The Quasi-Molecular Model of Atomic Collisions

  • William Lichten


My mentor, Robert S. Mulliken, once said to me, “Molecules are just like a puzzle. They may seem hard to understand, but if you just think about them, you can always solve the problem.” Can we be as confident about atomic collisions? Considering the progress we have made in the past dozen years, the answer seems to be yes.


Molecular Orbital Exit Channel Atomic Collision Positron Formation Separate Atom 
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  1. 1.
    W. Brandt and R. Laubert, Phys. Rev. Letters 24, 1037 (1970).ADSCrossRefGoogle Scholar
  2. 2.
    It is questionable whether the concept of diabatic states can be applied to level crossings in which there is a change in angular momentum (o-7, 7–6, etc.) The author is not aware of any such set of diabatic states.Google Scholar
  3. 3.
    J.E. Bayfield, accompanying article, p. 397.Google Scholar
  4. 4.
    D.R. Bates and R.H.G. Reid, in Advances in Atomic and Molecular Physics 4, 13 (1968); D.R. Bates, K. Ledsham and A.L. Stewart, Phil. Trans. Roy. Soc. (Lond) 246, 215 (1953).MathSciNetMATHGoogle Scholar
  5. 5.
    G.J. Lockwood and E. Everhart, Phys. Rev. 125, 567 (1962).ADSCrossRefGoogle Scholar
  6. 6.
    F.P. Ziemba and E. Everhart, Phys. Rev. Letters 2, 299 (1959).ADSCrossRefGoogle Scholar
  7. 7.
    D.R. Bates and D.A. Williams, Proc. Phys. Soc. (London) 83, 425 (1964).ADSCrossRefGoogle Scholar
  8. 8.
    F. Hund, Z. Physik 40, 742 (1927); R.S. Mulliken, Phys. Rev. 32, 186 (1928).CrossRefGoogle Scholar
  9. 9.
    H. Rosenthal, Phys. Rev. Letters 27, 635 (1971).CrossRefGoogle Scholar
  10. 10.
    R.F. Stebbings, R.A. Young, C.L. Oxley, and H. Ehrhardt, Phys. Rev. 138, A1312 (1965).ADSCrossRefGoogle Scholar
  11. 11.
    J.E. Bayfield, Phys. Rev. 185, 105 (1969).ADSCrossRefGoogle Scholar
  12. 12.
    M.C. Chidichimo-Frank and R.D. Piacentini, J. Phys. B: Atom. Molec. Phys. 7, 548 (1974).ADSCrossRefGoogle Scholar
  13. 13.
    J.C. Houver, J. Fayeton, M. Abignoli, and M. Barat, Phys. Rev. Letters 28, 1433 (1972); also J.C. Houver, J. Fayeton and M. Barat, Proc. VIII International Conference on the Phys. of Electronic and Atomic Collisions, Belgrade (1973), p. 759; also M. Barat (private communication).Google Scholar
  14. 14.
    V. SethuRaman, W.R. Thorson and C.F. Lebeda, Phys. Rev. A 8, 1316 (1973). References to several earlier papers by Thorson et al. are given here.Google Scholar
  15. 15.
    M.E. Rudd, C.A. Sautter and C.L. Bailey, Phys. Rev. 151, 20 (1966); G.B. Crooks and M.E. Rudd, Phys. Rev. A 3, 1628 (1971).CrossRefGoogle Scholar
  16. 16.
    N. Stolterfoht, Z. Phys. 248, 81 (1971).ADSCrossRefGoogle Scholar
  17. 17.
    W.J.B. Oldham, Jr., Phys. Rev. 140, A1477 (1965); 161, 1 (1967). See also A. Salin,,J. Phys. B, Atom. Molec. Phys. 2, 631 (1969); J. Macek, Phys. Rev. A 1, 235 (1970) and T.F.M. Bonsen and D. Banks, J. Phys. B, Atom. Molec. Phys. 4, 706 (1971).Google Scholar
  18. 18.
