1. Multiple ionization including post-collisional contributions Claudia Montanari Instituto de Astronomía y Física del Espacio Buenos Aires, Argentina

2. H + + Kr

3. 10 -18 sec projectile

4. 10 -15 sec

5. Multiple ionization data includes PCI PCI=time delayed electron emision Independent of the projectile

6. )1()(... 1 21 qN i q i q qqq N i i i q pp q N bP iii N                 Multinomial distribution Direct multiple ionization Cross section for ionization of q target electrons   dbbb P qq )(2  Independent particle model (IPM) ionization probability per electron p i (b), of the i-subshell

7. First Born )1()(... 1 21 qN i q i q qqq N i i i q pp q N bP iii N                 MultinomialdistributionCDW-EIS Angular expansion in spherical harmonics The radial Scrödinger eq. is numericallly solved initial bound final continuum states Ortogonality, asymptotic condicions T-matrix expanded in Fourier series Projectile: Hartree-Fock positive ions Miraglia & Gravielle Phys Rev A 78 (2008)

8. Multiple ionization including PCI Multinomial distribution )(... 1 21 qqqq N  i i q ( p i x 1 ) q i q N bP N              )1( qN i p ii    n F i,n = 1

9.  n F ,n = 1 n o of Auger electrons Single ionization of an electron in the subshell  F n Landers et al 2009, Phys. Rev Lett Krause & Carlson in the 60s Brünken et al 2002, Phys. Rev A Tamenori et al 2004, J. Phys. B Hikosaka et al 2004, Phys. Rev. A Hayaishi et al 2002, J.Phys. B

10. 3p -2 3s -1  n F ,n = 1 n o of Auger electrons Single ionization of an electron in the subshell  F n Landers et al 2009, Phys. Rev Lett Krause & Carlson in the 60s Brünken et al 2002, Phys. Rev A Tamenori et al 2004, J. Phys. B Hikosaka et al 2004, Phys. Rev. A Hayaishi et al 2002, J.Phys. B 3p 3s Ar PCI of valence electrons ? L-shell 0.81 0.112 0.008 0.00

11. Multiple ionization including PCI Multinomial distribution )(... 1 21 qqqq N  i i q ( p i x 1 ) q i q N bP N              )1( qN i p ii    n F i,n = 1

12. Multiple ionization including PCI Multinomial distribution )(... 1 21 qqqq N  i i q ( p i  n F i,n ) q i q N bP N              )1( qN i p ii    n F i,n = 1 P  (b)=   P PCI  i   1s  2s  …   PCI including PCI Number of total emitted electron (direct+PCI)

13. Xe Kr Ar Ne Results E= (0.1-10) MeV/amu

14. Xe Kr Ar Ne Results He 2 + B2+B2+ +2 Li 2+, Be 2 + +2 H +, He + +1 Li 3 + +3 E= (0.1-10) MeV/amu Be 3+, B 3+

15. H + + Xe

16. H + + Kr

17. He + + Kr

18. He +2 + Kr

19. H + + Ar

21. He + + Ar

22. He +2 + Ar

24. H + + Ne K-shell PCI

25. H + + Ne 2s & 2p – PCI ? Shake-off ? Carlson & Nestor (1973) Kochur et al (2006)

26. H + + Ne

28. He 2+ + Ne

30. B 2+ + Ne

31. B 2+

34. Ion effective charge for multiple ionization

35. Summary  Multiple ionization cross sections, independent particle model, multinomial distribution, CDW-EIS  PCI is included using photoionization branching ratios.  Good description of Ar, Kr and Xe targets. Overestimation of Ne in the intermediate energy region (direct ionization)  Effective ion charge for multiple ionization, lower for single than for multiple  Open questions that deserve research +Limits of the IPM?: Multinomial statistic? Importance of correlation? Changes in the target potential? Why a different answer for Ne and Kr? +Other PCI contributions in Ne, shake off? Again, why a different answer for Ne and Kr?  More experimental data is needed for different ions in gases

36. Maria Silvia Gravielle Diego Arbo Dario Mitnik Claudio Archubi Dep Physics, University of Missouri, USA Robert DuBois Instituto de Astronomia y Física del Espacio, Buenos Aires, Argentina Jorge Miraglia Universidad Federal de Rio de Janeiro, Rio de Janeiro, Brasil Eduardo Montenegro Wania Wolf Hugo Luna Antonio Santos

37. Thank you

40. Carlson & Nestor (1973) Mukoshama (1989) Kochur et al (2006)

41. He + + Xe

42. He + + Ne

47. Total ionization cross section Miraglia and Gravielle, Phys. Rev A 81 (2010) 042709