Skip to main content
SpringerLink
Log in

Review of theories on double electron capture in fast ion-atom collisions

  • Review Paper
  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Abstract

This work reviews quantum-mechanical four-body distorted wave theories for double electron capture in collisions between fast heavy multiply charged ions and heliumlike atomic systems. The widely used distorted wave methods of the first- and second-order in the pertinent perturbation series expansions are compared with each other. This tests the presumed importance of double continuum intermediate states of two electrons. Further, the relative performance is evaluated of the second-order theories with and without the eikonalization of the two-electron Coulomb wave functions for double continuum intermediate states. This checks the correctness and usefulness of the eikonalized Coulomb waves when two electrons participate actively to the transition from the initial to the final state of the entire system. We also analyze the significance of the contributions from excited heliumlike states especially in comparison between theory and measurement. The overall goal of the present study is to determine how much of the unprecedented experience gained over several decades in studying high-energy theories of pure three-body charge exchange could be exported directly to four-body double-electron capture without much of additional and essential eleaborations, besides the naturally increased computational demand. In particular, we address the unexpected breakdown of the continuum distorted wave eikonal initial state approximation and the anticipated success of continuum distorted wave theory for double charge exchange in ion-atom collisions at high impact energies.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Belkić Dž.: Principles of quantum scattering theory. Institute of Physics Publishing, Bristol (2004)

    Book  Google Scholar 

  2. Belkić Dž.: Quantum theory of high-energy ion-atom collisions. Taylor and Francis, London (2008)

    Book  Google Scholar 

  3. Belkić Dž., Mančev I., Hanssen J.: Rev. Mod. Phys. 80, 249–314 (2008)

    Article  CAS  Google Scholar 

  4. Belkić Dž.: Adv. Quantum Chem. 56, 251–321 (2009)

    Article  CAS  Google Scholar 

  5. Belkić Dž.: Phys. Rev. A 47, 3824–3844 (1993)

    Article  Google Scholar 

  6. Martínez A.E., Rivarola R.D., Gayet R., Hanssen J.: Phys. Scr. T 80, 124–127 (1999)

    Article  Google Scholar 

  7. Belkić Dž., Mančev I.: Phys. Scr. 45, 35–42 (1992)

    Article  Google Scholar 

  8. Belkić Dž., Gayet R., Salin A.: Phys. Rep. 56, 279–369 (1979)

    Article  Google Scholar 

  9. Bransden B.H., Dewangan D.P.: Adv. Atomic Mol. Opt. Phys. 25, 343–374 (1988)

    CAS  Google Scholar 

  10. B.H. Bransden, M.R.C. McDowell, Charge exchange and the theory of ion-atom collisions. The international series of monographs in physics (Clarendon, Oxford 1992)

