Projectile States Research Articles

Electron capture by slow multiply charged ions from H(1s)

Over the last 11 years a considerable experimental and theoretical effort has been devoted to electron capture collisions involving slow ( v < 1 a.u.) multiply charged ions and atomic hydrogen. These collisions result in the selective population of a relatively small number of excited projectile states. Translational energy spectroscopy (TES) and the complementary technique of photon emission spectroscopy (PES) have been developed to provide state selective cross sections. In the last 5 years the merged beams technique has been used to measure total one electron capture cross sections in the energy range 1–1000 eV amu −1 enabling comparison with theory at much lower energies than was previously possible. The majority of the experimental measurements have been for fully stripped, Li-like or He-like ions. Theoretical models such as the semiclassical close coupling methods and fully quantal molecular orbital methods have been developed in parallel with experiment. In general the agreement is good although there is a need for state selective data at lower energies and for differential experimental measurements. Also experiments are needed with pure ground state or metastable ion beams.

Energy-transfer processes during Xe30+-Ar collisions for projectile velocities between 0.3 and 1.0 a.u.

Electron capture by Xe[sup 30+] from Ar has been studied for projectile velocities between 0.3 and 1.0 a.u. Coincidence measurements were used to identify experimentally the final states of both target and projectile. The capture of up to eight electrons from the target was observed, while retention of more than three electrons by the projectile was found to be rare. Longitudinal recoil momentum spectroscopy was used to determine average [ital Q] values for the capture process as a function of recoil charge state. The [ital Q] values were found to have no measurable dependence on projectile velocity and were found to be in good agreement with those values predicted by the extended overbarrier model. Relative cross sections for the different final channels were measured and found to be in adequate agreement with the model prediction. A slight increase with increasing projectile velocity in the radiative-stabilization probability for the two-electron states finally formed on the projectile was observed.

The interaction of hydrogenic ions with metal and semiconductor surfaces

We present K-Auger spectra arising from collisions of hydrogenic C, N, O, F and Ne ions with p-conducting Si(100), Ni(110) and polycrystalline W surfaces for different beam energies and observation angles. These spectra exhibit sharp peaks which, using Hartree-Fock atomic structure calculations, can be assigned to distinct projectile states prior to KLL decay. Moreover, we find that the measured spectra show target-specific features which can be explained by different free electron densities in metals and silicon.

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.

Fusion of 32S+154Sm at sub-barrier energies.

Fusion-evaporation cross sections for the $^{32}\mathrm{S}$${+}^{154}$Sm system at bombarding energies near the Coulomb barrier have been measured by off-line observation of the K x rays emitted in the radioactive decay of the residual nuclei. The total fusion cross sections were obtained by adding the contributions from evaporation and fission processes. The fusion excitation function for this system is compared with coupled-channel calculations that include the deformation of the target and vibrational states of both target and projectile.

Electronic processes in slow ion-surface collisions. Xe + with clean and cesiated W(110) surfaces

Electron spectra arising in grazing incidence collisions of Xe + ions with clean and cesiated W(110) single crystal surfaces are analyzed using a recently developed theoretical model. The electron spectra have been published before, and the model has been described elsewhere. Electron spectra obtained for Cs coverages below one monolayer at a grazing angle of 5° and at a beam energy of 50 eV are selected for the analysis. The analysis yields a complete reconstruction of the time evolution of the ion-surface system during the interaction. This time evolution is described in terms of the relevant electronic processes and populations of electronic projectile states. The time evolution is found to depend very strongly on the Cs coverage, whereby the dependence can simply be ascribed to the Cs-dependent work function. The analysis further yields a determination of the absolute distance dependent transition rates of the resonant one-electron transitions and of the two-electron Auger-type transitions occurring during the interaction. The secondary electron yield calculated with these rates reproduces qualitatively the experimentally determined coverage dependence. A discrepancy concerning the strength of the dependence is ascribed to reduction of the “effective” metal surface due to the adsorbed Cs ions.

Alignment of magnetic substates in double-electron-capture collisions.

