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Multiple ionization including post-collisional contributions

Multiple ionization including post-collisional contributions. Claudia Montanari. Instituto de Astronomía y Física del Espacio Buenos Aires, Argentina. H + + Kr. -18. 10. sec. projectile. photon. 3+. photon. 10 -15 sec. -5. 10. sec. 6+. PCI=time delayed electron emision

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Multiple ionization including post-collisional contributions

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

  2. H+ + Kr

  3. -18 10 sec projectile

  4. photon 3+ photon 10-15 sec

  5. -5 10 sec 6+ PCI=time delayed electron emision Independent of the projectile Multiple ionization data includes PCI

  6. ò s = p 2 b P ( b ) db q q Multinomial distribution æ ö N N å Õ ç ÷ - i = - q N q P ( b ) p ( 1 p ) i i i ç ÷ q i i q è ø + + + = q q ... q i 1 i = q 1 2 N ionization probability per electron pi(b), of the i-subshell Direct multiple ionization Cross section for ionization of q target electrons Independent particle model (IPM)

  7. CDW-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 First Born æ ö N N å Õ ç ÷ - i = - q N q P ( b ) p ( 1 p ) i i i ç ÷ q i i q è ø + + + = q q ... q i 1 i = q 1 2 N Miraglia & Gravielle Phys Rev A 78 (2008) Multinomial distribution

  8. Sn Fi,n= 1 æ ö N N å Õ ç ÷ i = P ( b ) ( pix1)qi - - N q ç ÷ ( 1 p ) i i q q i è ø + + + = = q q ... q q i 1 i 1 2 N Multiple ionization including PCI Multinomial distribution

  9. no of Auger electrons Single ionization of an electron in the subshellm Fm,n SnFm,n = 1 Krause & Carlson in the 60s Landers et al 2009, Phys. Rev Lett 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. no of Auger electrons Single ionization of an electron in the subshellm Fm,n SnFm,n = 1 Ar 3p 3s 3p-2 3s-1 L-shell 0.81 0.112 0.008 0.00 0.00 Krause & Carlson in the 60s Landers et al 2009, Phys. Rev Lett Brünken et al 2002, Phys. Rev A PCI of valence electrons ? Tamenori et al 2004, J. Phys. B Hikosaka et al 2004, Phys. Rev. A Hayaishi et al 2002, J.Phys. B

  11. Sn Fi,n= 1 æ ö N N å Õ ç ÷ i = P ( b ) ( pix1)qi - - N q ç ÷ ( 1 p ) i i q q i è ø + + + = = q q ... q q i 1 i 1 2 N Multiple ionization including PCI Multinomial distribution

  12. Sn Fi,n= 1 æ ö N N å Õ ç ÷ i = P ( b ) ( pi SnFi,n)qi - - N q ç ÷ ( 1 p ) i i q q i è ø + + + = = q q ... q q i 1 i 1 2 N PCI Pa (b)= SP P PCI (ai) including PCI a1s + a2s + …= a i Number of total emitted electron (direct+PCI) Multiple ionization including PCI Multinomial distribution

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

  14. +2 Li2+, Be2+ Results E= (0.1-10) MeV/amu Xe Kr Ar Ne +1 H+,He+ +3 +2 Be3+, B3+ He2+ B2+ Li3+

  15. H+ + Xe

  16. H+ + Kr

  17. He+ + Kr

  18. He+2 + Kr

  19. H+ + Ar

  20. H+ + Ar

  21. He+ + Ar

  22. He+2 + Ar

  23. He+2 + Ar

  24. K-shell PCI H+ + Ne

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

  26. H+ + Ne

  27. H+ + Ne

  28. He2+ + Ne

  29. He2+ + Ne

  30. B2+ + Ne

  31. B2+

  32. B2+

  33. B2+

  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 neededfor different ions in gases

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

  37. Thank you

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

  39. He+ + Xe

  40. He+ + Ne

  41. He+ + Ne

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

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