What have we learned from coupled-channel calculations

WHAT HAVE WE LEARNED FROM COUPLED-CHANNEL CALCULATIONS 

Virtually all non-trivial collision theories are based on the impact-parameter method and on the independent-electron model, where one active electron moves under the influence of the combined field of the nuclei and the remaining electrons frozen in their initial state. Most theories additionally rely on much more serious assumptions as, e.g., adiabatic or sudden electronic transitions, perturbative or even classical projectile/electron interactions. All these assumptions are circumvented in this work by solving the time-dependent Schrodinger equation numerically exact using the atomic-orbital coupled-channel (AO) method. This non-perturbative method provides full information of the basic single-electron mechanisms such as target excitation and ionization, electron capture and projectile excitation and ionization. Since the complex populations amplitudes are available for all important states as a function of time at any given impact parameter, practically all experimentally observable quantities may be computed. 

We have applied our code to kinetic projectile energies of up to a few hundred keV per nucleon. In most cases good agreement with experimental 

Another problematic point appears in the treatment of electron loss due to heavy (neutral) targets. In this case, unrealistic capture processes come into play where the projectile electron is transferred into populated bound target states. In principle, this problem may be circumvented by using the multielectron anti-symmetrization method, where the Pauli exclusion principle is enforced for the transitions amplitudes. Thus, an explicit and time-consuming treatment of these occupied bound states would then be necessary. 

The AO results may also be used for benchmark tests of simpler models. In this context we have also checked a simple non-perturbative model, the UCA. This model includes the main features of fast heavy-ion stopping, as is shown by comparison with large-scale AO results for the impact-parameter dependent electronic energy transfer. The computation of the energy loss within the UCA is much simpler and by many orders of magnitude faster than the full numerical solution of the time-dependent Schrodinger equation. 

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What have we learned from coupled-channel calculations Acknowledgements... 

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