On the Role of Projectile Electrons in an Independent Electron Model Description of Dressed-Ion Impact on Atoms
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The presence of electrons on ions which collide with neutral atoms constitutes a challenge to theoretical descriptions of the collision dynamics. These collisions pose quantum-mechanical many-body problems that cannot be fully solved; one has to resort to approximations, such as the independent electron model (IEM), in which the N-electron problem is reduced to N single-electron problems. The time-development of a given electron is governed by the nuclear Coulomb potentials and an electronic mean-field potential formed by the other electrons. This framework is used in the present work to explore the active role of projectile electrons in collisions of dressed boron- and carbon-ions with neon atoms, as well as the seemingly simple HeHe collision system. In the present IEM description the collision problem is expressed in the form of time-dependent Schrdinger equations with a common single-electron Hamiltonian. The single-electron equations are solved numerically with a two-centre basis expansion method in which the continuum is represented by dynamically generated basis states. From these calculations single-electron transition amplitudes are obtained and many-electron quantities are computed with different statistical final-state analyses, which do or do not respect the Pauli exclusion principle. In BNe collisions transfer ionization processes that involve electrons at both centres were found to contribute to target multiple ionization coincident with an unchanged projectile charge state. Total cross sections for collision channels where the projectile charge state is changed are presented for BNe and CNe collisions. The present method reliably provides total cross sections for most collision channels, except for the loss of projectile electrons. The contributions of these collision channels to the net recoil ion production are investigated. These results are compared with those for collisions of equicharged bare helium and lithium ions with neon. In a modification of the present approach a piecewise definition of the common Hamiltonian is proposed. It ensures the correct asymptotic behaviour of the mean-field potential at large internuclear distances before the collision for active electrons of both centres. The model is applied to the HeHe collision system and compared with the (unmodified) present approach.