Introduction and references

Excitation and electron capture cross sections in ion-atom collisions

The cross section calculations available on this page are based on a non perturbative approach : the SemiClassical Atomic Orbital Coupled Channel (SC AOCC) method which is fully documented in many articles, reviews or books, e.g. [1,2,3].

* The main features and limitations of the present implementation are :
  • limitation to hydrogenic systems, i.e. in collisions between one-electron target with bare ions, e.g. H+-H, He2+-He+, He2+-H, ... collision systems,

  • classical description of the target-projectile relative motion, within the straight-line, constant velocity approximation (impact parameter method),

  • the scattering wavefunction is developped on a set of eigenstates (exact hydrogenic states) centered on both target (which holds by convention the initial electronic state) and projectile (if required),

  • this expansion is augmented by plane-wave Electronic Translation Factors (ETF) to insure galilean invariance of the results,

  • the cross sections are computed by impact parameter integration of the transition probabilities for the states included in the basis set, i.e. for excitation and electron transfer channels,

  • ionization is not taken into account in the present implementation,

  • the range of applicability of the method is typically from about 0.1 to 500 keV.u-1 impact energies (i.e. relative velocities 0.05 < v < 5 a.u. [4]).

* The reliability and accuracy of the cross sections are not controlled by the code and therefore the users are recommended to check the validity of theirs results :
  • the values of the cross sections depend on the relevance and the number of the states selected on the target and on the projectile. Due to the hardware characteristics (RAM and CPU speed) the size of the basis sets is limited to 35 nlm states in the present implementation,

  • seven parameters (defined in the input form) control the accuracy of the cross sections :

    • vmin, vmax define the range in which the cross sections are computed (cf. above the range of applicability),

    • bmin, close to zero (but different), bmax maximum impact parameter for which the calculations are performed. It should be set to cover the impact parameter range in which excitation and capture are important so that the cross sections for inelastic processes are converged (bmax depends on collision systems and velocities),

    • nb, number of impact parameters for which the calculations are performed to have accurate integrations of the probabilities,

    • Rmax target-projectile relative distance from/to which the collision starts/finishes: not too small (depending on the important inelastic channels and on target, projectile charges), but not too large either (to avoid useless computations),

    • nor, number of mesh points for which the overlap and coupling matrix elements are computed for further interpolation in the propagation stage (typically about 200-400 but depends also on Rmax).

The users should change these parameters (whatever the default values are) to check the convergence of the cross sections. The examination of the probabilities and norm conservation are important for that purpose.

[1] B.H. Bransden and M.R.C. McDowell, Charge Exchange and the Theory of Ion-Atom Collisions (Clarendon, Oxford, 1992).
[2] W. Fritsch and C.D. Lin, Phys. Rep. 202, 1 (1991).
[3] J. P. Hansen, A. Dubois, and S. E. Nielsen, Phys. Rev. A 44, 6130 (1991); A. Dubois, S.E. Nielsen and J.P. Hansen, J. Phys. B 26, 705 (1993); J. Caillat, A. Dubois and J.P. Hansen, J. Phys. B 33, L715 (2000).
[4] The atomic unit (a.u.) of velocity is about 2.2 106 m s-1. The conversion between velocity and energy is va.u. = (EkeV/u / 25 )1/2.