Two-electron Targets Research Articles

Characteristics of single capture nl distributions and double capture probabilities in slow collisions of Al13+, Al12+ and Ne9+ ions with two-electron targets (He, H2)

Relative intensities of Lyman X-rays consecutive to one- or two-electron capture have been measured for collisions of 4 keV u-1 Al13+, Al12+, Ne9+ ions with He and H2 targets. A method is presented to extract separate information on single and double transfer processes. Preferential n states, proportion of p substrates and mean l values populated by single capture are measured, together with double capture probabilities. Comparison of experimental results with theoretical predictions for one-electron systems with near-crossing radii suggest that the location of these crossings may be more important than target internal structure to determine final l distributions. Finally, for the investigated systems with different ionic charges but near-crossing radii, double capture probabilities are found to be quite similar.

K-Shell excited Li-like ions: Electron spectroscopy of the doublet term system

Electron energies of autoionising doubly excited 1s2 ln′ l′ ( n′ = 2, 3) L-states of Li-like ions are reported for C IV, N V, and O VI. The autoionising states are produced in electron capture reactions from two-electron targets (He, H 2) by slow ( E ion ≦ 5 keV/amu) charge selected ion beams. In this way, differentiation of doublet and quartet terms is possible and the charge state of the emitting ion is unambiguously defined. Comparison is made with available data from other experiments and with relativistic atomic structure calculations. A multiconfiguration variational approach as well as a Z-expansion calculation are found to give better agreement with experimental data than a multiconfigurational Dirac-Fock method.

Electron spectroscopy in collisions with multiply charged ions

Projectile autoionisation of doubly excited states created in slow ( υ ion ⩽ 0.5 a.u.) collisions of multiply charged ions with two-electron targets (He, H 2) are discussed. New electron spectra obtained from H-like and He-like ions of C, N, O, Ne and from Ne-like Ar 8+ are reported. Good agreement is found with a recently proposed extended classical barrier model (ECB), which predicts positions and overall shape of the electron spectra ‘reaction windows”. Relative cross sections for electron emission are derived from experiment and compared with ECB predictions. General features of the capture reaction (spin-conservation, core conservation, successive capture) and the relative importance of the possible decay modes (radiative decay, radiative decay to autoionising states, autoionisation) are discussed.

Radiative and Auger decay channels in K-Shell excited Li-like ions ( Z = 6–8)

Different decay modes for doubly excited Li-like ions (1s21 n′ l′) produced in slow ( E ion < 5 KeV/amu) collisions of multiply charged ions with two-electron targets (He, H 2) are discussed. Using the typical differences in the decay of quartet and doublet states we can prove that the spin of the captured electrons is not changed in the collision. It is shown, that the quartet states 1s2s3s, 1s2s3d actually do not autoionise (i.e. the fluorescence yield exceeds 0.95) and there is strong experimental evidence that this should hold as well as for the majority of the other 1s21 n′ l′-quartet states with n′ > 2. The radiative quartet decay feeds 1s2p21′ quartet states; cascades leading to 1s2p21′ doublet states are discussed as well.

Sum rules and other properties involving resonance projection operators.

A sum rule is derived for the auxiliary eigenvalues of an equation whose eigenspectrum pertains to projection operators which describe electron scattering from multielectron atoms and ions. The sum rule's right-hand side depends on an integral involving the target system eigenfunctions. The sum rule is checked for several approximations of the two-electron target. It is shown that target functions which have a unit eigenvalue in their auxiliary eigenspectrum do not give rise to well-defined projection operators except through a limiting process. For Hylleraas target approximations, the auxiliary equations are shown to contain an infinite spectrum. However, using a Rayleigh-Ritz variational principle, it is shown that a comparatively simple aproximation can exhaust the sum rule to better than five significant figures. The auxiliary Hylleraas equation is greatly simplified by conversion to a square root equation containing the same eigenfunction spectrum and from which the required eigenvalues are trivially recovered by squaring.

Construction of resonance projection operators: Application to two-electron targets.