    Y.B. Band (preprint).Google Scholar
  19. 19.
    W. Lichten, Phys. Rev. 131, 229–238 (1963).ADSCrossRefGoogle Scholar
  20. 20.
    R.P. Marchi and Felix Smith, Phys. Rev. 139, A1025 (1965).ADSCrossRefGoogle Scholar
  21. 21.
    F.T. Smith, D.C. Lorents, W. Aberth and R.P. Marchi, Phys. Rev. Letters 15, 742 (1965).ADSCrossRefGoogle Scholar
  22. 22.
    H. Rosenthal and H. Foley, Phys. Rev. Letters 23, 1480 (1969). H. Rosenthal, Phys. Rev. A 4, 1030 (1971).Google Scholar
  23. 23.
    J.N. Bardsley, Phys. Rev. A 3, 1317 (1971).ADSCrossRefGoogle Scholar
  24. 24.
    W.C. Keever and E. Everhart, Phys. Rev. 150, 43 (1966).ADSCrossRefGoogle Scholar
  25. 25.
    M. Lipeles, R. Novick, and N. Tolk, Phys. Rev. Letters 15, 815 (1965); S. Dworetsky, R. Novick, W.W. Smith, and N. Tolk, Phys. Rev. Letters 18, 939 (1967). See also references 22 and 38 for listing of references.Google Scholar
  26. 26.
    M. Barat, D. Dhuicq. R. Francois, R. McCarroll, R.D. Piacentini, A. Salin, J. Phys. B 5, 1343 (1972).ADSCrossRefGoogle Scholar
  27. 27.
    R. McCarroll and R.D. Piacentini, J. Phys. B 4, 1026 (1971).ADSCrossRefGoogle Scholar
  28. 28.
    F.T. Smith, Phys. Rev. 179, 111 (1969).ADSCrossRefGoogle Scholar
  29. 29.
    B.A. Lippman and T.F. O’Malley, Phys. Rev. A 2, 2115 (1970); T.F. O’Malley, Phys. Rev. 150, 14 (1966); 162 98 (1967); T.F. O’Malley and H.S. Taylor, ibid, 176 207 (1968); V. Sidis and H. LeFebvre-Brion, J. Phys. B, Atom. Molec. Phys. 4, 1040 (1971); B. Andresen and S.E. Nielsen, Mol. Phys. 21, 523 (1971).Google Scholar
  30. 30.
    H. Gabriel and K. Taulbjerg, Phys. Rev. (July, 1974 issue, in press).Google Scholar
  31. 31.
    Yu. N. Demkov, J. Exptl. Theoret. Phys. (U.S.S.R.) 45, 195 (1963) (English Translation: Soviet Physics, JETP 18, 138 (1964)).Google Scholar
  32. 32.
    R.E. Olson, Phys. Rev. A 6, 1822 (1972).ADSCrossRefGoogle Scholar
  33. 33.
    W. Lichten, Phys. Rev. 139, A27 (1965).ADSCrossRefGoogle Scholar
  34. 34.
    H.F. Helbig and E. Everhart, Phys. Rev. 136, A674 (1964).ADSCrossRefGoogle Scholar
  35. 35.
    U. Fano and W. Lichten, Phys. Rev. Letters 14, 627 (1965).ADSCrossRefGoogle Scholar
  36. 36.
    W. Lichten, Advances in Chemical Physics 13, 41 (1967).CrossRefGoogle Scholar
  37. 37.
    W. Lichten, Phys. Rev. 164, 131 (1967).ADSCrossRefGoogle Scholar
  38. 38.
    M. Barat and W. Lichten, Phys. Rev. A 6, 211 (1972).ADSCrossRefGoogle Scholar
  39. 39.