We have determined the magnetic-substate alignment produced in double-electron capture by the H-like projectiles C[sup 5+] and B[sup 4+] from He atoms by measuring the anisotropy of the Auger electron emission from the doubly excited 1[ital s]2[ital l]2[ital l][prime] [sup 2][ital L] projectile states formed in the collision. This work includes additional measurements and expands upon our previous short communication on the (C[sup 5+],He) system [Phys. Rev. A 43, 607 (1991)]. The measurements yield [ital M][sub [ital L]] substate population fractions which challenge theory at nearly the finest quantum state detail. We observe large differences between the results for B[sup 4+] and C[sup 5+] over the velocity range 0.25--0.50 a.u. for the substate and total 1[ital s]2[ital l]2[ital l][prime] [sup 2][ital L] relative cross sections. Substantial population of [ital M][sub [ital L]][gt]0 states shows the importance of rotational coupling in these slow collisions. The large anisotropies observed demonstrate that substantial errors can result from inferring cross sections'' from single-angle measurements and the assumption of isotropic electron emission.

Measurements of recoil ion longitudinal momentum transfer in multiply ionizing collisions of fast heavy ions with multielectron targets.

The longitudinal momentum transfer to the recoil ion in collisions of 1 MeV/amu bare F ions with Ne are resolved for final charge states of both projectile and recoil ions. We observe the recoil to be thrown backwards in electron-capture events, reflecting the physical impact of the electron translation factor. The size of the momentum transfer is in agreement with classical trajectory Monte Carlo calculations for low charge state recoil ions but not for high charge state recoil ions.

One-and-a-half-centered expansion method in charge-transfer calculations of proton-hydrogen scattering.

In this paper, we undertake a feasibility study of improving the one-and-a-half-centered expansion (OHCE) method of Reading, Ford, and Becker [J. Phys. B 14, 1995 (1981); 15, 3257 (1982)]. We have explored the efficacy of an alternative method to evaluate the charge-transfer matrix elements and improved the estimated time dependence of the charge-transfer scattering amplitudes. More projectile states have been included in the calculations than used hitherto. A unitary matrix, U matrix, which can propagate the wave functions from -\ensuremath{\infty} to t, where t denotes time, has been constructed using the single-centered expansion (SCE) method. A complex basis set of nine radial s states and nine radial p states has been used in the expansion of trial wave functions for the target. Charge-transfer matrix elements have been evaluated by a Feynman integral technique; one numerical integral using Gaussian quadrature is needed. The radial parts of the matrix elements are stored on circles and used for all the impact parameters. In a OHCE calculation, we have to choose a function ${\mathrm{\ensuremath{\beta}}}_{\mathit{m}}$(z) to modulate the charge-transfer amplitudes. The only constraints on ${\mathrm{\ensuremath{\beta}}}_{\mathit{m}}$(z) are ${\mathrm{\ensuremath{\beta}}}_{\mathit{m}}$(-\ensuremath{\infty})=0 and ${\mathrm{\ensuremath{\beta}}}_{\mathit{m}}$(\ensuremath{\infty})=1. In this paper, ${\mathrm{\ensuremath{\beta}}}_{\mathit{m}}$(z) has been obtained from a SCE calculation. This ${\mathrm{\ensuremath{\beta}}}_{\mathit{m}}$(z) function increases gradually in the whole collision region.It offers an improvement over the step function used in previous work. A computer code has been developed to include s and p states for the target and projectile. The calculations have been performed in the proton energy range from 30 to 250 keV. The charge transfer to the 1s state has been calculated and gives good agreement with the experimental data. The proton energy ranges have been extended from the 100 keV used in previous work to 250 keV. The charge-transfer cross sections to the 2p state fit the experimental data at 30 keV and are almost the same as those calculated using the four-state, two-centered expansion method proposed by Cheshire and Gallaher [J. Phys. B 3, 813 (1970)] and Shakeshaft [Phys. Rev. A 14, 1626 (1976)]. The results of the charge exchange to the 2s state are also in fairly good agreement with the measurements of Ryding [listed in Tawara, Kato, and Nakar, At. Data Nucl. Data Tables 32, 235 (1985)].

Multiple electron capture in slow Ar9+ and 13C5+ on Ne, studied by e--Neq+ coincidences

The authors have investigated multiple electron capture into autoionizing projectile states during 108 keV Ar9+ and 80 keV 13C5+ collisions on Ne by measuring autoionization electrons in coincidence with charge state selected target ions. They have determined partial electron energy spectra, corresponding to a well defined number of initially captured electrons. The set-up of the ion and electron spectrometer is described. Trajectory calculations for the determination of detection efficiencies are presented. The partial spectra are discussed in terms of the 'extended classical barrier' model.

