Advertisement

History of Surface Phonons and Helium Atom Scattering

  • Giorgio BenedekEmail author
  • Jan Peter Toennies
Chapter
  • 423 Downloads
Part of the Springer Series in Surface Sciences book series (SSSUR, volume 63)

Abstract

The chapter starts with an overview of the history of the theory of surface phonons. Next the history of helium atom and electron inelastic scattering experiments are briefly reviewed. Present day helium atom scattering experiments are described next and some important related concepts are introduced. The chapter closes with a short history of the classical and quantum theory of inelastic surface scattering.

References

  1. 1.
    J.W. Strutt (Baron Rayleigh): Proc. London Math. Soc., 17, 4 (1885); see also: The Theory of Sound (MacMillan, London 1896; unabridged 2nd revised edition: Dover Publ., New York 1945)Google Scholar
  2. 2.
    G.W. Farnell, in Physical Acoustics, vol. 6, ed. by W.P. Mason, R.N. Thurston (Academic Press, New York, 1970), p. 109Google Scholar
  3. 3.
    A.A. Maradudin, in Nonequilibrium Phonon Dynamics, ed. by W.E. Bron (Plenum, New York, 1985), p. 395Google Scholar
  4. 4.
    M. Born, Th von Kármán, Phys. Zeit. 13, 297 (1912)Google Scholar
  5. 5.
    M. Born, K. Huang, Dynamical Theory of Crystal Lattices (Oxford University Press, London, 1954)zbMATHGoogle Scholar
  6. 6.
    I.M. Lifshitz, L.M. Rozenzweig, Zh. Eksp. Teor. Fiz. 18, 1012 (1948)Google Scholar
  7. 7.
    I.M. Lifshitz, Nuovo Cimento Suppl. 3, 732 (1956)Google Scholar
  8. 8.
    I.M. Lifshitz, A.M. Kosevich, Rep. Progr. Phys. 29(I), 217 (1966)CrossRefADSGoogle Scholar
  9. 9.
    E.N. Economou, Green’s Functions in Quantum Physics (Springer, Berlin, 1979)CrossRefGoogle Scholar
  10. 10.
    A.A. Maradudin, E.W. Montroll, G.H. Weiss and I.P. Ipatova: Theory of Lattice Dynamics in the Harmonic Approximation, Solid State Physics, suppl. 3 (Academic Press, New York, 1971)Google Scholar
  11. 11.
    A.A. Maradudin, R.F. Wallis, L. Dobrzynski, Handbook of Surfaces and Interfaces, vol. 3 (Garland, New York, 1980)Google Scholar
  12. 12.
    L. Dobrzynski, G. Leman, J. Phys. (Paris) 30, 116 (1970)CrossRefGoogle Scholar
  13. 13.
    P. Masri, L. Dobrzynski, J. Phys. (Paris) 32, 295 (1971)CrossRefGoogle Scholar
  14. 14.
    F. Garcia-Moliner, Ann. Phys. (Paris) 2, 179 (1977)ADSGoogle Scholar
  15. 15.
    G. Armand, Phys. Rev. B 14, 2218 (1976)CrossRefADSGoogle Scholar
  16. 16.
    G. Armand, P. Masri, Surf. Sci. 130, 89 (1983)CrossRefADSGoogle Scholar
  17. 17.
    R.A. Allen, Surf. Sci. 76, 91 (1978)CrossRefADSGoogle Scholar
  18. 18.
    A.A. Maradudin, J. Melngailis, Phys. Rev. 133, A1188 (1964)CrossRefADSGoogle Scholar
  19. 19.
    T.P. Martin, Phys. Rev: B 1, 3480 (1970)CrossRefADSGoogle Scholar
  20. 20.
    S.W. Musser, K.H. Rieder, Phys. Rev. B 2, 3034 (1970)CrossRefADSGoogle Scholar
  21. 21.
    M. Croitoru, D. Grecu, Surf. Sci. 38, 60 (1973); Rev. Roum. Phys. 18, 805 (1973)Google Scholar
  22. 22.
    J.E. Black, B. Lacks, D.L. Mills, Phys. Rev. B 22, 1818 (1980)CrossRefADSGoogle Scholar
  23. 23.
    W. Goldhammer, W. Ludwig, W. Zierau, C. Falter, Surf. Sci. 141, 139 (1984)CrossRefADSGoogle Scholar
  24. 24.
    G. Benedek, Phys. Status Sol. B58, 661 (1973)CrossRefADSGoogle Scholar
  25. 25.
    G. Benedek, Surf. Sci. 61, 603 (1976)CrossRefADSGoogle Scholar
  26. 26.
    G. Benedek, L. Miglio, in Surface Phonons, ed. by F.W. de Wette, W. Kress, Springer Ser. Surf. Sci., vol. 27 (Springer, Berlin, 1991), p. 37Google Scholar
  27. 27.
    G. Benedek, M. Miura, W. Kress, H. Bilz, Phys. Rev. Lett. 52, 1907 (1984)CrossRefADSGoogle Scholar
  28. 28.
    T.E. Feuchtwang, Phys. Rev. 155, 731 (1967)CrossRefADSGoogle Scholar
  29. 29.
    A simplified approach based on one single exponential function, used by B.N.N. Achar, G.R. Barsch, Phys. Rev. 188, 1356, 1361 (1969) within the scattering-matrix method (SMM), has been argued to be incorrect by R.E. Allen, Phys. Rev. B 3, 3580 (1971)Google Scholar
  30. 30.
    V. Bortolani, F. Nizzoli, G. Santoro, in Lattice Dynamics, ed. by M. Balkanski (Flammarion, Paris, 1978), p. 302Google Scholar
  31. 31.
    J. Szeftel, A. Khater, J. Phys. C 20, 4725 (1987)CrossRefADSGoogle Scholar
  32. 32.
    J. Szeftel, A. Khater, F. Mila, S. d’Addato, N. Auby, J. Phys. C 21, 2133 (1988)CrossRefADSGoogle Scholar
  33. 33.
    A. Khater, N. Auby, R.F. Wallis, Phys. B 167, 273 (1991)CrossRefADSGoogle Scholar
  34. 34.
    S. Trullinger, J. Math. Phys. 17, 1884 (1976)Google Scholar
  35. 35.
    A. Fasolino, G. Santoro, E. Tosatti, J. Phys. 42, C6–846 (1981)Google Scholar
  36. 36.
    J.E. Black, in Dynamical Properties of Solids (Chap. 5), ed. by G.K. Horton, A.A. Maradudin (Elsevier, Amsterdam, 1990)Google Scholar
  37. 37.
    D.C. Gazis, R. Herman, R.F. Wallis, Phys. Rev. 119, 533 (1960)CrossRefADSMathSciNetGoogle Scholar
  38. 38.
    D.C. Gazis, R.F. Wallis, Surf. Sci. 5, 482 (1966)CrossRefADSGoogle Scholar
  39. 39.
    R.F. Wallis, Phys. Rev. 105, 540 (1957)CrossRefADSGoogle Scholar
  40. 40.
    R.F. Wallis, Phys. Rev. 116, 302 (1959)CrossRefADSMathSciNetGoogle Scholar
  41. 41.
    A.A. Lucas, J. Chem. Phys. 48, 3156 (1968)CrossRefADSGoogle Scholar
  42. 42.
    R. Fuchs, K.L. Kliever, Phys. Rev. 140, A2076 (1965)CrossRefADSGoogle Scholar
  43. 43.
    K.L. Kliever, R. Fuchs, Phys. Rev. 144, 495 (1966)CrossRefADSGoogle Scholar
  44. 44.
    K.L. Kliever, R. Fuchs, Phys. Rev. 150, 573 (1966)CrossRefADSGoogle Scholar
  45. 45.
    W.E. Jones, R. Fuchs, Phys. Rev. B 4, 3581 (1971)CrossRefADSGoogle Scholar
  46. 46.
    V.V. Bryksin, Y.A. Firsov, Fiz. Tverd. Tela 11, 2167 (1969) [Sov. Phys. Solid State 11, 1751 (1970)]Google Scholar
  47. 47.
    A.D. Boardman (ed.), Electromagnetic Surface Modes (Wiley, New York, 1982)Google Scholar
  48. 48.