A derivation of resonance projection operators, in the Feshbach sense, is presented in detail, with inclusion of angular momentum and spin variables. The resultant operators, P and Q, are written in a transparent and manifestly symmetric form. The operators depend on eigensolutions of a homogeneous integral equation. The equation is solved and hence the operators are explicitly constructed for the two-electron (i.e., He-like) targets in a nonseparable (the open-shell) approximation; this procedure can readily be extended to any configuration-interaction-type target function. The kernel of the auxiliary integral equation is also explicitly derived for a Hylleraas-type target function; a Rayleigh-Ritz variational principle is written down for its eigenfunctions. It is pointed out that these (Feshbach) P and Q operators are not formally idempotent, but it is shown that their matrix elements between antisymmetric functions are. This makes them completely suitable for calculation of autoionization states via diagonalization of QHQ. A basic problem in using the concomitant optical potential for scattering calculations remains and is briefly discussed. The generalization of these operators to the inelastic domain is also given (in an appendix).

Two-electron capture into autoionising configurations N4+(1snln'l') with n=2, 3, 4 and n'⩾n, observed by electron spectrometry in collisions of N6+(1s) with He and H2, at 4.2 keV amu-1

Double electron transfer into autoionising states N4+ (1snln'l'), with n=2, 3, 4 and n'>or=n, has been observed in a collision between a one-electron highly charged N6+(1s) ion and a two-electron target (He or H2), by electron spectrometry at 11.6 degrees and 4.2 keV amu-1. The same configurations are excited in the two collisional systems, but with very different probabilities. Electron capture mainly occurs into 1s2ln'l' in N6+-He whereas transfer into 1s3ln'l' is stronger in N6+-H2.

Autoionisation of N5+(nln'l') with n=2,3,4 and n'⩾n measured by electron spectrometry in collisions of N7+with He and H2, at 4.9 keV amu-1

A spectroscopic investigation of electrons coming from autoionising states N5+(nln'l'), with n=2,3,4 and n'>or=n, of the fast ion has been made at 11.6 degrees and 4.89 keV amu-1. These excited states are formed by two-electron capture in a single collision between a bare atom 15N7+ and a two-electron target (He or H2). Only exothermic reactions are observed. It is shown that the ionisation potential of the target has a strong influence on the more probable values of n and n'. In N7+-He collisions, the n=3, n'=3 configurations are the more excited. In N7+-H2, the capture process is less selective since n=3, n'>3 and also n=4, n'>or=4 configurations are strong populated. In all these cases, the residual N6+ ion is left in an excited state (n=2 or 3). The n=2, n'>2 excitation probability is found to be much smaller for the two collisional systems.

Classical-trajectory theory of high-energy collisions between one-electron projectiles and two-electron targets

The classical-trajectory impact-parameter method is used as the basis for deriving an equation of motion for the electronic state of two colliding, composite particles, one a projectile atom or ion consisting of a single valence electron outside a closed inner shell and the other, a target species comprised of two electrons plus a closed inner shell and/or atomic nucleus. The three outer-shell electrons are treated as being indistinguishable from one another, whereas the inner-shell, core electrons serve as sources of static, local pseudopotentials. We adopt for the electronic basis, products of isolated target states and projectile states which are distorted by exclusion forces emanating from the target. The associated set of close-coupled equations are written in the same form as that specific to the quasi-one-electron model of a projectile, such as Li or ${\mathrm{Be}}^{+}$, colliding with a target such as an He or Mg atom, modeled as a structureless scattering center. We then extract from these equations an effective, one-electron Hamiltonian comprised of parts identifiable as Coulombic and exchange interactions, suitably modified by projection operators which take account of the exclusion forces stemming from the indistinguishability of the projectile and target electrons, i.e., from the Pauli principle. Although the formulas for these interactions may be too complicated for direct use in scattering calculations, they are essentially exact and so can serve as useful guides in the search for approximate, model interactions.

Spin conservation in electron-capture collisions

The coupling between electron spin and collisional angular momentum has been studied for ${\mathrm{He}}^{++}$-He, Ne, ${\mathrm{H}}_{2}$, and ${\mathrm{O}}_{2}$ collisions (4-600 eV) by observing radiation resulting from double electron capture into excited states of Hei and comparing the triplet and singlet emissions. The two-electron targets provide a rigid test of the spin-conservation rule, but of these only ${\mathrm{H}}_{2}$ yields data in accord with the rule. The apparently anomalous ${\mathrm{He}}^{++}$-He results are attributed to the domination of short-range effects. These short-range effects are not restricted to double-electron capture, but can apply in any process which involves spin flip.