    W; Brandt and S. Lundgvist, Physics Letters 4, 47 (1963), Arkiv For Fysik 28, 399 (1964); J. Quant. Spectroscopy Radiative Transfer 4, 679 (1964); A. Russek and M. Tom Thomas, Phys. Rev. 109,-2015 (1958); 114, 1538 (1959); A. Russek and J.B. Bulman, Phys. Rev. 122, 506 (1961); A. Russek 132, 246 (1963); M. Ya. Amusia, Phys. Lett. 14, 36 (1965), Zh. Tekh. Fiz. 36, 1409 (1966) [English Transi: Soviet Physics,-Tech. Phys. 11, 1053 (1967)].Google Scholar
  40. 40.
    A.V. Afrosimov, Yu. S. Gordeev, M.N. Panov, and N.V. Federenko, Zh. Tekh. Fiz. 34, 1613 [1964-English: Soviet Phys-Technical Physics 9, 1248 (1965)].Google Scholar
  41. 41.
    J.D. Garcia, R.J. Fortner, and T.M. Kavanagh, Revs. Mod. Physics 45, 111 (1973).ADSCrossRefGoogle Scholar
  42. 42.
    F.W. Saris, “Characteristic X-Ray Production in Heavy-IonAtom Collisions.” in VII ICPEAC, Invited Talks and Progress Reports T.R. Govers and F.J. deHeer, eds., ( North-Holland, Amsterdam, 1971 ).Google Scholar
  43. 43.
    M.E. Rudd, “Introduction to Inner-Shell Excitation and De-excitation Processes, ref. 42, see also, ”Mechanisms of Inner Shell Excitation and De-excitation in Multiply Ionized Beams.“ p. 1485, Proceedings of the International Conference on Inner Shell Ionization Phenomena and Future Applications, CONF720404, U.S. Atomic Energy Commission, Technical Information Center, Oak Ridge, Tenn. (1973).Google Scholar
  44. 44.
    G.N. Ogurtsov, Reviews of Modern Physics 44, 1 (1972).ADSCrossRefGoogle Scholar
  45. 45.
    Quentin C. Kessel, “Coincidence Measurements,” in Case Studies in Atomic Physics, Vol. I, 401 (1969), edited by M.R.C. McDowell and E.W. McDaniel; Q.C. Kessel and B. Fastrup, “The Production of Inner-Shell Vacancies in Heavy Ion-Atom Collisions.” Ibid, 3, 139 (1973).Google Scholar
  46. 46.
    For several other review articles and discussions of current research see the Proceedings listed in footnote 43, Part B-Heavy Ion-Atom and Atom-Atom Collisions articles by F.T. Smith, D.G. Lorents and R.E. Olson, p. 1175; B. Fastrup, p. 1188; J.S. Briggs, p. 1209; J.A. Cairns, p. 1223; F.W. Saris, I.V. Mitchell, D.C. Santry, J.A. Davies and R. Laubert, p. 1255; P.H. Mokier, H.J. Stein, and P. Armbruster, p. 1283; V.S. Afrosimov, p. 1297; F.W. Bingham, p. 1320; T.M. Kavanagh, R.J. Fortner and R.C. Der, p. 1332; F.C. Jundt, H. Kubo and K.H. Purser, p. 1450. All these articles discuss application of the electron promotion model to collision experiments.Google Scholar
  47. a. See “Theory of Charged-Particle Excitation,” D.H. Madison and E. Merzbacher in Atomic Inner-Shell Process,B. Crasemann, ed. (Academic Press, to be published).Google Scholar
  48. 47.
    Q.C. Kessel and E. Everhart, Phys. Rev. 146, 16 (1966).ADSCrossRefGoogle Scholar
  49. 48.
    M.P. McCaughey, E.J. Knystautas, H.C. Hayden, and E. Everhart, Phys. Rev. Letters 21, 65 (1968).ADSCrossRefGoogle Scholar
  50. 49.
    B. Fastrup. G. Hermann, and Q.C. Kessel, Phys. Rev. Letters 27, 771 (1971).ADSCrossRefGoogle Scholar
  51. 50.
    B. Fastrup, E. B$ving, G.A. Larsen and P. Dahl, J. Phys. B: Atom. Molec. Phys. 7, L206 (1974).ADSCrossRefGoogle Scholar
  52. 51.
