Review of theories on ionization in fast ion-atom collisions with prospects for applications to hadron therapy

This work reviews quantum-mechanical four-body distorted wave theories for double electron capture in collisions between fast heavy multiply charged ions and heliumlike atomic systems. The widely used distorted wave methods of the first- and second-order in the pertinent perturbation series expansions are compared with each other. This tests the presumed importance of double continuum intermediate states of two electrons. Further, the relative performance is evaluated of the second-order theories with and without the eikonalization of the two-electron Coulomb wave functions for double continuum intermediate states. This checks the correctness and usefulness of the eikonalized Coulomb waves when two electrons participate actively to the transition from the initial to the final state of the entire system. We also analyze the significance of the contributions from excited heliumlike states especially in comparison between theory and measurement. The overall goal of the present study is to determine how much of the unprecedented experience gained over several decades in studying high-energy theories of pure three-body charge exchange could be exported directly to four-body double-electron capture without much of additional and essential eleaborations, besides the naturally increased computational demand. In particular, we address the unexpected breakdown of the continuum distorted wave eikonal initial state approximation and the anticipated success of continuum distorted wave theory for double charge exchange in ion-atom collisions at high impact energies.     

Selectivity of electron capture probabilities on the initial state magnetic quantum numbers in ion-atom collisions

Close-coupling calculations have been carried out for ion-atom collisions to show that electron capture probabilities depend strongly on the magnetic quantum number of the initial target state ifthe quantization axis is chosen to be perpendicular to the scattering plane. In thenatural frame of reference, the probability for electron capture is largest form _i=?l substates and decreases rapidly with increasingm _i. This propensity rule is the result of the rotation of the electron cloud following the rotation of the internuclear axis during the collision.     

Second-order theories for electron loss in fast collisions with He atoms

The momentum distribution of projectile electrons ejected in collisions with light targets is calculated within the second-order Born approximation for direct ionisation and within the electron impact approximation and the impulse approximation for electron capture to the target continuum. From comparison with available experimental data it is found that for forward emission angles the electron is well described by a projectile eigenstate, while at backward angles a target final state is more appropriate. At all angles the inclusion of simultaneous target excitation is very important.     

Semiclassical description of multiple electron capture and ionization in fast bare nucleus-rare gas collisions

Multiple electron capture plus ionization processes inX ⁱ⁺-Ne collisions (i=6, 12, 20) in the energy regime from 50 keV/amu up to several MeV/amu are studied within a semiclassical quantum statistical (?=0) independent particle model. Good agreement is found with existing experimental data for the production of recoil ions with charges up toq=8.     

Semiclassical description of multiple electron capture and ionization in fast bare nucleus — Rare gas collisions

A quantum statistical semiclassical (?=0) method describing the time evolution of the electron density of a rare gas atom under the impact of a fast bare ion is presented. The independent particle model proposed features mean field effects and is solved by a Classical Trajectory Monte Carlo method. Recoil ion charge state production cross sections compare substantially better with experiment than previous calculations.     

K-shell ionization in relativistic ion-atom collisions

We present calculations ofK-shell ionization probabilities in asymmetric ion-atom collisions at relativistic velocities of the projectile. The time-dependent Dirac equation is represented as a system of coupled differential equations. The transition probabilities are determined using the coordinate space method. This necessitates an extension of the angular momentum coupling compared with nonrelativistic collision systems. Effects of the relativistic projectile motion on the coupling matrix elements and their consequences onK-shell ionization are discussed.     

State-selective electron capture processes in collisions involving boron ions

A full theoretical treatment of electron capture processes using ab initio configuration interaction methods within, according to the collision energy range concerned, a semiclassical or a quantal collisional formalism including translation effects has been developed recently. An application for collisions involving boron, an important impurity in fusion reactors, is presented on examples of the ground state: B³⁺(1s²) + He, B⁴⁺(1s) + H, and the metastable ion B³⁺(1s2s) + H reactions. © 1996 John Wiley & Sons, Inc.     