    B.C. Clark, R. Herman, R.F. Wallis, Phys. Rev. 139, A860 (1965)CrossRefADSGoogle Scholar
  49. 49.
    R.E. Allen, F.W. de Wette, Phys. Rev. 179, 873 (1969)CrossRefADSGoogle Scholar
  50. 50.
    R.E. Allen, F.W. de Wette, A. Rahman, Phys. Rev. 179, 887 (1969)CrossRefADSGoogle Scholar
  51. 51.
    G.P. Alldredge, R.E. Allen, F.W. de Wette, J. Acoust. Soc. Am. 49, 1453 (1971)CrossRefADSGoogle Scholar
  52. 52.
    R.E. Allen, G.P. Alldredge, F.W. de Wette, Phys. Rev. Lett. 23, 1285 (1969)CrossRefADSGoogle Scholar
  53. 53.
    R.E. Allen, G.P. Alldredge, F.W. de Wette, Phys. Rev. B 4, 1648 (1971)CrossRefADSGoogle Scholar
  54. 54.
    R.E. Allen, G.P. Alldredge, F.W. de Wette, Phys. Rev. B 4, 1661 (1971)CrossRefADSGoogle Scholar
  55. 55.
    T.S. Chen, G.P. Alldredge, F.W. de Wette, R.E. Allen, Phys. Rev. Lett. 26, 1543 (1971)CrossRefADSGoogle Scholar
  56. 56.
    T.S. Chen, G.P. Alldredge, F.W. de Wette, Solid State Commun. 10, 941 (1972)CrossRefADSGoogle Scholar
  57. 57.
    T.S. Chen, G.P. Alldredge, F.W. de Wette, Phys. Lett. 40 A, 401 (1972)Google Scholar
  58. 58.
    T.S. Chen, F.W. de Wette, G.P. Alldredge, Phys. Rev. B 15, 1167 (1977)CrossRefADSGoogle Scholar
  59. 59.
    F.W. de Wette, W. Kress (eds.), in Surface Phonons, Springer Ser. Surf. Sci., vol. 21 (Springer, Berlin, 1991)Google Scholar
  60. 60.
    G.P. Alldredge, Phys. Lett. 41A, 291 (1972)ADSGoogle Scholar
  61. 61.
    V.L. Zoth, G.P. Alldredge, F.W. de Wette, Phys. Lett. 47A, 247 (1974)CrossRefADSGoogle Scholar
  62. 62.
    H. G. Smith, N. Wakabayashi, in Dynamics of Solids and Liquids by Neutron Scattering, ed. by S. W. Lovesey, T. Springer (Springer, Berlin, 1977), p. 78Google Scholar
  63. 63.
    L. Miglio, L. Colombo, Phys. Rev. B 37, 3025 (1988)CrossRefADSGoogle Scholar
  64. 64.
    K.M. Ho, K.P. Bohnen, Phys. Rev. Lett. 56, 934 (1986)CrossRefADSGoogle Scholar
  65. 65.
    K.P. Bohnen, K.M. Ho, Surf. Sci. 207, 105 (1988)CrossRefADSGoogle Scholar
  66. 66.
    K.P. Bohnen, K.M. Ho, Surf. Sci. Rep. 19, 99 (1993)CrossRefADSGoogle Scholar
  67. 67.
    K.P. Bohnen, K.M. Ho, in Tutorials on Selected Topics in Modern Surface Science, ed. by T. Barr, D. Saldin (Elsevier, Dordrecht, 1993), pp. 100–117Google Scholar
  68. 68.
    C. Bungaro, S. de Gironcoli, S. Baroni, Phys. Rev. Lett. 77, 2491 (1996)CrossRefADSGoogle Scholar
  69. 69.
    S. Baroni, S. de Gironcoli, A. dal Corso, P. Giannozzi, Rev. Mod. Phys. 73, 515 (2001)CrossRefADSGoogle Scholar
  70. 70.
    M. Lazzeri, S. de Gironcoli, Phys. Rev. Lett. 81, 2096 (1998)CrossRefADSGoogle Scholar
  71. 71.
    J. Fritsch, C. Eckl, P. Pavone, U. Schröder, Festkörperprobleme 36, 135 (1997)Google Scholar
  72. 72.
    J. Fritsch, U. Schröder, Phys. Rep. 309, 209 (1999)CrossRefADSGoogle Scholar
  73. 73.
    R. Ravelo, M. El-Batanouny, Phys. Rev. B 40, 9574 (1989)CrossRefADSGoogle Scholar
  74. 74.
    R. Ravelo, M. El-Batanouny, J. Electr. Spectr. Rel. Phenom. 54(55), 255 (1990)CrossRefGoogle Scholar
  75. 75.
    T.E. Karakasidis, D.G. Papageorgiou, G.A. Evangelakis, Appl. Surf. Sci. 162, 233 (2000)CrossRefADSGoogle Scholar
  76. 76.
    P.C. Weakliem, E.A. Carter, J. Chem. Phys. 96, 3240 (1992)CrossRefADSGoogle Scholar
  77. 77.
    M.R. Baldan, E. Granato, S.C. Ying, Phys. Rev. B 62, 2146 (2000)CrossRefADSGoogle Scholar
  78. 78.
    D.D. Koleske, S.J. Sibener, Surf. Sci. 268, 406 (1992)CrossRefADSGoogle Scholar
  79. 79.
    D.D. Koleske, S.J. Sibener, Surf. Sci. 268, 418 (1992)CrossRefADSGoogle Scholar
  80. 80.
    X.Q. Wang, G.L. Chiarotti, F. Ercolessi, E. Tosatti, Phys. Rev. B 38, 8131 (1988)CrossRefADSGoogle Scholar
  81. 81.
    C.Z. Wang, E. Tosatti, A. Fasolino, Phys. Rev. Lett. 60, 2661 (1988)CrossRefADSGoogle Scholar
  82. 82.
    L. Yang, T.S. Rahman, Phys. Rev. Lett. 67, 2327 (1991)CrossRefADSGoogle Scholar
  83. 83.
    L. Yang, T.S. Rahman, M.S. Daw, Phys. Rev. B. 44, 13725 (1991)CrossRefADSGoogle Scholar
  84. 84.
    T.S. Rahman, Z.J. Tian, J. Electr. Spectr. Rel. Phenom. 64(65), 651 (1993)CrossRefGoogle Scholar
  85. 85.
    D.D. Koleske, S.J. Sibener, Surf. Sci. 290, 179 (1993)CrossRefADSGoogle Scholar
  86. 86.
    Y. Beaudet, L.J. Lewis, M. Persson, Phys. Rev. B 50, 12084 (1994)CrossRefADSGoogle Scholar
  87. 87.
    R. Zivieri, G. Santoro, V. Bortolani, Phys. Rev. B 59, 15959 (1999)CrossRefADSGoogle Scholar
  88. 88.
    K.S. Smirnov, G. Raseev, Surf. Sci. 459, 124 (2000)CrossRefADSGoogle Scholar
  89. 89.
    A.N. Al-Rawi, A. Kara, T.S. Rahman, Surf. Sci. 446, 17 (2000)CrossRefADSGoogle Scholar
  90. 90.
    A. Kara, T.S. Rahman, Surf. Sci. Rep. 56, 159 (2005)CrossRefADSGoogle Scholar
  91. 91.
    R. Car, M. Parrinello, Phys. Rev. Lett. 55, 2471 (1985)CrossRefADSGoogle Scholar
  92. 92.
    F. Ancillotto, W. Andreoni, A. Selloni, R. Car, M. Parrinello, Phys. Rev. Lett. 65, 3148 (1990)CrossRefADSGoogle Scholar
  93. 93.
    F. Ancillotto, A. Selloni, W. Andreoni, S. Baroni, R. Car, M. Parrinello, Phys. Rev. B 43, 8930 (1991)CrossRefADSGoogle Scholar
  94. 94.
    C.M. Bertoni, A.I. Shkrebtii, R. Di Felice, F. Finocchi, Prog. Surf. Sci. 42, 319 (1993)CrossRefADSGoogle Scholar
  95. 95.
    D.R. Alfonso, D.A. Drabold, S.E. Ulloa, Phys. Rev. B 51, 1989 (1995)CrossRefADSGoogle Scholar
  96. 96.
    D.R. Alfonso, D.A. Drabold, S.E. Ulloa, Phys. Rev. B 51, 14669 (1995)CrossRefADSGoogle Scholar
  97. 97.
