Ionization-excitation of Helium by Fast Electrons Using Generalized Sturmian Functions

I. A. GOMEZ, ; AMBROSIO M. J.; D. M. MITNIK; G. GASANEO; L. U. ANCARANI

Frankfurt

Conferencia; 12th European Conference on Atoms Molecules and Photons; 2016

In recent years the ionization?excitation process of Helium by fast electron impact has provided great challengesboth for experimentalists and for theoreticians. In spite of significant advances in the understanding of thisstrongly correlated process, important discrepancies between the experimental data and theoretical calculationsstill can not be explained satisfactorily.Recently the Generalized Sturmian Functions (GSF) method [1,2] helped towards resolving the controversy[3] for the Helium (e,3e) process in the fast projectile and small momentum transfer regimes [4,5], presentingfully differential cross sections in complete agreement with those obtained by the Convergent Close Coupling [6]approach. This led us to explore other kinematic conditions.In this contribution, we calculate the triply differential cross section (TDCS) of ionization?excitation of Heliumin the strongly asymmetric kinematics used in the experiment performed by Dupre´ et al. [7] leaving the residualion in the n = 2 excited state. In their coplanar experiment, the scattered electron energy was fixed at 5.5 keVand the values of the ejected electron energy were 5, 10, or 75 eV, with scattering angles 0.35◦, 0.32◦and 1◦,respectively. In these kinematics, the amount of momentum transferred to the target is very small (large impactparameter), meaning that the dipolar or quasiphoton limit is approached.The accurate solution of the corresponding four?body Schrodinger equation remains a formidable task from a ¨numerical point of view. However, in the high-energy regime it is possible to reduce this problem to a three?bodyone, by keeping the first order of a series expansion of the exact solution. In previous works, we have shown thatthe three?body equivalent problem for the (e,3e) ionization can be described by the time?independent Schrodinger ¨equation [5,8,9]:[Ea −hHe]Φ+sc(r2, r3) = 4πq21(2π)3−2+eiq·r2 +eiq·r3Φi(r2, r3). (1)Here the wave function Φ+sc(r2, r3) dictates the ionized electron dynamics, while Φi(r2, r3) is the 1s2state of He,with Hamiltonian hHe, Ea is the energy of the ejected electrons and q is the momentum transferred to the target bythe projectile. In order to calculate the wave function of the ground state of Helium, the single?continuum stateand the scattering wave function, we use GSFs basis sets generated with their respective, adequate, asymptoticconditions. Thereafter, as it is typical of the GSF methodology, scattering amplitudes can be extracted directlyfrom the asymptotic limit of each partial wave and, finally, TDCSs are calculated without requiring a matrixelement evaluation.References[1] G. Gasaneo, L.U. Ancarani, D.M. Mitnik, J.M. Randazzo, A.L. Frapiccini and F.D. Colavecchia, Three-Body Coulomb Problems withGeneralized Sturmian Functions, Adv. Quantum Chem. 67, 153 (2013).[2] D.M. Mitnik, F.D. Colavecchia, G. Gasaneo and J.M. Randazzo, Computational Methods for Generalized Sturmians Basis, Comp. Phys.Comm. 45, 1145 (2011).[3] L.U. Ancarani, C. Dal Cappello and G. Gasaneo, Double Ionization of Two?Electron Systems, J. Phys.: Conf. Ser. 212, 012025 (2010).[4] M.J. Ambrosio, F.D. Colavecchia, D.M. Mitnik and G. Gasaneo, Discrepancy Between Theory and Experiment in Double Ionization ofHelium by Fast Electrons, Phys. Rev. A 91, 012704 (2015).[5] M.J. Ambrosio, F.D. Colavecchia, G. Gasaneo, D.M. Mitnik, and L.U. Ancarani Double ionization of helium by fast electrons with theGeneralized Sturmian Functions method, J. Phys. B 48, 055204 (2015).[6] A. Kheifets, I. Bray, L. Bennani, A. Duguet and I. Taouil, A comparative experimental and theoretical investigation of the electron-impactdouble ionization of He in the keV regime, J. Phys. B 32 5047 (1999).[7] C. Dupre, A. Lahmam-Bennani, A. Duguet, F. Mota-Furtado, P.F. O?Mahony and C. Dal Cappello, ´ (e,2e) Triple Differential Cross Sectionsfor the Simultaneous Ionization and Excitation of Helium, J. Phys. B 25, 259 (1992).[8] G. Gasaneo, D.M. Mitnik, J.M. Randazzo, L.U. Ancarani and F.D. Colavecchia, S-Model Calculations for High?Energy?Electron?ImpactDouble Ionization of Helium, Phys. Rev. A 87, 042707 (2013).[9] M.J. Ambrosio, G. Gasaneo and F.D. Colavecchia, Insights From the Zero?Ang