Electron correlation in multiple excitation of atoms by high-energy ions

We derive a general expression for the transition amplitude when assuming that the correlation time is much larger than the collision time. This frozen-correlation approximation provides a reference calculation without dynamic correlation, which allows, for the first time, a quantitative evaluation of the role of electron correlation during the collision in a multiple excitation process. In a close-coupling formalism, the procedure is equivalent to fixing configuration mixing during the collision while allowing one-electron orbitals to evolve in time. The variation under a change of the projectile charge sign of double excitation of He by high-energy ion impact can be explained by the weak role of dynamic correlation.