    G. Kresse, J. Furthmüller, J. Hafner, Europhys. Lett., 729 (1995)Google Scholar
  98. 98.
    D. Marx, J. Hutter, in Modern Methods and Algorithms of Quantum Chemistry, ed. by J. Grotendorst, John von Neumann Institute for Computing, Jülich, NIC Series, vol. 1, ISBN 3-00-005618-1, pp. 301–449, 2000; and references thereinGoogle Scholar
  99. 99.
    D. Marx, J. Hutter, Ab-Initio Molecular Dynamics (Cambridge University Press, Cambridge, 2009)CrossRefGoogle Scholar
  100. 100.
    R.F. Wallis, in Atomic Structure and Properties of Solids, ed. by E. Burstein (Academic, New York, 1972)Google Scholar
  101. 101.
    R.F. Wallis, in Progress in Surface Science, ed. by S.G. Davison, vol. 4, (Pergamon, New York, 1974), p. 234Google Scholar
  102. 102.
    R.F. Wallis, in Dynamical Properties of Solids, ed. by G.K. Horton, A.A. Maradudin, vol. 2, (North-Holland, Amsterdam, 1975), p. 443Google Scholar
  103. 103.
    M.G. Lagally, in Surface Physics of Materials, ed. by J.M. Blakeley, vol. II, (Academic, New York, 1975), p. 419Google Scholar
  104. 104.
    G.I. Stegeman, F. Nizzoli, in Surface Excitations (Chap. 2), ed. by V.M. Agranovich, R. Loudon (North-Holland, Amsterdam 1984), p. 195Google Scholar
  105. 105.
    J.E. Black, in Structure and Dynamics of Surfaces I, ed. by W. Schommers, P. von Blanckenhagen (Springer, Berlin, 1986), p. 153Google Scholar
  106. 106.
    F.W. de Wette, in Dynamical Properties of Solids (Chap. 5), ed. by G.K. Horton, A.A. Maradudin (Elsevier, Amsterdam, 1990)Google Scholar
  107. 107.
    B.N. Brockhouse, A.T. Stewart, Phys. Rev. 100, 756 (1955)CrossRefADSGoogle Scholar
  108. 108.
    R.R. Cavanagh, R.D. Kelley, J.J. Rush, J. Chem. Phys. 77, 1540 (1982)Google Scholar
  109. 109.
    B.N. Brockhouse, S. Hanteder, H. Stiller, in Interaction of Radiation with Solids, ed. by Strumane et al. (North-Holland, Amsterdam, 1963)Google Scholar
  110. 110.
    B. Dorner, Coherent Inelastic Neutron Scattering in Lattice Dynamics (Springer, Berlin, 1982)CrossRefGoogle Scholar
  111. 111.
    K.H. Rieder, E.M. Hörl, Phys. Rev. Lett. 20, 209 (1968)CrossRefADSGoogle Scholar
  112. 112.
    K.H. Rieder, W. Drexel, Phys. Rev. Lett. 34, 148 (1975)CrossRefADSGoogle Scholar
  113. 113.
    E.R. Jones, J.T. McKinney, M.B. Webb, Bull. Am. Phys. Soc. 10, 324 (1965)Google Scholar
  114. 114.
    J. Aldag, R.M. Stern, Phys. Rev. Lett. 14, 857 (1965)CrossRefADSGoogle Scholar
  115. 115.
    D.L. Huber, Phys. Rev. 153, 772 (1967)CrossRefADSGoogle Scholar
  116. 116.
    N. Cabrera, V. Celli, J.R. Manson, Phys. Rev. Lett. 22, 346 (1969)CrossRefADSGoogle Scholar
  117. 117.
    J.R. Manson, V. Celli, Surf. Sci. 24, 495 (1971)CrossRefADSGoogle Scholar
  118. 118.
    J.R. Manson, J. Phys.: Condens. Matter 22, 300401 (2010)Google Scholar
  119. 119.
    R.W. Wood, Phil. Mag., London, 30, 300–304 (1915)Google Scholar
  120. 120.
    R.W. Wood, Phil. Mag., London, 32, 364 (1916)Google Scholar
  121. 121.
    M. Knudsen, Ann. Phys. (Leipzig) 47, 697–708 (1915)CrossRefADSGoogle Scholar
  122. 122.
    M. Knudsen, Ann. Phys. (Leipzig) 48, 1113–1121 (1915)ADSGoogle Scholar
  123. 123.
    L. Dunoyer, Radium 8, 142 (1911)CrossRefGoogle Scholar
  124. 124.
    O. Stern, Naturwiss. 17, 391 (1929)CrossRefADSGoogle Scholar
  125. 125.
    I. Estermann, O. Stern, Z. Phys. 61, 95 (1930)CrossRefADSGoogle Scholar
  126. 126.
    I. Estermann, R. Frisch, O. Stern, Z. Phys. 73, 348 (1931)CrossRefADSGoogle Scholar
  127. 127.
    T.H. Johnson, J. Franklin Inst. 210, 135 (1930)CrossRefGoogle Scholar
  128. 128.
    T.H. Johnson, Phys. Rev. 37, 847–861 (1931)CrossRefADSGoogle Scholar
  129. 129.
    L. De Broglie, Recherches sur la Théorie des Quanta (Thesis (Sorbonne), Paris, 1924)zbMATHGoogle Scholar
  130. 130.
    De Broglie, L., Ann. de Phys. 10(3), 22 (1925)Google Scholar
  131. 131.
    O.R. Frisch, What Little I Remember (Cambridge University Press, Cambridge, 1979)Google Scholar
  132. 132.
    R.G.J. Fraser, Molecular Rays (Cambridge University Press, Cambridge, 1931)Google Scholar
  133. 133.
    E. Fues, Beugungsversuche mit Materiewellen: Einführung in die Quantenmechanik (Akad. Verlangsges, Leipzig, 1935)zbMATHGoogle Scholar
  134. 134.
    M. Von Laue, in Materiewellen und ihre Interferenzen (Akadem. Verl.-Ges. Becker & Erler, 1944; Geest und Portig, 1948)Google Scholar
  135. 135.
    K.F. Smith, Molecular Beams (Wiley, New York, 1955)zbMATHGoogle Scholar
  136. 136.
    G. Comsa, Surf. Sci. 299, 77 (1994)CrossRefADSGoogle Scholar
  137. 137.
    E.C. Beder, Advan. At. Mol. Phys. 3, 205–290 (1967)CrossRefADSGoogle Scholar
  138. 138.
    R.E. Stickney, R.M. Logan, S. Yamamoto, J.C. Keck, in Fundamentals of Gas-Surface Interactions, ed. by H. Saltsburg (Academic Press Inc., New York 1967), p. 422. Quantenmechanik (Akad. Verlangsges., Leipzig 1935)Google Scholar
  139. 139.
    R.E. Stickney, J. Vac. Sci. Technol. 6, 920 (1969)Google Scholar
  140. 140.
    R.E. Stickney, J. Vac. Sci. Technol. 7, 90 (1970)CrossRefADSGoogle Scholar
  141. 141.
    N. Cabrera, V. Celli, F.O. Goodman, R. Manson, Surf. Sci. 19, 67 (1970)CrossRefADSGoogle Scholar
  142. 142.
    S.S. Fisher, J.R. Bledsoe, J. Vac. Sci. Technol. 9, 814 (1971)CrossRefADSGoogle Scholar
  143. 143.
    S.S. Fisher, J.R. Bledsoe, Surf. Sci. 46, 129 (1974)CrossRefADSGoogle Scholar
  144. 144.
    R.E. Subbarao, D.R. Miller, J. Chem. Phys. 51, 4679 (1969)CrossRefADSGoogle Scholar
  145. 145.
    R.E. Subbarao, D.R. Miller, J. Vac. Sci. Technol. 9, 808 (1972)CrossRefADSGoogle Scholar
  146. 146.
    J.M. Horne, D.R. Miller, Phys. Rev. Lett. 41, 511 (1978)CrossRefADSGoogle Scholar
  147. 147.
    G. Benedek, G. Boato, Europhys. News 8, 5 (1977)CrossRefGoogle Scholar
  148. 148.
    B.R. Williams, J. Chem. Phys. 55, 3220 (1971)CrossRefADSGoogle Scholar
  149. 149.
