensity increases if a larger number of interactions between the electron and the projectile is included in the calculation. For strongly asymmetric systems with light projectiles, a peaking approximation becomes valid which factorizes the capture cross section into the ionization cross section times the projectile Coulomb normalization. Thus capture from excited states is easily included, and the factorization allows for a fast evaluation not only of the electron spectra but also of the impact-parameter distribution and the alignment. The theory is also extended to capture into Rydberg states. The collision systems ${\mathrm{He}}^{2+}$+He, p+He, and p+Ne are investigated, and comparison is made with available experimental data.

Electron capture by slow multicharged ions: core effect on final 1 distributions

The authors have calculated sigma nl partial cross sections for collisions Iq++H to I(q-1)+(nl)+H+ in the keV amu -1 impact energy range (Iq+=C4+, N5+, O6+, C6+, O8+, Ne8+ and Ar8+). The molecular expansion has been used with a basis set of OEDM orbitals and a specific form of the common translation factor. They have investigated the competition between the Stark and core-electron interactions by comparing the results obtained for bare and non-bare projectiles with the same charge q. The most spectacular result concerns the increase of the population of the ns sublevels dominantly populated by capture at low impact energies (v<0.4 au). A very good agreement has been found between the present calculations and the experimental data. In the velocity range 0.2<v<0.7 au the agreement is very good with other theoretical calculations when available.