  11. Crothers D.S.F., Dubé L.J.: Adv. Atomic Mol. Opt. Phys. 30, 287–337 (1993)

    Article  CAS  Google Scholar 

  12. Dewangan D.P., Eichler J.: Phys. Rep. 247, 59–219 (1994)

    Article  CAS  Google Scholar 

  13. Belkić Dž.: J. Comput. Meth. Sci. Eng. 1, 1–74 (2001)

    Google Scholar 

  14. Bransden B.H., Joachain C.J.: Physics of atoms and molecules, 2nd edn. Prentice Hall, New York (2003)

    Google Scholar 

  15. Crothers D.S.F., McCann J.F.: J. Phys. B 16, 3229–3242 (1983)

    Article  CAS  Google Scholar 

  16. Fainstein P.D., Ponce V.H., Rivarola R.D.: J. Phys. B 24, 3091–3119 (1991)

    Article  CAS  Google Scholar 

  17. Stolterfoht N., DuBois R., Rivarola R.D.: Electron emission in heavy ion-atom collisions. Springer, Berlin (1997)

    Google Scholar 

  18. Cheshire I.M.: Proc. Phys. Soc. 84, 89–98 (1964)

    Article  CAS  Google Scholar 

  19. Belkić Dž.: J. Phys. B 11, 3529–3552 (1978)

    Article  Google Scholar 

  20. Crothers D.S.F.: J. Phys. B 15, 2061–2074 (1982)

    Article  CAS  Google Scholar 

  21. Belkić Dž.: Nucl. Inst. Meth. Phys. Res. B 86, 62–81 (1994)

    Article  Google Scholar 

  22. Belkić Dž., Mančev I., Mudrinić M.: Phys. Rev. A 49, 3646–3658 (1994)

    Article  Google Scholar 

  23. Dodd L.R., Greider K.R.: Phys. Rev. 146, 675–686 (1966)

    Article  CAS  Google Scholar 

  24. McCann J.F.: J. Phys. B 25, 449–461 (1992)

    Article  CAS  Google Scholar 

  25. Pedlow R.T., O’Rourke S.F.C., Crothers D.S.F.: Phys. Rev. A 72, 062719 (2005)

    Article  CAS  Google Scholar 

  26. Belkić Dž., Salin A.: J. Phys. B 9, L397–L402 (1976)

    Article  Google Scholar 

  27. Belkić Dž., Salin A.: J. Phys. B 11, 3905–3911 (1978)

    Article  Google Scholar 

  28. Rivarola R.D., Piacentini R.D., Salin A., Belkić Dž.: J. Phys. B 13, 2601–2609 (1980)

    Article  CAS  Google Scholar 

  29. Belkić Dž.: Phys. Rev. A 37, 55–67 (1988)

    Article  Google Scholar 

  30. Abramowitz M., Stegun I.: Handbook of mathematical functions. Dover, New York (1956)

    Google Scholar 

  31. Press W., Teukolsky S., Vetterling W., Flannery B.: Numerical recipes in Fortran 77: the art of scientific computing. Cambridge University Press, Cambridge (1992)

    Google Scholar 

  32. Thomas L.H.: Proc. R. Soc. Lond. A 114, 561–576 (1927)

    Article  CAS  Google Scholar 

  33. Salin A.: J. Phys. B 3, 937–951 (1970)

    Article  CAS  Google Scholar 

  34. Belkić Dž., Janev R.: J. Phys. B 6, 1020–1027 (1973)

    Article  Google Scholar 

  35. Belkić Dž., Janev R.K.: J. Phys. B 6, 2613–2617 (1973)

    Article  Google Scholar 

  36. Belkić Dž., Gayet R.: J. Phys. B 10, 1911–1921 (1977)

    Article  Google Scholar 

  37. Belkić Dž., Gayet R.: J. Phys. B 10, 1923–1932 (1977)

    Article  Google Scholar 

  38. Belkić Dž., McCarroll R.: J. Phys. B 10, 1933–1943 (1977)

    Article  Google Scholar 

  39. Banyard K.E., Szuster B.: J. Phys. B 10, L503–L511 (1977)

    Article  CAS  Google Scholar 

  40. Banyard K.E., Szuster B.: Phys. Rev. A 16, 129–132 (1977)

    Article  CAS  Google Scholar 

  41. Moore J.C., Banyard K.E.: J. Phys. B 11, 1613–1621 (1978)

    Article  CAS  Google Scholar 

  42. Banyard K.E., Shirtcliffe G.W.: J. Phys. B 12, 3247–3256 (1979)

    Article  CAS  Google Scholar 

  43. Shirtcliffe G.W., Banyard K.E.: Phys. Rev. A 21, 1197–1201 (1980)

    Article  CAS  Google Scholar 

  44. Banyard K.E., Shirtcliffe G.W.: Phys. Rev. A 22, 1452–1454 (1980)

    Article  CAS  Google Scholar 

  45. Belkić Dž., Gayet R., Salin A.: Comput. Phys. Commun. 23, 153–167 (1981)

    Article  Google Scholar 

  46. Belkić Dž., Gayet R., Salin A.: Comput. Phys. Commun. 30, 193–205 (1983)

    Article  Google Scholar 

  47. Belkić Dž., Gayet R., Salin A.: Comput. Phys. Commun. 32, 385–397 (1984)

    Article  Google Scholar 

  48. Chetioui A., Wohrer K., Rozet J.P., Joly A., Stephan C., Belkić Dž., Gayet R., Salin A.: J. Phys. B 16, 3993–4003 (1983)

    Article  CAS  Google Scholar 

  49. Andriamonje S., Chemin J.F., Routier J., Saboya B., Scheurer J.N., Belkić Dž., Gayet R., Salin A.: J. Physique 46, 349–353 (1985)