    B.R. Williams, J. Chem. Phys. 56, 1895 (1972)CrossRefADSGoogle Scholar
  150. 150.
    B.F. Mason, B.R. Williams, J. Chem. Phys. 61, 2765 (1974)CrossRefADSGoogle Scholar
  151. 151.
    B.F. Mason, B.R. Williams, Jpn. J. Appl. Phys., suppl., Pt. 2, 557 (1974)Google Scholar
  152. 152.
    G. Boato, P. Cantini, in Dynamics Aspects of Surface Physics, ed. by F.O. Goodman (Compositori, Bologna, 1974), p. 707Google Scholar
  153. 153.
    L. Van Hove, Phys. Rev. 89, 1189 (1953)CrossRefADSMathSciNetGoogle Scholar
  154. 154.
    G. Benedek, Phys. Rev. Lett. 35, 234 (1975)CrossRefADSGoogle Scholar
  155. 155.
    G. Benedek, L. Miglio, G. Seriani, in Helium Atom Scattering from Surfaces, ed. by E. Hulpke (Springer, Berlin, 1992), p. 207Google Scholar
  156. 156.
    F.O. Goodman (ed.), in Dynamic Aspects of Surface Physics, vol. 19 (Compositori, Bologna, 1974)Google Scholar
  157. 157.
    R. Avila, M. Lagos, Surf. Sci. 103, L104 (1981)CrossRefADSGoogle Scholar
  158. 158.
    P. Cantini, G.P. Felcher, R. Tatarek, Phys. Rev. Lett. 37, 606 (1976)CrossRefADSGoogle Scholar
  159. 159.
    G. Brusdeylins, R.B. Doak, J.P. Toennies, Phys. Rev. Lett. 44, 1417 (1980)CrossRefADSGoogle Scholar
  160. 160.
    G. Brusdeylins, R.B. Doak, J.P. Toennies, Phys. Rev. Lett. 46, 437 (1981)CrossRefADSGoogle Scholar
  161. 161.
    G. Brusdeylins, R.B. Doak, J.P. Toennies, Phys. Rev. B 27, 3662 (1983)CrossRefADSGoogle Scholar
  162. 162.
    B. Feuerbacher, R.F. Willis, Phys. Rev. Lett. 47, 526 (1981)CrossRefADSGoogle Scholar
  163. 163.
    O. Gunnarsson, K. Schönhammer, Phys. Rev. B 25, 2514 (1982)CrossRefADSGoogle Scholar
  164. 164.
    R.B. Doak, U. Harten, J.P. Toennies, Phys. Rev. Lett. 51, 578 (1983)CrossRefADSGoogle Scholar
  165. 165.
    J.B. Anderson, J.B. Fenn, Phys. Fluids 8, 780 (1965)CrossRefADSGoogle Scholar
  166. 166.
    J.P. Toennies, K. Winkelmann, J. Chem. Phys. 66, 3965 (1977)CrossRefADSGoogle Scholar
  167. 167.
    G. Brusdeylins, H.-D. Meyer, J.P. Toennies, K. Winkelmann, in Progress in Astronautics and Aeronautics, vol. 51, ed. by J.L. Poetter (AIAA, New York, 1977), p. 1047Google Scholar
  168. 168.
    J.P. Toennies, in Surface Phonons, ed. by F.W. de Wette, W. Kress, Springer Ser. Surf. Sci., vol. 21 (Springer, Berlin, 1991)Google Scholar
  169. 169.
    J.P. Toennies, Europhys. News 23, 63 (1992); A. Lahee, J. P. Toennies, Physics World, April 1993, p. 61Google Scholar
  170. 170.
    R.F. Wallis, A.A. Maradudin, Phys. Rev. 148, 962 (1966)CrossRefADSGoogle Scholar
  171. 171.
    F.M. Probst, T.C. Piper, J. Vac. Sci. Technol. 4, 53 (1967)CrossRefADSGoogle Scholar
  172. 172.
    H. Ibach, Phys. Rev. Lett. 24, 1416 (1970)CrossRefADSGoogle Scholar
  173. 173.
    H. Ibach, J. Vac. Sci. Technol. 9, 713 (1971)CrossRefADSGoogle Scholar
  174. 174.
    A. Otto, Z. Phys. 216, 398 (1968)CrossRefADSGoogle Scholar
  175. 175.
    H. Ibach, Phys. Rev. Lett. 27, 253 (1971)CrossRefADSGoogle Scholar
  176. 176.
    W. Ludwig, Jpn. J. Appl. Phys., suppl. 2, Pt. 2 (1974), p. 879Google Scholar
  177. 177.
    C.H. Li, S.Y. Tong, D.L. Mills, Phys. Rev. B 21, 3057 (1980)CrossRefADSMathSciNetGoogle Scholar
  178. 178.
    J.M. Szeftel, S. Lehwald, H. Ibach, T.S. Rahman, J.E. Black, D.L. Mills, Phys. Rev. Lett. 51, 268 (1983)CrossRefADSGoogle Scholar
  179. 179.
    S. Lehwald, J.W. Szeftel, H. Ibach, T.S. Rahman, D.L. Mills, Phys. Rev. Lett. 50, 518 (1983)CrossRefADSGoogle Scholar
  180. 180.
    H. Ibach, Surf. Sci. 299–300, 116 (1994)CrossRefADSGoogle Scholar
  181. 181.
    H. Ibach, D.L. Mills, Electron Energy Loss Spectroscopy and Surface Vibrations (Academic Press, Inc., New York, 1982)Google Scholar
  182. 182.
    H. Ibach, in Electron Energy Loss Spectrometers: The Technology of High Performance, Springer Series in Optical Sciences, vol 63 (Springer, Berlin, 1991)Google Scholar
  183. 183.
    H. Ibach, in Physics of Surfaces and Interfaces (Chap. 7) (Springer, Berlin, 2007)Google Scholar
  184. 184.
    H. Ibach, J. Chem Soc.-Faraday Trans. 92, 4771–4774 (1996)Google Scholar
  185. 185.
    J.C. Maxwell, Phil. Trans. R. Soc. Lond. 170, 231 (1879)CrossRefADSGoogle Scholar
  186. 186.
    B. Baule, Ann. der Phys. 44, 145 (1914)CrossRefADSGoogle Scholar
  187. 187.
    H. Saltsburg (ed.), Fundamentals of Gas-Surface Interactions (Academic Press, New York, 1967)Google Scholar
  188. 188.
    R.M. Logan, in Theory of Gas-Surface Scattering and Accommodation, Solid State Surface Science, ed. by M. Green, vol. 3 (Dekker, New York, 1973), p. 1Google Scholar
  189. 189.
    R.E. Stickney, Adv. At. Mol. Phys. 3, 143–204 (1968)CrossRefADSGoogle Scholar
  190. 190.
    S. Yamamoto, R.E. Stickney, J. Chem Phys. 53, 1594 (1970)CrossRefADSGoogle Scholar
  191. 191.
    R.M. Logan, R.E. Stickney, J. Chem. Phys. 44, 195 (1966)CrossRefADSGoogle Scholar
  192. 192.
    R.M. Logan, J.C. Keck, J. Chem. Phys. 49, 860 (1968)CrossRefADSGoogle Scholar
  193. 193.
    J.A. Barker, D.J. Auerbach, Chem. Phys. Lett. 67, 393 (1979)CrossRefADSGoogle Scholar
  194. 194.
    L.D. Landau, Phys. Z. Sowjet. 8, 489 (1935)Google Scholar
  195. 195.
    See, e.g., B.L. Bonch-Bruevich, Usp. Fiz. Nauka 40, 369 (1950) [English translation: National Research Council of Canada TT.509]Google Scholar
  196. 196.
    R.W. Zwanzig, J. Chem. Phys. 32, 1173 (1960)CrossRefADSGoogle Scholar
  197. 197.
    B. McCarroll, J. Chem. Phys. 39, 1317 (1963)CrossRefADSGoogle Scholar
  198. 198.
    F.O. Goodman, in Rarefied Gas Dynamics, ed. by J.H. De Leeuw, vol. 2 (Academic Press, New York, 1966), p. 336Google Scholar
  199. 199.
    C. Caroli, B. Roulet, D. Saint-James, Phys. Rev. B 18, 545 (1978)CrossRefADSGoogle Scholar
  200. 200.