Statistical theory of charged-particle stopping and straggling in the presence of charge exchange

General expressions have been derived for the mean energy loss and straggling of a heavy charged particle penetrating through a thin slice of matter. The main input parameter is a differential energy loss rate that allows for transitions within an arbitrary number of projectile states. Both spontaneous and collision-induced events are potentially induced, but different events are assumed statistically independent. Asymptotically, the mean energy loss is shown to approach a linear dependence on time or path length. The slope is given by the equilibrium energy loss rate, and the intercept at zero path length depends on the incident projectile state. Energy-loss straggling can be split into a collisional part and a contribution from variations in projectile state. The latter turns out to be related to the intercept in the mean energy loss for the pertinent projectile states. Previous results applying to a two-state system have been generalized to an arbitrary number of states. A full evaluation has been presented for a three-state system. A procedure is outlined that allows to empirically determine the magnitude of charge-exchange straggling.

Energy loss of hydrogen and helium ions in hydrogen and helium gas: looking for exceptions from velocity proportionality

At projectile velocities ν 1 below the Bohr velocity the electronic stopping cross section ε of hydrogen (H 2, D 2) and helium gas for hydrogen isotopes (H, D) and of helium gas for helium projectiles has been measured by a time-of-flight technique. We find the hydrogen stopping in He to show a significant departure from the ν 1-proportionality commonly assumed (ε α ν 1 3.3 at 4 keV per nucleon) [R. Golser and D. Semrad, Phys. Rev. Lett. 66 (1991) 1831]. Electronic stopping of H, D onto H 2, D 2 (ε α ν 1 0.9 at 4 keV per nucleon) and He onto He (ε α ν 1 0.8 at 4 keV per nucleon,if nuclear stopping is not subtracted) may be considered velocity proportional. We attribute this behavior to the probability of charge changing processes, which is small if projectile and target ground state levels are strongly different. The helium to hydrogen stopping ratio of helium gas has the strange value 5.8 at 4 keV per nucleon; possible implications to the concept of “effective charge” are discussed.

Analysis of electron spectra from grazing-incidence collisions of Ar 2+ with Pb(111) single-crystal surfaces

Electron spectra are reported for the scattering of Ar 2+ ions by a well defined Pb(111) single-crystal surface. The measurements are performed for beam energies in the range 0.6–10 keV at a grazing angle of 2°. The spectra at these conditions are found to be dominated by contributions from “spontaneous” electron emission processes, i.e., from Auger-type transitions in which two electrons are involved. They show a rather rich structure, especially at the lowest beam energies. A rather detailed analysis in terms of a model is possible. The model describes the time evolution of the ion-surface system during the slow approach. The processes involved are resonant one-electron exchange processes and Auger-type processes. The first processes lead to the distance-dependent population of various singly and doubly excited projectile states, the second lead to electron emission with distance dependent probability and kinetic energy. The analysis in terms of this model yields: (1) an identification of the main electronic states and processes that play a role during the slow surface approach of the projectile, (2) the absolute distance-dependent probabilities for the main resonant electron exchange and Auger-type processes, (3) the distance-dependent population probabilities for the electronic states involved. For the Ar 2+-Pb(111) system it is found that at the low primary energies, autoionization of Ar ∗∗ and Penning ionization of Ar +∗ dominate the first neutralization step leading to the ground state of Ar +, whereas with increasing energy the direct Auger-capture process of Ar 2+ becomes more important. The second neutralization step leading to the ground state of Ar is found to be always due to direct Auger-capture. In the mentioned primary beam energy range the neutralization to the ground state of Ar is found to be completed at the turning point of the trajectory.

Inclusive inelastic scattering of heavy ions in the independent particle model

The authors consider the inclusive inelastic scattering of heavy ions using the Glauber model and the independent particle approximation. Inclusive inelastic distributions for projectile excitation of the target and total inelastic scattering, where all projectile and target excited states are summed, are discussed using closure. The total inelastic distribution when integrated is shown to be equivalent to the absorption cross section found from applying the optical theorem to the elastic scattering amplitude in the coherent approximation. Calculations are presented for several heavy-ion pairs using realistic nuclear densities in a large mass number approximation.

