Projectile influence on the angular distributions in (e,3e) processes

G. GASANEO, S. OTRANTO, K.V. RODRIGUEZ AND R.H. PRATT

Buenos Aires, Argentina

Simposio; International Symposium on (e,2e), Double Photoionization and Related Topics; 2005

This work is focused on the final state dependence of the fivefold differential cross section (FDCS) for the double ionization of He by electron impact [1]. The projectile energies considered ranged from 250 eV to 5599 eV to show the departure from the Born regime. The FDCS for the (e,3e) process is defined in [1] in terms  of the transition amplitude Tfi   Tfi = áYf-|Vi|Yiñ   Here, the initial state Yi is represented by a two-electron ground state wave function times a plane wave for the projectile. In this Born approximation, the potential Vi is given by the sum of the nucleus-projectile and  bound electrons-projectile Coulomb interactions. To represent the initial state of the He atom a variational wave function introduced in [2] is used: jGRII = f [1+r23/2 e-br23 + gr232 e-dr23 ] Here, f = e-Z(r2+ r3) represents the electron-nucleus interaction and the bracket the electron-electron interaction. jGRII exactly satisfies the Kato cusp conditions at each of the two-body coalescence and gives a mean binding energy EGRII = -2.87933 a.u., close to the angular correlation limit. The final state wave function Yf- is represented by the product of a Coulomb wave function for the projectile-nucleus and a C3 function for the He subsystem. All the Sommerfeld parameters included in the functions are written in terms off effective charges [2]. In Fig. 1 a projectile of 250 eV is scattered at 3° and two electrons are ejected with an energy of 10 eV each. One of the electrons is measured at 180°. The FDCS is evaluated as a function of the angle of the second ejected electron. Our model is compared with the Born-C3 approach for the final channel. As we can see, the interaction with the projectile strongly modifies the distribution as compared with the Born-C3 model. This effect is observed for different ejected angles and different projectiles energies.   Figure1: FDCS for the (e,3e) process in atomic units.   The present model includes the emitted electrons-receding projectile interaction which is important at intermediate impact energies. On the other hand, the Born limit is naturally recovered as the impact energy is increased. New experimental data are necessary to evaluate the quality of the final channel model here discussed. This work has been supported by PICTR 2003/0437 of the ANPCYT (Argentina).   References [1] J. Berakdar et al, Phys. Rep. 374, 91 (2003) [2] G. Gasaneo, S. Otranto and K. V. Rodriguez, submitted to J. Phys. B (2005)