    D.R. Dion, J.A. Barker, R.P. Merril, Chem. Phys. Lett. 57, 218 (1978)CrossRefGoogle Scholar
  201. 201.
    S.A. Adelman, J.D. Doll, J. Chem. Phys. 64, 2375 (1976)CrossRefADSGoogle Scholar
  202. 202.
    S.A. Adelman, J. Chem. Phys. 71, 4471 (1979)CrossRefADSGoogle Scholar
  203. 203.
    S.A. Adelman, Adv. Chem. Phys. 44, 143 (1980)Google Scholar
  204. 204.
    M. Shugard, J.C. Tully, A. Nitzan, J. Chem. Phys. 66, 2534 (1977)CrossRefADSGoogle Scholar
  205. 205.
    M. Shugard, J.C. Tully, A. Nitzan, J. Chem. Phys. 69, 336 (1978)CrossRefADSGoogle Scholar
  206. 206.
    M. Shugard, J.C. Tully, A. Nitzan, J. Chem. Phys. 69, 2525 (1978)CrossRefADSGoogle Scholar
  207. 207.
    J.C. Tully, J. Chem. Phys. 73, 1975 (1980)CrossRefADSGoogle Scholar
  208. 208.
    J.C. Tully, Surf. Sci. 111 (1981)Google Scholar
  209. 209.
    C.W. Muhlhausen, J.A. Serri, J.C. Tully, G.E. Becker, M.J. Cardillo, Israel J. Chem. 22, 315 (1982)CrossRefGoogle Scholar
  210. 210.
    R.B. Gerber, Chem. Rev. 87, 29–79 (1987)CrossRefGoogle Scholar
  211. 211.
    F.O. Goodman, Surf. Sci. 3, 386 (1965)CrossRefADSGoogle Scholar
  212. 212.
    J.A. Barker, W.A. Steele, Surf. Sci. 74, 596 (1978)CrossRefADSGoogle Scholar
  213. 213.
    J.A. Barker, D.R. Dion, R.P. Merrill, Surf. Sci. 95, 15 (1980)CrossRefADSGoogle Scholar
  214. 214.
    J.A. Barker, D.J. Auerbach, Surf. Sci. Rep. 4, 1 (1984)CrossRefADSGoogle Scholar
  215. 215.
    W. Brenig, Z. Phys. B 48 (1982), p. 127Google Scholar
  216. 216.
    G. Fan, J.R. Manson, Phys. Rev. Lett. 101, 063202 (2008)CrossRefADSGoogle Scholar
  217. 217.
    G. Fan, J.R. Manson, Phys. Rev. B 79, 045424 (2009)CrossRefADSGoogle Scholar
  218. 218.
    G. Fan, J.R. Manson, Chem. Phys. 370, 175 (2010)CrossRefGoogle Scholar
  219. 219.
    W.W. Hayes, J.R. Manson, Phys. Rev. Lett. 109, 063203 (2012)CrossRefADSGoogle Scholar
  220. 220.
    W.W. Hayes, J.R. Manson, Phys. Rev. B 89, 045406 (2014)CrossRefADSGoogle Scholar
  221. 221.
    E. Drauglis, Phys. Rev. 178, 1527 (1969)CrossRefADSGoogle Scholar
  222. 222.
    J.I. Kaplan, E. Drauglis, Surf. Sci. 36, 1 (1973)CrossRefADSGoogle Scholar
  223. 223.
    H.-D. Meyer, Surf. Sci. 104, 117 (1981)CrossRefADSGoogle Scholar
  224. 224.
    W.H. Miller, J. Chem. Phys. 53, 1949, 3578 (1970)Google Scholar
  225. 225.
    W.H. Miller, in Classical-Limit Quantum Mechanics and the Theory of Molecular Collisions, Advances in Chemical Physics, vol. 25, ed. by S.A. Rice (Wiley, New York, 1974), p. 69Google Scholar
  226. 226.
    W.H. Miller, The Classical S-Matrix in Molecular Collisions, Advances in Chemical Physics, vol. 30, ed. by K.P. Lawley (Wiley, New York, 1975), p. 77Google Scholar
  227. 227.
    R.A. Marcus, Chem. Phys. Letters 7, 525 (1970)CrossRefADSGoogle Scholar
  228. 228.
    R.A. Marcus, J. Chem. Phys. 54, 3965 (1971)CrossRefADSGoogle Scholar
  229. 229.
    H.D. Meyer, R.D. Levine, Chem. Phys. 85, 189 (1984)CrossRefGoogle Scholar
  230. 230.
    V. Celli, D. Evans, in Dynamics of Gas-Surface Interaction, ed. by G. Benedek, U. Valbusa (Springer, Berlin, 1982), p. 2Google Scholar
  231. 231.
    J.R. Manson, Phys. Rev. B 43, 6924 (1991)CrossRefADSGoogle Scholar
  232. 232.
    J.R. Manson, V. Celli, D. Himes, Phys. Rev. B 49, 2782 (1994)CrossRefADSGoogle Scholar
  233. 233.
    J. R. Manson, Energy Transfer to Phonons in Atom and Molecule Collisions with Surfaces, in Handbook of Surface Science, vol. 3, Surface Dynamics, ed. by W.N. Unertl (North Holland, Amsterdam, 2006)Google Scholar
  234. 234.
    A. Bilić, B. Gumhalter, Phys. Rev. B 52, 12307 (1995)CrossRefADSGoogle Scholar
  235. 235.
    B. Gumhalter, A. Šiber, J.P. Toennies, Phys. Rev. Lett. 83, 1375 (1999)CrossRefADSGoogle Scholar
  236. 236.
    B. Gumhalter, Phys. Rep. 351, 1 (2000)CrossRefADSGoogle Scholar
  237. 237.
    A. Šiber, B. Gumhalter, Ch. Wöll, J. Phys. Cond. Matter 14, 5193 (2002)CrossRefGoogle Scholar
  238. 238.
    A. Šiber, B. Gumhalter, Phys. Rev. Lett. 90, 126103 (2003)CrossRefADSGoogle Scholar
  239. 239.
    G.D. Billing, J. Phys. Chem. 99, 15378 (1995)CrossRefGoogle Scholar
  240. 240.
    G.D. Billing, Appl. Surf. Sci. 142, 7 (1999)CrossRefADSGoogle Scholar
  241. 241.
    G.D. Billing, J. Chem. Phys. 112, 335 (2000)CrossRefADSGoogle Scholar
  242. 242.
    S. Adhikari, G.D. Billing, J. Chem. Phys. 112, 3884 (2000)CrossRefADSGoogle Scholar
  243. 243.
    G.D. Billing, Dynamics of Molecule Surface Interactions (Wiley, New York, 2000)Google Scholar
  244. 244.
    W. Brenig, Z. Phys. B 36, 81 (1976)CrossRefADSGoogle Scholar
  245. 245.
    R. Sedlmeir, W. Brenig, Z. Phys. B 36, 235 (1976)Google Scholar
  246. 246.
    J. Böheim, W. Brenig, Z. Phys. B 41, 243 (1981)CrossRefADSGoogle Scholar
  247. 247.
    J. Stutzki, W. Brenig, Z. Phys. B 45, 49 (1981)CrossRefADSGoogle Scholar
  248. 248.
    D.M. Newns, Surf. Sci. 154, 658 (1985)CrossRefADSGoogle Scholar
  249. 249.
    R. Brako, D.M. Newns, Phys. Rev. Lett. 48, 1859 (1982)CrossRefADSGoogle Scholar
  250. 250.
    R. Brako, D.M. Newns, Surf. Sci. 117, 42 (1982)CrossRefADSGoogle Scholar
  251. 251.
    R. Brako, Surf. Sci. 123, 439 (1982)CrossRefADSGoogle Scholar
  252. 252.
    M. Persson, J. Harris, Surf. Sci. 187, 67 (1987)CrossRefADSGoogle Scholar
  253. 253.
    V. Bortolani, A.C. Levi, Riv. Nuovo Cim. 9, 1 (1986)CrossRefADSGoogle Scholar
  254. 254.
    V. Celli, D. Himes, P. Tran, J.P. Toennies, Ch. Wöll, G. Zhang, Phys. Rev. Lett. 66, 3160 (1991)CrossRefADSGoogle Scholar
  255. 255.
