Technique for the evaluation of double excitation of atoms by fast charged particles

A technique for evaluating cross sections for two-electron excitation in collisions of atoms with fast particles of charge Zp is presented. The atomic wave function is approximated by a sum of pair products of one-electron wave functions, with the coefficients chosen by diagonalizing the fully correlated two-electron Hamiltonian. Thus spatial correlation is included in both the asymptotic and scattering regions by using these configuration-interaction (CI) wave functions for initial, intermediate, and final states. Use of CI wave function also allows the first-order contributions to be expressed in closed, analytical form. Both the energy-conserving and energy-nonconserving parts of the second-order amplitude are evaluated. The former (a correlated generalization of the independent-electron approximation) is analytical and the latter is a one-dimensional integral. In helium it is found that the double-excitation cross sections are sensitive to the sign of the projectile charge, but that the energy region where this sensitivity is of the same order as for double ionization is 0.1 to 0.5 MeV/amu, whereas the latter has peak charge sensitivity at 1.5 MeV/amu. Comparison is made with some experimental results