    Article  CAS  Google Scholar 

  50. Belkić Dž.: Phys. Scr. 43, 561–571 (1991)

    Article  Google Scholar 

  51. Belkić Dž., Gayet R., Salin A.: Atomic Data Nucl. Data Tables 51, 59–150 (1992)

    Article  Google Scholar 

  52. Kunikeev S.D.: J. Phys. B 31, L849–L853 (1998)

    Article  CAS  Google Scholar 

  53. Ferreira da Silva M.F.: J. Phys. B 36, 2357–2370 (2003)

    Article  CAS  Google Scholar 

  54. Mančev I.: J. Phys. B 36, 93–104 (2003)

    Article  Google Scholar 

  55. Mančev I., Mergel V., Schmidt L.: J. Phys. B 36, 2733–2746 (2003)

    Article  Google Scholar 

  56. Mančev I.: J. Comput. Meth. Sci. Eng. 5, 73–89 (2005)

    Google Scholar 

  57. Mančev I.: Europhys. Lett. 69, 200–206 (2005)

    Article  CAS  Google Scholar 

  58. Dž. Belkić, J. Phys. B 10, 3491–3510 (1977) [Corrigendum: Dž. Belkić, J. Phys. B 12, 337 (1979)]

  59. Purkait M.: Eur. Phys. J. D 30, 11–14 (2004)

    Article  CAS  Google Scholar 

  60. Purkait M., Sounda S., Dhara A., Mandal C.R.: Phys. Rev. A 74, 042723 (2006)

    Article  CAS  Google Scholar 

  61. Belkić Dž., Gayet R., Hanssen J., Salin A.: J. Phys. B 19, 2945–2953 (1986)

    Article  Google Scholar 

  62. Belkić Dž., Saini S., Taylor H.S.: Z. Phys. D 3, 59–76 (1986)

    Article  Google Scholar 

  63. Belkić Dž., Saini S., Taylor H.S.: Phys. Rev. A 36, 1601–1617 (1987)

    Article  Google Scholar 

  64. Belkić Dž., Taylor H.S.: Phys. Rev. A 35, 1991–2006 (1987)

    Article  Google Scholar 

  65. Dewangan D.P., Eichler J.: J. Phys. B 19, 2939–2944 (1986)

    Article  CAS  Google Scholar 

  66. Belkić Dž.: Phys. Scr. T 28, 106–111 (1989)

    Article  Google Scholar 

  67. Grozdanov T.P., Krstić P.S.: Phys. Scr. 38, 32–36 (1988)

    Article  CAS  Google Scholar 

  68. Alston S.: Phys. Rev. A 41, 1705–1708 (1990)

    Article  CAS  Google Scholar 

  69. Belkić Dž.: Phys. Rev. A 47, 189–200 (1993)

    Article  Google Scholar 

  70. Belkić Dž.: J. Phys. B 26, 497–508 (1993)

    Article  Google Scholar 

  71. Gulyás L., Szabo Gy.: Z. Phys. D 29, 115–119 (1994)

    Article  Google Scholar 

  72. Hylleraas E.A.: Z. Phys. 54, 347–366 (1929)

    Article  CAS  Google Scholar 

  73. Silverman J., Platas O., Matsen F.A.: J. Chem. Phys. 32, 1402–1406 (1960)

    Article  CAS  Google Scholar 

  74. Green L.C., Mulder M.M., Lewis M.N., Woll J.W. Jr.: Phys. Rev. 93, 757–761 (1954)

    Article  CAS  Google Scholar 

  75. Löwdin P.-O.: Phys. Rev. 90, 120–125 (1953)

    Article  Google Scholar 

  76. Belkić Dž., Mančev I.: Phys. Scr. 46, 18–23 (1993)

    Article  Google Scholar 

  77. Lin C.D.: Phys. Rev. A 19, 1510–1516 (1979)

    Article  CAS  Google Scholar 

  78. Gerasimenko V.I.: J. Exp. Theor. Phys. 14, 789–791 (1962)

    Google Scholar 