    D. Himes, V. Celli, Surf. Sci. 272, 139 (1992)CrossRefADSGoogle Scholar
  256. 256.
    K. Burke, B. Gumhalter, D.C. Langreth, Phys. Rev. B 47, 12852 (1993)CrossRefADSGoogle Scholar
  257. 257.
    B. Gumhalter, K. Burke, D.C. Langreth, Surf. Rev. Lett. 1, 133 (1994)CrossRefADSGoogle Scholar
  258. 258.
    J.R. Manson, Comp. Phys. Comm. 80, 145 (1994)CrossRefADSGoogle Scholar
  259. 259.
    W. Brenig, B. Gumhalter, J. Phys. Chem. B 108, 14549 (2004)CrossRefGoogle Scholar
  260. 260.
    A. Muis, J.R. Manson, Phys. Rev. B 54, 2205 (1996)CrossRefADSGoogle Scholar
  261. 261.
    A. Muis, J.R. Manson, J. Chem. Phys. 107, 1655 (1996)CrossRefADSGoogle Scholar
  262. 262.
    F. Hofmann, J.P. Toennies, J.R. Manson, Surf. Sci. 349, L184 (1996)CrossRefADSGoogle Scholar
  263. 263.
    A. Šiber, B. Gumhalter, Surf. Sci. 385, 270 (1997)CrossRefADSGoogle Scholar
  264. 264.
    A. Šiber, B. Gumhalter, Phys. Rev. Lett. 81, 1742 (1998)CrossRefADSGoogle Scholar
  265. 265.
    C. Zener, Phys. Rev. 37, 557 (1931)CrossRefADSGoogle Scholar
  266. 266.
    C. Zener, Proc. Roy. Soc. (London) 40, 178, 335(1932)Google Scholar
  267. 267.
    J.M. Jackson, Proc. Cambridge Phil. Soc. 28, 136 (1932)CrossRefADSGoogle Scholar
  268. 268.
    J.M. Jackson, N.F. Mott, Proc. Roy. Soc. (London) A 137, 703 (1932)Google Scholar
  269. 269.
    J.M. Jackson, A. Howarth, Proc. Roy. Soc. (London) A 142, 447 (1933)Google Scholar
  270. 270.
    P. Morse, Phys. Rev. 34, 57 (1929)CrossRefADSGoogle Scholar
  271. 271.
    J.E. Lennard-Jones, C. Strachan, Proc. Roy. Soc. (London) A 150, 442 (1935) (I)Google Scholar
  272. 272.
    C. Strachan, Proc. Roy. Soc. (London) A 150, 456 (1935) (II)Google Scholar
  273. 273.
    J.E. Lennard-Jones, A.F. Devonshire, Proc. Roy. Soc. (London) A 156, 6 (III), 29 (IV) (1936)Google Scholar
  274. 274.
    J.E. Lennard-Jones, A.F. Devonshire, Nature 137, 1069 (1936)Google Scholar
  275. 275.
    A.F. Devonshire, Proc. Roy. Soc. (London) A 156, 37 (1936) (V)Google Scholar
  276. 276.
    J.E. Lennard-Jones, A.F. Devonshire, Proc. Roy. Soc. (London) A 158, 242 (VI), 253 (VII) (1937)Google Scholar
  277. 277.
    A. F. Devonshire, Proc. Roy. Soc. (London) A 158, 269 (1937) (VIII)Google Scholar
  278. 278.
    C. Strachan, Proc. Roy. Soc. (London) A 158, 591 (1937) (IX)Google Scholar
  279. 279.
    R. Frisch, O. Stern, Z. Phys. 84, 430 (1933)CrossRefADSGoogle Scholar
  280. 280.
    R. Frisch, Z. Phys. 84, 443 (1933)CrossRefADSGoogle Scholar
  281. 281.
    D.M. Gilbey, J. Phys. Chem. Solids 23, 1453 (1962)CrossRefADSGoogle Scholar
  282. 282.
    R.T. Allen, P. Feuer, J. Chem. Phys. 43, 4500 (1965)CrossRefADSGoogle Scholar
  283. 283.
    A.J. Howsmon, in Proc. IV. Int. Symp. on Rarefied Gas Dynamics, vol. 1, Rarefied Gas Dynamics, suppl. 4 (1967), p. 67Google Scholar
  284. 284.
    A.E. Sisson, A.J. Howsmon, J. Vac. Sci. Technol. 6, 921 (1969)Google Scholar
  285. 285.
    J.W. Gadzuk, Phys. Rev. 153, 759 (1967)CrossRefADSGoogle Scholar
  286. 286.
    D. Secrest, B.R. Johnson, J. Chem. Phys. 45, 4556 (1966)Google Scholar
  287. 287.
    D.W. Roach, R.E. Harris, J. Chem. Phys. 51, 3404 (1969)CrossRefADSGoogle Scholar
  288. 288.
    C.B. Duke, G.E. Laramore, Phys. Rev. B 2, 4765 (1970)CrossRefADSGoogle Scholar
  289. 289.
    J.E. Lennars-Jones, E.T. Goodwin, Proc. Roy. Soc. (London) A 163, 101 (1937) (X)Google Scholar
  290. 290.
    J.E. Lennard-Jones, Proc. Roy. Soc. (London) 163, 127 (XI), 132 (XII) (1937)Google Scholar
  291. 291.
    M. Gell-Mann, M.L. Goldberger, Phys. Rev. 91, 398 (1953)Google Scholar
  292. 292.
    M.L. Goldberger, K.M. Watson, Collision Theory (Wiley, New York, 1964)zbMATHGoogle Scholar
  293. 293.
    F.O. Goodman, Surf. Sci. 19, 93 (1970)CrossRefADSGoogle Scholar
  294. 294.
    F.O. Goodman, Surf. Sci. 26, 327 (1971)CrossRefADSGoogle Scholar
  295. 295.
    F.O. Goodman, Surf. Sci. 24, 667 (1971), 26, 364 (1971)Google Scholar
  296. 296.
    F.O. Goodman, Surf. Sci. 30, 1 (1972)CrossRefADSGoogle Scholar
  297. 297.
    F.O. Goodman, W.-K. Tan, J. Chem. Phys. 59, 1805 (1973)CrossRefADSGoogle Scholar
  298. 298.
    F.O. Goodman, Surf. Sci. 46, 118 (1974)CrossRefADSGoogle Scholar
  299. 299.
    G. Benedek, G. Seriani, Jpn. J. Appl. Phys. Suppl 2(Pt. 2), 545 (1974)CrossRefADSGoogle Scholar
  300. 300.
    G.F. Miller, H. Pursey, Proc. Roy. Soc. (London) A 223, 521 (1975)Google Scholar
  301. 301.
    M. Lagos, L. Birstein, Surf. Sci. 51, 469 (1975)CrossRefADSGoogle Scholar
  302. 302.
    M. Lagos, L. Birstein, Surf. Sci. 52, 391 (1975)CrossRefADSGoogle Scholar
  303. 303.
    A. Tsuchida, Surf. Sci. 14, 375 (1969)CrossRefADSGoogle Scholar
  304. 304.
    J.N. Smith, Surf. Sci. 34, 613 (1973)CrossRefADSGoogle Scholar
  305. 305.
    J.P. Toennies, Appl. Phys. 3, 114 (1974)Google Scholar
  306. 306.
    W.H. Weinberg, Adv. Colloid Surf. Sci. 4, 301 (1975)CrossRefADSGoogle Scholar
  307. 307.
    F.O. Goodman, H. Wachman, in Dynamics Aspects of Surface Physics, ed. by F.O. Goodman (Compositori, Bologna, 1974)Google Scholar
  308. 308.
    F.O. Goodman, H. Wachman, Dynamics of Gas-Surface Scattering (Academic Press, Boston, 1976)Google Scholar
  309. 309.
    R. Smouchowski, Phys. Rev. 60, 661 (1941)CrossRefADSGoogle Scholar
  310. 310.
    J.L. Beeby, J. Phys. C: Solid State Phys. 5, 3438 (1972)CrossRefADSGoogle Scholar
  311. 311.
    J.L. Beeby, J. Phys. C: Solid State Phys. 5, 3457 (1972)CrossRefADSGoogle Scholar
  312. 312.
