Electron impact ionization--excitation of Helium.

We calculate triple differential cross sections (TDCS) for the process of ionization--excitation of Helium by fast electron impact in which the residual ion is left in the n$=$2 excited state. We chose the strongly asymmetric kinematics used in the experiment performed by Dupr\'{e} et al. [1]. In a perturbative scheme, for high projectile energies the four--body problem reduces to a three--body one [2] and, within that framework, we solve the time- independent Schr\"{o}dinger equation with a Sturmian approach [3]. The method, based on Generalized Sturmian Functions (GSF), is employed to obtain the initial ground state of Helium, the single-continuum state and the scattering wave function; for each of them, the GSF basis is constructed with the corresponding adequate asymptotic conditions. Besides, the method presents the following advantage: the scattering amplitudes can be extracted directly in the asymptotic region of the scattering solution, and thus the TDCS can be obtained without requiring a matrix element evaluation. [1] C. Dupr\'{e} et al. (1992) J. Phys. B 25, 259. [2] M.J. Ambrosio et al. (2014) Phys. Rev. A 89, 012713. [3] G. Gasaneo et al. (2013) Adv. Quantum Chem. 67, 153.