  79. Gerasimenko V.I.: Zh. Eksp. Teor. Fiz. 41, 1104–1106 (1961)

    CAS  Google Scholar 

  80. Schryber U.: Helv. Phys. Acta 40, 1023–1051 (1967)

    CAS  Google Scholar 

  81. Toburen L.H., Nakai M.Y.: Phys. Rev. 177, 191–196 (1969)

    Article  CAS  Google Scholar 

  82. Fogel’ Y.M., Mitin R.V., Kozlov V.F., Romashko N.D.: J. Exp. Theor. Phys. 8, 390–398 (1959)

    Google Scholar 

  83. Fogel’ Y.M., Mitin R.V., Kozlov V.F., Romashko N.D.: Zh. Eksp. Teor. Fiz. 35, 565–573 (1958)

    Google Scholar 

  84. Williams J.F.: Phys. Rev. A 150, 7–10 (1966)

    Article  CAS  Google Scholar 

  85. Schuch R., Justiniano E., Vogt H., Deco G., Grün N.: J. Phys. B 24, L133–L138 (1991)

    Article  CAS  Google Scholar 

  86. Pivovar L.I., Novikov M.T., Tubaev V.M.: J. Exp. Theor. Phys. 15, 1035–1039 (1962)

    Google Scholar 

  87. Pivovar L.I., Novikov M.T., Tubaev V.M.: Zh. Eksp. Teor. Fiz. 42, 1490–1494 (1962)

    CAS  Google Scholar 

  88. E.W. McDaniel, M.R. Flannery, H.W. Ellis, F.L. Eisele, W. Pope, US Army Missile Research and Development command technical report, No. H, 1, 78 (1977)

  89. DuBois R.D.: Phys. Rev. A 36, 2585–2593 (1987)

    Article  CAS  Google Scholar 

  90. Castro Faria N.V., Freire F.L. Jr., Pinho A.G.: Phys. Rev. A 37, 280–283 (1988)

    Article  Google Scholar 

  91. Berkner K.H., Pyle R.V., Stearns J.W., Warren J.C.: Phys. Rev. 166, 44–46 (1968)

    Article  CAS  Google Scholar 

  92. Gerasimenko V.I., Rosentsveig L.N.: J. Exp. Theor. Phys. 4, 509–512 (1957)

    CAS  Google Scholar 

  93. Gerasimenko V.I., Rosentsveig L.N.: Zh. Eksp. Teor. Fiz. 31, 684–687 (1956)

    CAS  Google Scholar 

  94. Gravielle M.S., Miraglia J.E.: Phys. Rev. A 45, 2965–2973 (1992)

    Article  CAS  Google Scholar 

  95. Belkić Dž.: Nucl. Instr. Meth. Phys. Res. B 99, 218–224 (1995)

    Article  Google Scholar 

  96. Belkić Dž.: Phys. Scr. 53, 414–430 (1996)

    Article  Google Scholar 

  97. Belkić Dž.: Nucl. Instr. Meth. Phys. Res. B 154, 220–246 (1999)

    Article  Google Scholar 

  98. Mergel V., Dörner R., Achler M., Khayyat K., Lencinas S., Euler J., Jagutzki O., Nüttgens S., Unverzagt M., Spielberger L., Wu W., Ali R., Ullrich J., Cederquist H., Salin A., Wood C., Olson R.E., Belkić Dž., Cocke C.L., Schmidt-Böcking H.: Phys. Rev. Lett. 79, 387–390 (1997)

    Article  CAS  Google Scholar 

  99. Shah M.B., Gilbody H.B.: J. Phys. B 18, 899–913 (1985)

    Article  CAS  Google Scholar 

  100. Gayet R., Hanssen J., Martínez A., Rivarola R.: Comments Atomic Mol. Phys. 30, 231–248 (1994)

    Google Scholar 

  101. Martínez A.E., Gayet R., Hanssen J., Rivarola R.D.: J. Phys. B 27, L375–L382 (1994)

    Article  Google Scholar 

  102. Martínez A.E., Busnengo H.F., Gayet R., Hanssen J., Rivarola R.D.: Nucl. Instr. Meth. Phys. Res. B 132, 344–349 (1997)