    D.R. Okeefe, J.N. Smith, R.L. Palmer, H. Saltsburg Surf. Sci. 20, 27 (1970)Google Scholar
  313. 313.
    R.L. Palmer, D.R. O’Keefe, H. Saltsburg, J.N. Smith, J. Vac. Sci. Technol. 7, 91 (1970)CrossRefADSGoogle Scholar
  314. 314.
    J.L. Beeby, J. Phys. C: Solid State Phys. 4, L359 (1971)CrossRefADSGoogle Scholar
  315. 315.
    D.V. Tendulkar, R.E. Stickney, Surf. Sci. 27, 516 (1971)Google Scholar
  316. 316.
    U. Garibaldi, A.C. Levi, R. Spadacini, G.E. Tommei, Surf. Sci. 38, 269 (1973)CrossRefADSGoogle Scholar
  317. 317.
    U. Garibaldi, A.C. Levi, R. Spadacini, G.E. Tommei, Surf. Sci. 48, 649 (1975)CrossRefADSGoogle Scholar
  318. 318.
    A.C. Levi, H.G. Suhl, Surf. Sci. 88, 221 (1979)CrossRefADSGoogle Scholar
  319. 319.
    J.D. McClure, J. Chem. Phys. 52, 2712 (1970). See also Rayleigh’s theory of sound wave scattering from an undulated surface in [1], p. 272Google Scholar
  320. 320.
    A. C. Levi, Nuovo Cim. 54 B, 357 (1979)Google Scholar
  321. 321.
    R.B. Gerber, A.T. Yinnon, J.N. Murrel, Chem. Phys. 31, 1 (1978)CrossRefGoogle Scholar
  322. 322.
    R. Schinke, R.B. Gerber, J. Chem. Phys. 82, 1567 (1985)CrossRefADSGoogle Scholar
  323. 323.
    J.E. Adams, W.H. Miller, Surf. Sci. 85, 77 (1979)CrossRefADSGoogle Scholar
  324. 324.
    R.I. Masel, R.P. Merrill, W.H. Miller, J. Chem. Phys. 65, 2690 (1976)CrossRefADSGoogle Scholar
  325. 325.
    N. Van Trong, Phys. Stat. Solidi (b) 93, 45 (1979)CrossRefADSGoogle Scholar
  326. 326.
    R. Conn, Phys. Rev. A 6, 439 (1972)CrossRefADSGoogle Scholar
  327. 327.
    G. Platero, V.R. Velasco, F. Garcia-Moliner, G. Benedek, L. Miglio, Surf. Sci. 143, 244 (1984)CrossRefADSGoogle Scholar
  328. 328.
    A.C. Levi, G. Benedek, L. Miglio, G. Platero, V.R. Velasco, F. Garcia-Moliner, Surf. Sci. 143, 253 (1984)CrossRefADSGoogle Scholar
  329. 329.
    H. Hoinkes, H. Nahr, H. Wilsch, Surf. Sci. 33, 516 (1972)CrossRefADSGoogle Scholar
  330. 330.
    H. Hoinkes, H. Nahr, H. Wilsch, Surf. Sci. 40, 457 (1973)CrossRefGoogle Scholar
  331. 331.
    A.A. Marvin, F. Toigo, Nuovo Cim. B 53, 25 (1979)CrossRefADSGoogle Scholar
  332. 332.
    M. Lagos, Surf. Sci. 71, 414 (1978); see, however, Levi’s comment in [279]Google Scholar
  333. 333.
    G. Armand, J. Lapujoulade, Y. Lejay, J. Phys. (Paris) 37, L187 (1976)CrossRefGoogle Scholar
  334. 334.
    G. Armand, J. Lapujoulade, Y. Lejay, Surf. Sci. 63, 143 (1977)CrossRefADSGoogle Scholar
  335. 335.
    J. Lapujoulade, Surf. Sci. 134, 529 (1983)CrossRefADSGoogle Scholar
  336. 336.
    G. Armand, J.R. Manson, Phys. Rev. Lett. 53, 1112 (1984)CrossRefADSGoogle Scholar
  337. 337.
    G. Armand, J.R. Manson, in Dynamics on Surfaces, ed. by B. Pullman, J. Jortner, A. Nitzan, B. Gerber (Reidel, Dordrecht, 1984), p. 59Google Scholar
  338. 338.
    J. Lapujoulade, Y. Lejay, G. Armand, Surf. Sci. 95, 107 (1980)CrossRefADSGoogle Scholar
  339. 339.
    G. Doyen, T.B. Grimley, Surf. Sci. 91, 51 (1980)CrossRefADSGoogle Scholar
  340. 340.
    G. Armand, J.R. Manson, Surf. Sci. 80, 532 (1979)CrossRefADSGoogle Scholar
  341. 341.
    N. Garcia, J. Ibanez, J. Solana, N. Cabrera, Surf. Sci. 60, 385 (1976)CrossRefADSGoogle Scholar
  342. 342.
    N. Garcia, Phys. Rev. Lett. 37, 912 (1976)CrossRefADSGoogle Scholar
  343. 343.
    N. Garcia, J. Chem. Phys. 67, 897 (1977)CrossRefADSGoogle Scholar
  344. 344.
    G. Benedek, N. Garcia, Ned. Tijdsch. Vacuumtechniek 16, 344 (1978)Google Scholar
  345. 345.
    G. Benedek, N. Garcia, Surf. Sci. 80, 543 (1979)CrossRefADSGoogle Scholar
  346. 346.
    G. Benedek, N. Garcia, Le Vide Suppl. 201, 818 (1980)Google Scholar
  347. 347.
    G. Benedek, N. Garcia, Surf. Sci. 103, L143 (1981)CrossRefADSGoogle Scholar
  348. 348.
    G. Benedek, in Dynamics of Gas-Surface Interaction, ed. by G. Benedek, U. Valbusa (Springer, Berlin, 1982), p. 227Google Scholar
  349. 349.
    G. Benedek, G. Brusdeylins, R.B. Doak, J.P. Toennies, J. Phys. (Paris) 42, C6–793 (1981)Google Scholar
  350. 350.
    G. Benedek, R.B. Doak, J.P. Toennies, Phys. Rev. B 28, 7277 (1983)CrossRefADSGoogle Scholar
  351. 351.
    J.H. Weare, J. Chem. Phys. 61, 2900 (1974)CrossRefADSGoogle Scholar
  352. 352.
    Y.W. Lin, S.A. Adelman, G. Wolken, Surf. Sci. 66, 376 (1977)CrossRefADSGoogle Scholar
  353. 353.
    E. Semerad, E.M. Hörl, Surf. Sci. 126, 661 (1983), observed an enhanced role of bulk phonons for scattering of Ne atoms in the one-phonon regime. However, under kinematic focussing conditions RW’s and also the optical Lucas modes (LM) seem to recover their major weight even for Ne scattering, as seen in [122, 125–126]Google Scholar
  354. 354.
    It was discovered by Doak, Harten and Toennies, [139], that in metals the surface longitudinal acoustic (LA) resonance (see Chapter 3) can yield large HAS intensities, sometimes even larger than RW’s (anomalous longitudinal resonance). G. Benedek, L. Miglio, Z. Phys. B 50, 93 (1983), have shown that in those symmetry directions where the RW is weakly localized the LA resonance may be dominant even in insulatorsGoogle Scholar
  355. 355.
    J. Hutchison, V. Celli, N. R. Hill, M. Haller, in Rarified Gas Dynamics, ed. by S.S. Fisher, Progr. Astron. Aeron. 74, 129 (1981)Google Scholar
  356. 356.
    V. Celli, N. Garcia, J. Hutchison, Surf. Sci. 87, 112 (1979)CrossRefADSGoogle Scholar
  357. 357.
    D. Evans, V. Celli, G. Benedek, J.P. Toennies, R.B. Doak, Phys. Rev. Lett. 50, 1854 (1983)CrossRefADSGoogle Scholar
  358. 358.
    W.L. Nichols, J.H. Weare, Phys. Rev. Lett. 56, 753 (1986)CrossRefADSGoogle Scholar
  359. 359.
    G. Lilienkamp, J.P. Toennies, Phys. Rev. B 26, 4752 (1982)CrossRefADSGoogle Scholar
  360. 360.
    G. Lilienkamp, J.P. Toennies, J. Chem. Phys. 78, 5210 (1983)CrossRefADSGoogle Scholar
  361. 361.