    T.M. Kavanagh, M.E. Cunningham, R.C. Der, R.J. Fortner, J.M. Khan, J. Zaharis, and J.D. Garcia, Phys. Rev. Letters 25, 1473 (1970).ADSCrossRefGoogle Scholar
  53. 52.
    K. Taulbjerg and P. Sigmund, Phys. Rev. A 5, 1285 (1972); see also K. Taulbjerg, B. Fastrup and E. Laegsgaard, Phys. Rev. A 8, 1814 (1973); also J. Macek, J.A. Cairns and J.S. Briggs, Phys. Rev. Letters 28, 1298 (1972); G. Bissinger and L.C. Feldman,Phys. Rev. A 8, 1624 (1973).Google Scholar
  54. 53.
    F.P. Larkins, J. Phys. B 5, 571 (1972). FICAP abstracts,p.613.Google Scholar
  55. 54.
    W. Brandt and R. Laubert, Phys. Lett. A 43, 53 (1973).ADSCrossRefGoogle Scholar
  56. 55.
    H. Tawara and J. Kistemaker, Phys. Lett. A 41, 287 (1972).ADSCrossRefGoogle Scholar
  57. 56.
    W.E. Meyerhof, Phys. Rev. Letters 31, 1341 (1973). For experiments on the K-vacancy sharing mechanism, see H. Kubo, F.C. Jundt and K.H. Purser, Phys. Rev. Letters 31, 674 (1973); H. Ziem, N. Stolterfocht, and D. Ridder, Paper to be presented at Helsinki Conference on X-ray Processes in Matter (July 1974 ).Google Scholar
  58. 57.
    B. Fastrup (private communication).Google Scholar
  59. 58.
    E.W. Thulstrup and H. Johansen, Phys. Rev. A 6, 206 (1972).ADSCrossRefGoogle Scholar
  60. 59.
    R.S. Mulliken, Chem. Phys. Letters 14, 137 (1972).ADSCrossRefGoogle Scholar
  61. 60.
    J.S. Briggs and M.R. Hayns, J. Phys. B 6, 514 (1973).ADSCrossRefGoogle Scholar
  62. 61.
    V. Sidis and M. Barat, VIII ICPEAC, p. 200 (1973), J. Phys. B (in press)Google Scholar
  63. 62a.
    J. Eichler and U. Wille, Phys. Rev. Letters 33, 56 (1974); b. J. Eichler and U. Wille, FICAP - Abstracts, p. 613.Google Scholar
  64. 63.
    Larkins, Ref. 53, has claimed that his diabatic correlations do not agree with that of the electron promotion model. However, inspection of his calculations shows that his steps in internuclear distance are too coarse to support his conclusions. His conclusions, in part, have been based on an apparent Landau-Zener crossing of the 2a and 3o curves (see Fig. 12 at 2R = 0.6 a.u.). B. Muller g(Dissertation, Frankfurt University, 1973) has shown that this type of pseudo-crossing does not obey the Landau-Zener theory, but follows the Demkov theory instead. That is, the eigenfunctions have a phase shift of 7r/4 rather than 7/2 in going through the pseudo-crossing. Thus there is no diabatic correlation possible at this pseudocrossing at very high velocities, where the promotion model breaks down.Google Scholar
  65. 64.
    J.S. Briggs and J.H. Macek, J. Phys. B 5, 579 (1972); 6, 982 (1973).Google Scholar
  66. 65.
    R.K. Cacek, Q.C. Kessel and M.E. Rudd, Phys. Rev. A 2, 1327 (1970).ADSCrossRefGoogle Scholar
  67. 66.
    S.K. Knudson and W.R. Thorson, Canad. J. of Physics 48, 313 (1970).ADSCrossRefGoogle Scholar
  68. 67.
    S. Sackmann, H.O. Lutz, and J. Briggs, Phys. Rev. Letters 32, 805 (1974).ADSCrossRefGoogle Scholar
  69. 68.