Angular distribution of scattered projectiles following double electron capture processes at low-energy C4+ and helium collisions

A four-body classical trajectory Monte Carlo method is applied in the study of double electron capture in low-energy ${\mathrm{C}}^{4+}$ and He atom collisions. The interaction between the two target electrons is neglected throughout the collisions. The angular differential cross-sections of the scattered projectiles, following double electron capture, are calculated and compared with experimental data.     

Multiple-electron processes in 1.4 MeV/u ion-atom collisions

Simultaneous multiple-electron capture and multiple ionization is studied for collisions of highly stripped ionsA ^q+ with rare gas atomsB=He, Ne, Ar, Kr and Xe. At a specific energy of 1.4 MeV/u coincidence measurements were conducted distinguishing between pure ionization, stripping and capture of up to four electrons by projectiles in charge states fromq=6 up toq=48. The coincident charge-state distributions of target recoil ionsB ⁱ⁺ range fromi=1 up toi=19 (in few cases). For highly charged projectiles the relative fractions of recoil ions for concomitant electron capture and ionization are found to be nearly independent of projectile charge or species. Average charge states 〈i〉 of the recoil ions produced by loss respectively capture ofk electrons (k=?2, ?1, 0, 1, 2, 3, 4) from/into the projectile ion were determined. Their systematic dependences onk, on the target atomic number and the projectile ion charge are discussed. A calculation of partial cross sections for multi-electron collision processes in the He target atoms using unitarized first order perturbation theory for impact parameter dependent probabilities and an independent-electron picture is presented and discussed on the basis of the experimental data.     

On the cluster-size dependence of electron capture cross sections in ion-cluster collisions

The dependence of the electron capture cross section on cluster size in proton-cluster collisions is investigated within two different theoretical models. At low collision velocities a strong increase in the cross section with cluster size is found, whereas the size-dependency of the cross section becomes less pronounced at higher velocities.     

Intensity and polarization of light emitted in slow ion-atom collisions

We study the intensity and polarization of light emitted during slow ion-atom collisions. We describe the nuclei as moving along classical trajectories while the electronic rearrangement is treated using time-dependent molecular orbitals. The intensity of emitted light is calculated from the diatomic time-dependent dipole. We evaluate the diatomic dipole matrix elements involving 1s, 2s, and 2p traveling atomic orbitals suitable for time-dependent collision studies. We calculate the intensity and the polarization of light emitted in p + H(1s) collisions at kinetic energies from 10 to 1000 eV, for several impact parameters, changing over time. The emitted intensity goes through a maximum as the collision energy increases and lasts between 10 and 1 fs; the polarized light components parallel and perpendicular to the incoming beam direction show pronounced dependences on impact parameters and time. © 1996 John Wiley & Sons, Inc.     

Application of inclusive probability theory to heavy ion-atom collisions

Using the independent particle model as our basis we present a scheme to reduce the complexity and computational effort to calculate inclusive probabilities in many-electron collision system. As an example we present an application toK?K charge transfer in collisions of 2.6 MeV Ne⁹⁺ on Ne. We are able to give impact parameter-dependent probabilities for many-particle states which could lead toKLL-Auger electrons after collision and we compare with experimental values.     

Charge asymmetry effects in inner-shell alignment induced by ion-atom collisions

Charge asymmetry effects in an alignment of inner-shell vacancies induced by ion-atom collisions are studied theoretically. The corrections to the first order calculations of the alignment which depend on the sign of the projectile charge are discussed. The effect of these corrections on the differential alignment is large and can be studied in coincidence experiments with proton and antiproton beams of low energies. The calculations show that with increasing projectile energy the charge asymmetry effects decrease and become practically negligible when the projectile velocity is comparable with the velocity of the electron in the shell under consideration. The total alignment depends only weakly on the charge of the projectile. The calculated differences of the integralA g (2p ₃ ^2/?1 ) alignment produced by protons and antiprotons are not greater than 20% in the whole energy range under study.     