    Article  Google Scholar 

  103. Gayet R., Hanssen J., Martínez A., Rivarola R.: Z. Phys. D 18, 345–350 (1991)

    Article  CAS  Google Scholar 

  104. Deco G., Grün N.: Z. Phys. D 18, 339–343 (1991)

    Article  CAS  Google Scholar 

  105. Roothaan C.C.J.: Rev. Mod. Phys. 23, 69–89 (1951)

    Article  CAS  Google Scholar 

  106. Roothaan C.C.J.: Rev. Mod. Phys. 32, 179–185 (1960)

    Article  Google Scholar 

  107. Huzinaga S.: Rev. Phys. 122, 131–138 (1961)

    Article  Google Scholar 

  108. Clementi E., Roetti C.: Atomic Data Nucl. Data Tables 14, 177–478 (1974)

    Article  CAS  Google Scholar 

  109. Crothers D.S.F., McCarroll R.: J. Phys. B 20, 2835–2842 (1987)

    Article  CAS  Google Scholar 

  110. Pluvinage P.: Ann. Phys. NY 5, 145–152 (1950)

    CAS  Google Scholar 

  111. Pluvinage P.: J. Phys. Radium 12, 789–792 (1951)

    Article  CAS  Google Scholar 

  112. Bachau H.: J. Phys. B 17, 1771–1784 (1984)

    Article  CAS  Google Scholar 

  113. Gayet R., Hanssen J., Jacqui L., Martínez A., Rivarola R.: Phys. Scr. 53, 549–556 (1996)

    Article  CAS  Google Scholar 

  114. Nordsieck A.: Phys. Rev. 93, 785–787 (1954)

    Article  CAS  Google Scholar 

  115. Belkić Dž.: J. Phys. B 14, 1907–1914 (1981)

    Article  Google Scholar 

  116. Belkić Dž: J. Phys. B 16, 2773–2784 (1983)

    Article  Google Scholar 

  117. Belkić Dž.: J. Phys. B 17, 3629–3636 (1984)

    Article  Google Scholar 

  118. Belkić Dž., Lazur V.Y.: Z. Phys. A 319, 261–267 (1984)

    Article  Google Scholar 

  119. Belkić Dž., Taylor H.S.: Phys. Scr. 39, 226–229 (1989)

    Article  Google Scholar 

  120. Belkić Dž.: Phys. Scr. 45, 9–17 (1992)

    Article  Google Scholar 

  121. Gayet R., Hanssen J., Martínez A., Rivarola R.: Nucl. Instr. Meth. Phys. Res. B 86, 158–160 (1994)

    Article  CAS  Google Scholar 

  122. Hippler R., Datz S., Miller P., Pepmiler P., Dittner P.: Phys. Rev. A 35, 585–590 (1987)

    Article  CAS  Google Scholar 

  123. Byron F.W. Jr., Joachain C.J.: Phys. Rev. Lett. 16, 1139–1142 (1966)

    Article  Google Scholar 

  124. Joachain C.J., Vanderpoorten R.: Physica 46, 333–343 (1970)

    Article  CAS  Google Scholar 

  125. Tweed R.J.: J. Phys. B 5, 810–819 (1972)

    Article  CAS  Google Scholar 

  126. C.J. Joachain, M. Terao, Private communication (1991)

  127. Belkić Dž.: Nucl. Instr. Meth. Phys. Res. B 124, 365–376 (1997)

    Article  Google Scholar 

  128. Belkić Dž.: J. Phys. B 30, 1731–1745 (1997)

    Article  Google Scholar 

  129. Lepage G.P.: J. Comput. Phys. 27, 192–203 (1978)

    Article  Google Scholar 

  130. Kawabata S.: Comput. Phys. Commun. 41, 127–153 (1986)

    Article  CAS  Google Scholar 

  131. Kawabata S.: Comput. Phys. Commun. 41, 309–326 (1995)

    Article  Google Scholar 

  132. Dörner R., Mergel V., Spielberger L., Jagutzki O., Schmidt-Böcking H., Ullrich J.: Phys. Rev. A 57, 312–317 (1998)

    Article  Google Scholar 

  133. Dörner R., Mergel V., Jagutzki O., Spielberger L., Ullrich J., Moshammer R., Schmidt-Böcking H.: Phys. Rep. 330, 95–192 (2000)

    Article  Google Scholar 

  134. R. Dörner, Private communication (2005)

Download references

Author information

Authors and Affiliations

  1. Karolinska Institute, P.O. Box 260, 171 76, Stockholm, Sweden

    Dževad Belkić

Authors
  1. Dževad Belkić
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dževad Belkić.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Belkić, D. Review of theories on double electron capture in fast ion-atom collisions. J Math Chem 47, 1420–1467 (2010). https://doi.org/10.1007/s10910-010-9663-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-010-9663-9

Keywords

Search

Navigation