    F.W. Saris, W.F. van der Weg, H. Tawara, and R. Laubert, Phys. Rev. Letters 28, 717 (1972).ADSCrossRefGoogle Scholar
  70. 69.
    F.W. Saris, in Seventh ICPEAC, Invited Talks and Progress Reports edited by T.R. Govers and F.J. deHeer ( North-Holland, Amsterdam, 1971.Google Scholar
  71. 70.
    F.W. Saris, I.V. Mitchell, D.C. Santry, J.A. Davies, and R. Laubert, in Proceedings of the International Conference on Inner Shell Ionization Phenomena edited by R.W. Fink, S.T. Manson, J.M. Palms, and P.V. Rao, CONF-720404 (U.S. Atomic Energy Commision, Oak Ridge, Tenn., 1973 ), p. 1255.Google Scholar
  72. 71.
    P.H. Mokier, H.J. Stein, and P. Armbruster, Phys. Rev. 29, 827 (1972).ADSGoogle Scholar
  73. 72.
    P.H. Mokler, H.J. p. in Ref. 70, 1283.Google Scholar
  74. 73.
    J.R. MacDonald, M.D. Brown, and T. Chiao, Phys, Rev. Letters 30, 471 (1973).ADSCrossRefGoogle Scholar
  75. 74.
    W.E. Meyerhof, T.K. Saylor, S.M. Lazerus, W.A. Little, B.B. Triplett, and L.F. Chase, Jr., Phys. Rev. Letters 30, 1279 (1973); erratum, 30, 1279 (1973).ADSGoogle Scholar
  76. 75.
    W.E. Meyerhof, T.K. Saylor, S.M. Lazerus, W.A. Little, B.B. Triplett, L.F. Chase, Jr., and R. Anholt, Phys. Rev. Letters 32, 1279 (1974).ADSCrossRefGoogle Scholar
  77. 76.
    G. Bissinger and L.C. Feldman, Phys. Rev. Letters 33, 1 (1974); Phys. Rev. A 8, 1624 (1973).Google Scholar
  78. 77.
    C.K. Davis and J.S. Greenberg, Phys. Rev. Letters 32, 1215 (1974).ADSCrossRefGoogle Scholar
  79. 78.
    J.A. Cairns, A.D. Marwick, J. Macek and J.S. Briggs, Phys. Rev. Letters 32, 509 (1974).ADSCrossRefGoogle Scholar
  80. 79.
    F.C. Jundt, H. Kubo, H.E. Gove, University of Rochester Nuclear Structure Laboratory report UR-NSRL-81 (1974).Google Scholar
  81. 80.
    W. Lichten, Phys. Rev. A 9, 1458 (1974).ADSCrossRefGoogle Scholar
  82. 81.
    G. Gerber and A. Niehaus, Phys. Rev. Letters 31, 1231 (1973).ADSCrossRefGoogle Scholar
  83. 82.
    J.S. Greenberg (private communication); J.S. Greenberg, C.K. Davis, B. Müller and W. Greiner (to be published in the Proceedings of the Int. Conf. on Reactions between Complex Nuclei, Nashville, 1974 ); J.S. Greenberg, C.K. Davis, P. Vincent, FICAP Abstracts, p. 617.Google Scholar
  84. 83.
    J.S. Briggs and J.H. Macek, (private communication). Similar conclusions have been reached by K. Smith, B. Müller, and W. Greiner (unpublished).Google Scholar
  85. 84.
    An X-ray-atom-coincidence experiment would be decisive (Q.C. Kessel - private communication).Google Scholar
  86. 85.
    F.W. Saris, C. Foster, A. Langenberg, and J.V. Eck (preprint).Google Scholar
  87. 86.
    W.E. Meyerhof, Bull. Am. Phys. Soc. 19, 663 (1974); Physical Review (in press - September, 1974 issue).Google Scholar
  88. 87.
    D. Burch, W.B. Ingalls, H. Wieman, and R. Vandenbosch (preprint).Google Scholar
  89. 88.