    G. Benedek, S. Miret-Artes, Surf. Sci. 339, L935 (1995)CrossRefADSGoogle Scholar
  362. 362.
    G. Benedek, R. Gerlach, A. Glebov, G. Lange, S. Miret-Artes, J.G. Skofronick, J.P. Toennies, Phys. Rev. B 53, 11211 (1996)CrossRefADSGoogle Scholar
  363. 363.
    G. Brusdeylins, R. Rechsteiner, J.G. Skofronick, J.P. Toennies, G. Benedek, L. Miglio, Phys. Rev. Lett. 54, 466 (1985)CrossRefADSGoogle Scholar
  364. 364.
    G. Bracco, M. D’Avanzo, C. Salvo, R. Tatarek, F. Tommasini, Surf. Sci. 189(190), 684 (1987)CrossRefADSGoogle Scholar
  365. 365.
    G. Wolken, J. Chem. Phys. 60, 2210 (1974)CrossRefADSGoogle Scholar
  366. 366.
    Y.W. Lin, G. Wolken Jr., J. Chem. Phys. 65, 2634 (1976)CrossRefADSGoogle Scholar
  367. 367.
    D. Eichenauer, J.P. Toennies, in Dynamics on Surfaces, ed. by B. Pullman, J. Jortner, A. Nitzan, B. Gerber (Reidel, Dordrecht, 1984), p. 1Google Scholar
  368. 368.
    D. Eichenauer, J.P. Toennies, J. Chem. Phys. 85, 532 (1986)CrossRefADSGoogle Scholar
  369. 369.
    B.H. Choi, R.T. Poe, J. Chem. Phys. 83, 1330 (1985)CrossRefADSGoogle Scholar
  370. 370.
    B.H. Choi, R.T. Poe, J. Chem. Phys. 83, 1344 (1985)CrossRefADSGoogle Scholar
  371. 371.
    H. Metiu, J. Chem. Phys. 67, 5456 (1977)CrossRefADSGoogle Scholar
  372. 372.
    W. Brenig, B. Gumhalter, J. Phys. Chem. B 108, 14549 (2004)Google Scholar
  373. 373.
    B. Gumhalter, D.C. Langreth, Phys. Rev. B 60, 2789 (1999)Google Scholar
  374. 374.
    W. Brenig, Phys. Rev. Lett. 92, 056102 (2004)Google Scholar
  375. 375.
    A. Šiber, B. Gumhalter, J. Phys.: Condens. Matter 20, 224002 (2008)ADSGoogle Scholar
  376. 376.
    A.L. Robinson, Science 218, 40 (1982)CrossRefADSGoogle Scholar
  377. 377.
    J.P. Toennies, in Solvay Conference on Surface Science, ed. by F.W. de Wette, Springer Ser. Surf. Sci., vol. 14 (Springer, Berlin, 1989)Google Scholar
  378. 378.
    C. Kaden, P. Ruggerone, J.P. Toennies, G. Zhang, G. Benedek, Phys. Rev. B 46, 13509 (1992)CrossRefADSGoogle Scholar
  379. 379.
    R. Heid, K.P. Bohnen, Phys. Rep. 387, 151 (2003)CrossRefADSMathSciNetGoogle Scholar
  380. 380.
    G. Benedek, M. Bernasconi, V. Chis, E. Chulkov, P.M. Echenique, B. Hellsing, J.P. Toennies, J. Phys. Cond. Matter 21, 084020 (2010)CrossRefADSGoogle Scholar
  381. 381.
    V. Chis, B. Hellsing, G. Benedek, M. Bernasconi, E.V. Chulkov, J.P. Toennies, Phys. Rev. Lett., 101, 206102 (2008); 103, 069902 (2009)Google Scholar
  382. 382.
    J. Braun, P. Ruggerone, G. Zhang, J.P. Toennies, G. Benedek, Phys. Rev. B 79, 205423 (2009)CrossRefADSGoogle Scholar
  383. 383.
    I.Y. Sklyadneva, G. Benedek, E.V. Chulkov, P.M. Echenique, R. Heid, K.-P. Bohnen, J.P. Toennies, Phys. Rev. Lett. 107, 095502 (2011)CrossRefADSGoogle Scholar
  384. 384.
    G. Benedek, M. Bernasconi, K.-P. Bohnen, D. Campi, E.V. Chulkov, P.M. Echenique, R. Heid, IYu. Sklyadneva, J.P. Toennies, Phys. Chem. Chem. Phys. 16, 7159 (2014)CrossRefGoogle Scholar
  385. 385.
    G. Benedek, U. Valbusa (eds.), Dynamics of Gas-Surface Interaction, Springer Series in Chemical Physics, vol. 21. (Springer, Berlin, 1981)Google Scholar
  386. 386.
    V. Celli, in Many-Body Phenomena at Surfaces, ed. by D. Langreth, H. Suhl (Academic, Orlando, 1984), p. 315Google Scholar
  387. 387.
    V. Celli, in Surface Phonons (Chap. 6), ed. by F.W. de Wette, W. Kress (Springer, Berlin, 1992)Google Scholar
  388. 388.
    F. Garcia-Moliner, in Interaction of Atoms and Molecules with Solid Surfaces, ed. by V. Bortolani, N.H. March, M.P. Tosi (Plenum, New York, 1990), pp. 71–116Google Scholar
  389. 389.
    Ch. Wöll, Appl. Phys. A 53, 377 (1991)CrossRefADSGoogle Scholar
  390. 390.
    R.B. Doak, in Atomic and Molecular Beam Methods, vol. 2, ed. by G. Scoles, D. Lané, U. Valbusa (Oxford University Press, New York, 1992), p. 384Google Scholar
  391. 391.
    J.P. Toennies, Superlattices Microstr. 7(3), 193 (1990)CrossRefADSGoogle Scholar
  392. 392.
    J.P. Toennies, J. Phys.: Condens. Matter 5, A25–A40 (1993)ADSGoogle Scholar
  393. 393.
    F. Hofmann, J.P. Toennies, Chem. Rev. 96, 1307 (1996)CrossRefGoogle Scholar
  394. 394.
    S.A. Safron, in Advances in Chemical Physics, vol. XCV, ed. by I. Prigogine and S.A. Rice (Wiley, New York, 1996)Google Scholar
  395. 395.
    G.G. Rusina, E.V. Chulkov, Russ. Chem. Rev. 82(6), 483–510 (2013)CrossRefADSGoogle Scholar
  396. 396.
    A.P. Jardine, H. Hedgeland, G. Alexandrowicz, W. Allison, J. Ellis, Prog. Surf. Sci. 84, 323 (2009)CrossRefADSGoogle Scholar
  397. 397.
    E. Hulpke (ed.), Helium Atom Scattering from Surfaces (Springer, Berlin, 1992)Google Scholar
  398. 398.
    V. Celli, Interaction of Atoms with Surfaces, in Landolt-Börnstein, New Series III, vol. 24: Physics of Solid Surfaces, ed. by G. Chiarotti (Springer, Berlin, 1994/1995), Part c, p. 278Google Scholar
  399. 399.
    R.F. Wallis, S.Y. Tong, Surface Phonons, in Landolt-Börnstein, New Series III, vol. 24: Physics of Solid Surfaces, ed. by G. Chiarotti (Springer, Berlin, 1994/1995) Part b, p. 434Google Scholar
  400. 400.
    M. Rocca, Surface Phonon Dispersion, in Landolt-Börstein, New Series III/42.A2/4.5 (Springer, Berlin, 2002)Google Scholar
  401. 401.
    G. Benedek, D. Campi, J.P. Toennies, In Physics of Solid Surfaces. Subvol. A, Landolf-Börnstein, New Series 45A ed. by P. Chiaradia and G.F. Ciarotti, Chap. 10, p. 572–646 (2015)Google Scholar
  402. 402.
    G. Benedek, J.P. Toennies, in The First Thirty Years of Surface Science, ed. by C.B. Duke (Elsevier, Amsterdam, 1994), and Surf. Sci. 299/300, 587 (1994)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Università di Milano-BicoccaMilanItaly
  2. 2.Max Planck Institute for Dynamics and Self-OrganizationGöttingenGermany
  3. 3.Donostia International Physics CenterDonostia/San SebastianSpain

Personalised recommendations