Hyperspherical Sturmian approach for break up processes

G.GASANEO, J.M. RANDAZZO, D.M. MITNIK, L.U. ANCARANI AND F.D. COLAVECCHIA

Dublin

Conferencia; International Symposium on (e,2e), Double Photo-Ionization & Related Topics & 16th International Symposium on Polarization & Correlation in electronic & Atomic Collisions; 2011

Institute of Physics - Atomic and Molecular Interactions Group

based on the use of Sturmian functions in hyper-spherical [1] and in spherical coordinates[2]; they allow to solve scattering problems by increasing the convergencerate when calculating the scattering wave function as well as the transition amplitude.This can be achieved by providing all basis functions with the appropriatedinformation (physics) of the problem, in particular the correct asymptotic behavior[2]. In this way the expansion on the basis is restricted to the region where the?interaction? between the particles takes place.For break-up processes, we separate the total wave function as Ψ+ = Ψ0+Ψ+scwhere Ψ0 is an asymptotically prepared initial state; Ψ+sc is the scattering wavefunction (containing all the information about the collision dynamics) solution of athree-body driven Schr¨odinger equation [T 􀀀 V () 􀀀 E]Ψ+sc = 􀀀WΨ0; whereT is the kinetic energy, and where the driven term is the product of Ψ0 times theleft-out interaction W.The first purpose of this contribution is to compare spherical and hypersphericalexpansions with respect to the asymptotic ionization region. Both of them canbe used to describe break-up processes, but the latter is naturally connected tothe wavelike geometry of the scattering wave function in the ionization asymptoticregion. Furthermore, it allows for a direct extraction of break-up amplitudes forlarge values of . Results for the Temkin-Poet model for electron impact ionizationof atomic hydrogen will be shown. Convergence rates with the two basis will becompared and related to geometry and asymptotic issues.As a second contribution, we present a fragmentation/ionization S-wave modelwhich includes a long range Coulomb potential V () = 􀀀Z=. The initial stateis taken as the product of a standing spherical wave in the relative coordinate r1between the incoming particle and the center of the target and a bound state in thetarget coordinate r2; the interaction neglected in the initial channel is given by theYukawa-like potential depending on the hyper-radius  =√r21 + r22. We derived, inclosed form, the general solution for Ψ+sc with outgoing asymptotic behavior and thescattering transition amplitude. The model can be used to test numerical approachesas, e.g., the exterior complex scaling [3]. Here, we use it to test numerically theefficiency of hyperspherical Sturmian functions. All of them possess the correctoutgoing Coulombic asymptotic behavior and diagonalize not only the kinetic energybut also the Coulomb interaction 􀀀Z=. This strongly accelerates the convergencerate: only a few Sturmian functions are necessary to reproduce the analytical results.References[1] G. Gasaneo et al 2009 J. Phys. Chem. A 113 (52) 14573[2] A. L. Frapiccini et al 2010 J. Phys. B 43 101001[3] C. W. McCurdy and T. N. Rescigno 1997 Phys. Rev. A 56 R4369