    See accompanying article by W. Greiner for a summary and references.Google Scholar
  90. 89.
    K. Smith, H. Peitz, B. Müller and W. Greiner, Phys. Rev. Letters 32, 554 (1974).ADSCrossRefGoogle Scholar
  91. 90.
    S. Datz, C.D. Moak, B.R. Appleton, and T.A. Carlson, Phys. Rev. Letters 27, 363 (1971).ADSCrossRefGoogle Scholar
  92. 91.
    W. Pieper and W. Greiner, Z. Physik 218, 327 (1969); L.P. Fulcher and W. Greiner, Lettere al Nuovo Cimento 2, 279 (1971); V.S. Popov, Sov. Jour. of Nucl. Phys. 12, 235 (1971) [Yad. Fiz. 12, 429 (1970)].Google Scholar
  93. 92.
    B. Müller, J. Rafelski and W. Greiner, Physics Letters 47B, 5 ( 1973 ); B. Müller, Dissertation, U. of Frankfurt (1973).Google Scholar
  94. 93.
    For a historical review, see S.J. Brodsky, SLAC-PUB-1337 (Nov. 1973-Stanford Linear Accelerator Center).Google Scholar
  95. 94.
    L. Schiff, H. Snyder, and J. Weinberg, Phys. Rev. 57, 315 (1940).ADSCrossRefGoogle Scholar
  96. 95.
    I. Ya. Pomeranchuk, Ya. A. Smorodinsky, Jour. Phys. USSR 9, 97 (1945).Google Scholar
  97. 96.
    E. Fermi, Nuclear Physics University of Chicago Press, (1950).Google Scholar
  98. 97.
    S.S. Gershtein and Ya. B. Zeldovich, Sov. Phys. JETP 30, 358 (1970) [Zh. Eksp. Teor. Fiz. 57, 654 (1969)].Google Scholar
  99. 98.
    Y.B. Zeldovich and V.S. Popov, Sov. Phys. Usp. 14, 673 (1972).ADSCrossRefGoogle Scholar
  100. 99.
    Recently, Mssrs. Aagaard, Uving and Fastrup (private communication) have measured the Ne-Ne K-shell excitation cross-section as a function of energy. They confirm the earlier Ne/Ne+ ratio of 0.6 at a velocity of 0.78 a.u. (300 KeV). But at lower impact energies, the ratio falls off. At 0.35 a.u. it is down to 0.1. These results are in excellent agreement with the (Nef - N2)/(N+ - Ne) curve on fig. 10, and show that the apparent discrepancy with the promotion model was due to Demkovtype excitation of the exit channels.Google Scholar
  101. 100.
    Further confirmation has been made by ab initio calculations of one-electron wavefunctions for the asymmetric case by Mssrs. Taulbjerg, Vaaben and Fastrup (private communication). They have solved the coupled differential equations for the 1s - 2p excitation and agree with the Demkov-Olson-Meyerhof formula to within about 20%. In addition, N. Stolterfoth, P. Ziem and D. Ridder (private communication) further confirm the DOM formula in several com-binations of asymmetric ion-atom collisions with gas targets.Google Scholar
  102. 101.
    For detailed discussions of MO x-rays, see the papers in this volume by F.J. de Heer (p.2 87) and P. Mokier (p.301).Google Scholar
  103. 102.
    Prof. W. Greiner has kindly informed me that a numerical error in the calculated cross sections of ref. 89 has been made. The corrected cross sections should be 500 barns at 1600 MeV.Google Scholar
  104. 103.
    At FICAP, several groups presented results which are not discussed in this paper, but have important bearing on it. The page number refers to the FICAP book of Abstracts of Contributed Papers (Heidelberg, July 22–26, 1974 ).Google Scholar

Copyright information

© Plenum Press, New York 1975

Authors and Affiliations

  • William Lichten
    • 1
  1. 1.Physics DepartmentYale UniversityNew HavenUSA

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