One- and two-electron capture in collisions of slow B4+ and Be4+ ions with helium.

One-electron and two-electron capture in slow ${\mathrm{B}}^{4+}$-He and ${\mathrm{Be}}^{4+}$-He collisions are studied within the semiclassical close-coupling description with two-electron atomic basis sets. For ${\mathrm{B}}^{4+}$-He collisions, we find large two-electron capture cross sections to 2l2l' doubly excited projectile states. Double-capture cross sections to 2${\mathit{s}}^{2}$ $^{1}$${\mathit{S}}^{\mathit{e}}$, 2s2p $^{1}$${\mathit{P}}^{\mathit{o}}$, and 2${\mathit{p}}^{2}$ $^{1}$${\mathit{D}}^{\mathit{e}}$ states and the relative M distributions are found to be in good agreement with recent experiments. Earlier data on ${\mathrm{B}}^{3+}$ production are found to contain large portions of double transfer followed by autoionization. For the ${\mathrm{Be}}^{4+}$-He system, the summed cross sections from this work agree with an earlier theoretical study within the adiabatic model. Discrepancies remain, however, for this system in the distribution of double transfer over final states.

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-hydrogen collisions with dressed target and Volkov projectile states in a laser field

Cross sections for the 1S-2S and 1S-2P0 transitions in laser-assisted e--H(1S) collisions are calculated in both the multichannel eikonal treatment and the Born wave approximation, as a function of impact energy and laser field intensity. The laser considered is a monotonic, plane-polarized CO2 laser (photon energy=0.117 eV) with the polarization direction parallel to the initial projectile velocity. The first part of this paper confines the laser perturbation to the bound electrons of the atom. A semiclassical Floquet approach is used to dress the hydrogen atom in this soft-photon weak-field regime, and is shown to reveal a concise description of the laser-assisted collision. The Floquet dressing is compared to dressing by the traditional time-dependent perturbation theory, showing that the perturbative approach gives an incomplete description of the laser interaction, and cannot predict the distinct features provided by the Floquet approach. The second part of this paper extends the laser perturbation to the projectile electron, and the familiar Volkov dressed states are used.

BUMPER DEBRIS CLOUD STRUCTURE ESTIMATED BY SHOCK CALCULATIONS

BUMPER DEBRIS CLOUD STRUCTURE ESTIMATED BY SHOCK CALCULATIONS

Production of doubly excited projectile states in collisions of 0.1-MeV/u Ag4+ ions with He, H2, and Ar targets.

In this work, we study the formation of doubly excited projectile states near the double-escape threshold in collisions of 0.1-MeV/u ${\mathrm{Ag}}^{4+}$ ions with He, ${\mathrm{H}}_{2}$, and Ar gas targets under single-collision conditions. We detect projectile states in which one electron occupies a high Rydberg state and a second electron occupies a low-lying continuum state. The cross sections for producing these doubly excited projectile states are on the order of ${10}^{\mathrm{\ensuremath{-}}20}$ ${\mathrm{cm}}^{2}$. The production probabilities are measured as a function of the continuum-electron laboratory-frame energy with the detected Rydberg electrons arising from a fixed band of energy levels. The width of the continuum-electron energy distribution measured in coincidence with a Rydberg electron is smaller than the width of the energy distribution measured without the coincidence requirement for ${\mathrm{H}}_{2}$ and Ar targets but not for He targets. The width of the continuum-electron energy distribution measured in coincidence with a Rydberg electron decreases as the fraction of doubly excited states formed by projectile double excitation and ionization decreases and the fraction formed by double-target-electron capture increases.

Convergence of the nucleus-nucleus Glauber multiple scattering series.

The Glauber S-matrix operator for nucleus-nucleus scattering is expressed as a finite series of matrix elements involving Bell's polynomials. Analyzing ${\mathrm{\ensuremath{\alpha}}}^{4}$He elastic-scattering data at the incident momentum of 4.32 GeV/c, we infer that our expansion is appreciably converging. Further, by applying closure over target and projectile states and neglecting a certain class of terms involving intermediate excitations, we arrive at a recurrence relation for nucleus-nucleus multiple scattering series terms, which invites further study as it seems to provide a simple method for calculating the nucleus-nucleus elastic-scattering cross section.