Effects of electron kinetic energy and ion-electron inelastic collisions in electron capture dissociation measured using ion nanocalorimetry

Ion nanocalorimetry is used to measure the effects of electron kinetic energy in electron capture dissociation (ECD). With ion nanocalorimetry, the internal energy deposited into a hydrated cluster upon activation can be determined from the number of water molecules that evaporate. Varying the heated cathode potential from -1.3 to -2.0 V during ECD has no effect on the average number of water molecules lost from the reduced clusters of either [Ca(H2O)15]2+ or [Ca(H2O)32]2+, even when these data are extrapolated to a cathode potential of zero volts. These results indicate that the initial electron kinetic energy does not go into internal energy in these ions upon ECD. No effects of ion heating from inelastic ion-electron collisions are observed for electron irradiation times up to 200 ms, although some heating occurs for [Ca(H2O)17]2+ at longer irradiation times. In contrast, this effect is negligible for [Ca(H2O)32]2+, a cluster size typically used in nanocalorimetry experiments, indicating that energy transfer from inelastic ion-electron collisions is negligible compared with effects of radiative absorption and emission for these larger clusters. These results have significance toward establishing the accuracy with which electrochemical redox potentials, measured on an absolute basis in the gas phase using ion nanocalorimetry, can be related to relative potentials measured in solution.     

Resonant double electron capture by fast He2+ from helium: the first-order Born approximation with correct boundary condition

The first-order Born approximation with correct boundary condition is applied in a study of the resonant double electron capture by fast He²⁺ from helium. A configuration-interaction wave function is employed to describe the ground state of helium. Total cross section as a function of the impact energy is calculated and compared with experimental and theoretical values.     

Laser-assisted electron capture by a fast proton from a hydrogen atom

The first Born approximation is used to study the laser-assisted electron capture by a fast proton from a hydrogen atom. The laser modification on differential cross section peaks sharply in the forward direction. With the impact energy increasing, the change in integral cross section becomes notable. The more intense the laser, the greater the cross section is; the lower the frequency, the greater the cross section.     

K x-ray emission in gas- and solid targets in close heavy ion-atom collisions

Impact parameter dependentK x-ray emission from both collision partners in²⁰⁸Pb⁺²⁶ →¹²⁰Sn and Xe collisions at 3,6 MeV/N projectile has been investigated. In solid target collisions the Sn-K emission yield shows impact parameter dependent structures. These structures are interpreted in terms of post-collisional capture processes. TheK x-ray emission from the heavier collision partner related to the 1s σ vacancy production, is found to be dependent on the primary projectile outer-shell configuration.     

Simultaneous electron capture and target ion excitation in collisions of C4+ and N5+ on He

Cross sections for simultaneous electron capture and target ion excitation have been measured for impact of slow He-like C⁴⁺ and N⁵⁺ ions on He. The energy of the primary ion beams has been varied over more than two orders of magnitude: 0.05–7 keV/amu. The results are discussed on basis of a slightly modified version of the dynamic classical over-barrier model for multiple electron capture. The differences in the energy dependences of the experimental results of C⁴⁺ and N⁵⁺ — He can be explained qualitatively by assuming that for N⁵⁺ binding energy sharing between the two participating electrons is of importance, particularly at the lower impact energies.     

Resonance electron capture for determining double bond and hydroxy group locations in fatty acids

The nature and location of modifications of fatty acids are determined by resonance electron capture (REC) ionization of free acids and their methyl esters and pyrrolidides. The molecular negative ions (MNI) formed in the high resonance region undergo both charge-remote and charge-driven decomposition. The spectra of fragments arising from dissociation of these high-energy MNI contain decisive information on the original structure of the neutrals. The pyrrolidides of fatty acids result in simpler spectra on the one hand, and on the other hand these spectra give complete structure information.     

An approximate description of the double capture process in He2+ + He collisions with static correlation

It is shown that the process of resonant double electron capture in high energy He²⁺+He collisions can be approximately described by a sum over products of one-electron CDW amplitudes. The summation coefficients are determined by stationary ground-state calculations with CI wavefunctions. Total and differential cross sections are calculated and compared with experimental values.