What do electrons dance before the break-up in transfer-ionization?

The transfer-ionization process offers a unique opportunity to reveal tiny details of radial and angular electron correlation in the ground states of atomic systems. We report a theoretical analysis and calculations for fully differential cross sections for the transfer ionization process. $$ {\rm Z^{q+} + He \rightarrow Z^{(q-1)+} + He^{2+} + e^-}. $$ The theoretical model includes both the first and second order terms on projectile-target interaction. The wavefunction for the ground state of helium was calculated in the multiconfigurational Hartree-Fock approximation (MCHF). Results of our calculations for different collision geometries demonstrate a clear target dependency and we thus conclude that the two- electron processes in fast transfer ionization reactions occur mainly due initial state correlations and post collision electron correlations have only a minor influence on the final- state momentum pattern. It terms of a Hartree-Fock description of the helium ground state we have shown that terms other than the (ns$^2$) give the dominant contributions to the transfer ionization fully differential cross section. We have, we believe, demonstrated conclusively that the mechanism proposed by Schmidt-Bocking does indeed give the dominant contribution to the transfer-ionization process. Both theory and experiment are now in good accord and indicate that transfer ionization in fast collisions at small scattering angles is very sensitive to high-level target correlation effects. \\ 1. A.L. Godunov, Colm T. Whelan and H.R.J. Walters, {\it J. Phys. B:} {\bf 37}, L201 (2004)\\ 2. A.L. Godunov, Colm T. Whelan and H.R.J. Walters et al, {\it Phys. Rev.} A (2005) (submitted)\\ 3. M. Sch\"offler, A.L. Godunov, Colm T. Whelan, et al {\it J. Phys. B:} (2005) (submitted)