Four-body model for transfer ionization in fast ion-atom collisions

Abstract

Total cross sections for transfer ionization in fast collisions of a bare nucleus with helium are examined in the four-body distorted-wave formalism. A special emphasis is given to a proper inclusion of dynamic electron-electron correlation effects. For this purpose, the four-body continuum distorted-wave (CDW-4B) approximation with the correct boundary conditions is introduced. Along with the appropriate potential operators containing a single electron placed on one and/or both nuclear centers, accompanied by the corresponding Coulomb waves for continuum intermediate states, the dielectronic interaction ${\mathrm{V}}_{12}$=1/${\mathrm{r}}_{12}$\ensuremath{\equiv}1/|r-${\ensuremath{\rightarrow}}_{1}$-r-${\ensuremath{\rightarrow}}_{2}$| also explicitly appears in the perturbation potential of the transition probability amplitude. The inclusion of the potential ${\mathrm{V}}_{12}$ is essential for the description of the Thomas P-e-e scattering, through which one of the target electrons could be captured or ionized without ever experiencing any direct interaction with the projectile P. The total cross sections ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{if}}$ due to such a correlated CDW-4B theory are computed exactly and very efficiently by means of precise evaluation of certain seven-dimensional quadratures in momentum space. The proposed method is shown to be superior to the corresponding independent event model (CDW-IEM), which also proceeds through the same effort on multidimensional scattering integrals, but largely overestimates the measured values for ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{if}}$ . Comparisons between the present results ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{if}}$ and the available experimental data at E=30--600 keV/amu for transfer ionization in the ${\mathrm{He}}^{2+}$ -He collision yield satisfactory agreement at impact energies E\ensuremath{\geqslant}80 keV/amu. This is in full harmony with the well-known low-energy limit of the validity of the CDW-3B method assessed previously for the genuine three-body charge exchange in collisions between a fully stripped projectile and a hydrogenlike atomic target.