next previous
Up: Charge transfer in collisions O+ H+


2 Scattering theory

As there is currently no theoretical approach which is applicable over the full energy range considered, processes (1) and (2) are investigated with four different methods each applicable in different, but generally overlapping, energy regimes. The intercomparison of the various theoretical approaches gives a measure of their accuracy and reliability as do comparisons with other theoretical and experimental data. A similar approach was successfully applied to the C+ + H and H+ + C collision systems (Stancil et al. [1998a], [1998b]).

For collision energies less than $\sim$10 keV/u, one of the most robust approaches, the molecular-orbital close-coupling (MOCC) method (e.g., Kimura & Lane [1990]; Zygelman et al. [1992]) was utilized incorporating the potential energy curves and nonadiabatic coupling matrix elements of Kimura et al. ([1997]). Table 1 lists the three molecular states included in the calculations and their experimental separated-atom energies. The collisional dynamics are solved in a semiclassical formalism including electron translation factors (ETFs) for energies between 1 eV/u and 10 keV/u and quantum-mechanically between 0.1 and 500 eV/u.

For collision energies less than $\sim 0.5$ eV/u, the fine-structure of the oxygen atom must be considered. The quantal MOCC method is extended to include the fine-structure levels following the approach of Chambaud et al. (1980) (see also Roueff & Dalgarno [1988]). As in Chambaud et al. we included the $1~^3\Sigma^-
- 2~^3\Sigma^-$ radial coupling, but neglected rotational coupling which was found to have a negligible effect in the three channel, fine-structure unresolved MOCC calculations. Spin-orbit coupling was included, but assumed to be independent of internuclear distance and equal to the experimental separated-atom energies given in Table 1. The fine-structure quantum MOCC (QMOCC-FS) calculation involved 12 scattering channels divided into two uncoupled blocks of five and seven channels of opposite total parity.

For collision energies greater than 5 keV/u, the cross sections were computed with the classical trajectory Monte Carlo (CTMC) method (e.g., Olson & Salop [1977]). CTMC has been shown to be reliable for a wide range of intermediate energies, but may not be accurate at low energies as it yields essentially a classical over-the-barrier result and neglects charge transfer by tunneling of the electron through the barrier. Further, to apply CTMC to multielectron projectiles, such as O+, traditional effective nuclear charge techniques used for single- and few-electron systems were found to be unsuitable. To address this problem we have developed an approach which utilizes a binding-energy-dependent effective charge deduced from standard atomic spectroscopic data to model the electronic structure of the projectile following capture. This approach is described in Schultz & Stancil ([1999]) along with state-dependent n,l charge transfer cross sections needed for studies of radiative emission following charge transfer of precipitating ions in the Jovian atmosphere.

To treat electron capture from the inner orbitals of O by proton impact, the CTMC model was extended (Schultz & Stancil [1999]) to include a constraining potential, enforcing a quantal representation of the ground state. At higher impact energies, capture from the O K-shell dominates and is otherwise significantly overestimated by the standard CTMC approach. This improved approximation is needed to benchmark state-selective charge transfer cross sections, not readily obtainable with other intermediate-energy methods.

The continuum distorted wave (CDW) method is used for high energies utilizing the methods of Belkic et al. ([1984]). The target and projectile atomic wave functions are described by linear combinations of Slater type orbitals taken from Clementi & Roetti ([1974]). The method should be reliable for collision energies greater than $\sim$500 keV/u.


   
Table 1: Asymptotic separated-atom energies of OH+
Molecular Asymptotic Energy a
States Atomic States (K) (meV)
$1~^3\Sigma^-, 1~^3\Pi$ O(3P2) + H+ 0 0
  O(3P1) + H+ 228 19.7
  O(3P0) + H+ 326 28.1
$2~^3\Sigma^-$ O+(4S) + H 227 19.6
a
Bashkin & Stoner (1975).


next previous
Up: Charge transfer in collisions O+ H+

Copyright The European Southern Observatory (ESO)