Abstract
An hyperspherical Sturmian approach recently developed for three-body break-up processes is presented. To test several of its features, the method is applied to two simplified models. Excellent agreement is found when compared with the results of an analytically solvable problem. For the Temkin-Poet model of the double ionization of He by high energy electron impact, the present method is compared with the Spherical Sturmian approach, and again excellent agreement is found. Finally, a study of the channels appearing in the break-up three-body wave function is presented.
Highlights
The incorporation of appropriate boundary conditions on break–up three–body problems is a very difficult task
By choosing a short range generating potential, all hyperradial Sturmian functions will possess the same asymptotic behavior dictated by the long range behavior of the auxiliary potential (outgoing behavior is taken in Eq (6))
Before tackling the full double ionization problem, we wanted to make sure that all developed numerical tools were working properly and proceeded in the following way
Summary
The incorporation of appropriate boundary conditions on break–up three–body problems is a very difficult task. Like the convergent close–coupling [1] or the J–Matrix [2] methods, impose the boundary conditions explicitly Other approaches, such as the exterior complex scaling [3] or the Generalized Sturmian Functions (GSF) [4] approach, circumvent an explicit imposition. It turns out that this generates for the scattering wave function an overall hyperspherical outgoing asymptotic shape Even though this is the expected behavior for a three–body collision problem, it is not completely clear how this front is generated. In order to do so, and to identify the advantages of each, we have used the Generalized Sturmian approach in both systems of coordinates (for a review see [4] and [5]) It consists of a spectral method with the essential feature that the asymptotic behavior can be explicitly imposed on the basis functions. By choosing a short range generating potential, all hyperradial Sturmian functions will possess the same asymptotic behavior dictated by the long range behavior of the auxiliary potential (outgoing behavior is taken in Eq (6))
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
