Single and double ionization of helium: a Sturmian approach*

The quantal description of three-body break-up processes is a~notoriously difficult problem, one major obstacle being the imposition of proper asymptotic boundary~conditions. In this contribution, single and double ionization of helium are investigated through a Sturmian approach in hyperspherical coordinates. A similar approach, in spherical coordinates, has been applied successfully to a number of two-electron systems (see, e.g., [1]). It is known, though, that for the three particles break-up the global asymptotic behavior (Peterkop) is best described in hyperspherical coordinates. The use of these more natural coordinates, within a Sturmian approach, provide the basis functions with more adequate outgoing asymptotic conditions [2]. In this way the scattering wave function expansion is~restricted to the region where the interaction between the particles takes place, considerably increasing the convergence rates. The application of the recently proposed hyperspherical Sturmian approach [2] is applied to ionization processes of helium. The scattering wave function and related differential cross sections will be presented.\\[4pt] [1] A. L. Frapiccini et al, J. Phys. B \textbf{43} 101001 (2010); J. M. Randazzo et al, Phys. Rev. A \textbf{84}, 052715 (2011).\\[0pt] [2] G. Gasaneo and L. U. Ancarani, J. Phys. A \textbf{45}, 045304 (2012).