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Review of theories on ionization in fast ion-atom collisions with prospects for applications to hadron therapy

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Abstract

This study emphasizes the need for a systematic and in-depth connection between the progress in quantum theory of energetic ion collisions and applications to hadron therapy. Scattering theory for fast ion beams has reached its stage of development where accurate and robustly applicable methodologies can advantageously be exported to applied fields such as space research, fusion energy program, medicine, etc. In particular, distorted wave collision theories at high energies readily provide total, partial and fully differential cross sections for inelastic collisions of ionic projectiles with any target system. By numerous and thorough testings, such theoretical cross sections were found to exhibit excellent agreement with experimental data on atomic targets. Adequate extensions of these methods to molecular targets were also accomplished with computational efforts that are approximately comparable to that for multi-electron atomic targets. This was done by using the standard Slater-type atomic basis functions for any molecular targets, including tissue-equivalent materials (e.g. water) of relevance to hadron therapy. This expertize needs to be brought to medicine through ion transport physics, which most frequently employs the crude Bragg sum rule for obtaining molecular cross sections as linear combination of atomic cross sections. Relativistic distorted wave theories are also available, but not currently in use for modeling the passage of relativistic ions through tissue, as needed in hadron therapy of deep-seated tumors. It is high time for extensive and thorough applications of the well-established distorted wave scattering theories to fast collisions of bare and partially clothed multiple charged ions with water molecule. This type of application would provide the most accurate data bases for various cross sections (on electron capture, excitation, ionization, etc) that can be used as reliable entry data for subsequent Monte Carlo simulations of energy losses of ions during their passage through tissue. In order to gain in overall efficiency, these theoretical cross sections could be precomputed at sufficiently dense multi-variable grids, thus yielding modules for advantageous direct sampling during stochastic simulations. Such a comprehensive strategy could provide both accurate and efficient algorithms that would incorporate the state-of-the-art methodologies from high-energy atomic scattering theory involving ion beams. This is currently missing in the physics part of hadron therapy, since all the major Monte Carlo codes customarily employ atomic cross section data bases that rely almost exclusively upon the Bethe–Bloch formula and some phenomenological expressions with fitting parameters adjusted to the limited sets of experimental data. Crucially, the need is emphasized for the introduction of a still missing Monte Carlo code which could simulate transport of ions together with secondary electrons in tissue. The current main Monte Carlo codes simulate transport of either ions or electrons, but not both simultaneously. However, energetic ions produce a large number of electrons by densely ionizing the traversed tissue and many of them are δ-electrons i.e. capable on their own of ionizing various targets. Due to their light mass and considerable energy, δ-electrons undergo multiple scatterings. Because of this cumulative effect, among all the double strand breaks of DNA molecules of tissue treated by ion therapy, some 70% are produced by δ-electrons. Hence the necessity to simulate transport of δ-electrons produced by primary ion beams. Such types of computations are presently missing from the major ion transport codes. Overall, this work thoroughly analyzes conceptual and computational advances of the leading quantum-mechanical distorted wave theories for energetic ion collisions aimed at applications to medicine. Additionally, the main strategic directions are also indicated to further cross-disciplinary fertilization between medicine and basic research on collision theory of fast heavy ions of relevance to hadron therapy.

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References

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

    Google Scholar 

  2. Belkić Dž.: Principles of Quantum Scattering Theory. Institute of Physics Publishing, Bristol (2004)

    Google Scholar 

  3. Belkić Dž.: Quantum Theory of High-Energy Ion-Atom Collisions. Taylor and Francis, London (2008)

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    CAS  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  9. Belkić Dž.: J. Phys. B 13, L589–L593 (1980)

    Google Scholar 

  10. Massey H.S.W.: Rep. Prog. Phys. 12, 248–269 (1949)

    CAS  Google Scholar 

  11. Bates D.R., Griffing G.W.: Proc. Phys. Soc. A 66, 961–971 (1953)

    Google Scholar 

  12. Boudrioua O., Champion C., Dal Cappello C., Popov Y.V.: Phys. Rev. A 75, 022720 (2007)

    Google Scholar 

  13. Champion C., Dal Cappello C., Boudrioua O., Lekadir H., Sato Y., Ohsawa D.: Phys. Rev. A 75, 032724 (2007)

    Google Scholar 

  14. Champion C., Boudrioua O., Dal Cappello C.: J. Phys. Conf. Ser. 101, 012010 (2008)

    Google Scholar 

  15. Dal Cappello C., Champion C., Boudrioua O., Lekadir H., Sato Y., Ohsawa D.: Nucl. Instr. Meth. Phys. Res. B 267, 781–790 (2009)

    CAS  Google Scholar 

  16. Bethe H.: Ann. Phys. Lpz. 5, 325–400 (1930)

    CAS  Google Scholar 

  17. Bloch F.: Ann. Phys. Lpz. 16, 285–320 (1933)

    Google Scholar 

  18. Crooks G.B., Rudd M.E.: Phys. Rev. Lett. 25, 1599–1601 (1970)

    CAS  Google Scholar 

  19. Lucas M.W., Harrison K.G.: J. Phys. B: Atom. Mol. Phys. 5, L20–L22 (1972)

    CAS  Google Scholar 

  20. Vane C.R.: IEEE Trans. Nucl. Sci. 26, 1078–1082 (1979)

    Google Scholar 

  21. Meckbach W., Nemirovsky I.B., Garibotti C.R.: Phys. Rev. A 24, 1793–1802 (1981)

    CAS  Google Scholar 

  22. Meckbach W., Vidal R., Focke P., Nemirovsky I.B., Gonzalez-Lepera E.: Phys. Rev. Lett. 52, 621–624 (1984)

    CAS  Google Scholar 

  23. P. Koschar, in Forward Electron Ejection in Ion Collisions, Book Series “Lecture Notes in Physics” (Springer, Berlin/Heidelberg, 1984), 213, pp. 129–149

  24. Glass G.A., Peter E., Berry S.D., Breinig M., Deserio R., Elston S.B., Sellin I.A.: Nucl. Instr. Meth. Phys. Res. B 10, 138–141 (1985)

    Google Scholar 

  25. Skutlartz A., Hagmann S., Schmidt-Böcking H.: J. Phys. B: At. Mol. Opt. Phys. 21, 3609–3618 (1988)

    CAS  Google Scholar 

  26. Bernardi G.C., Suárez S., Fainstein P.D., Garibotti C.R., Meckbach W., Focke P.: Phys. Rev. A 40, 6863–6872 (1989)

    CAS  Google Scholar 

  27. Bernardi G., Focke P., Suárez S., Meckbach W.: Phys. Rev. A 50, 5338–5341 (1994)

    CAS  Google Scholar 

  28. B. Fastrup, E. Horsdal-Pedersen, V.V. Afrosimov, A.A. Basalaev, M.N. Panov, in 21st International Conference on Physics of Electronic and Atomic Collisions, Sendai, Japan, July 21–27, 1999, ed. by Y. Itikawa, K. Okuno, H. Tanaka, A. Yagishita, M. Matsuzawa, AIP Conference Proceedings, 500, vol. 2 (1999), p. 462

  29. Afrosimov V.V., Basalaev A.A., Fastrup B., Horsdal-Pedersen E., Kashnikov K.V., Panov M.N.: J. Phys. B: At. Mol. Opt. Phys. 33, 4237–4242 (2000)

    CAS  Google Scholar 

  30. Hagmannn S., Ali I.: Phys. Scr. T80, 329–330 (1999)

    Google Scholar 

  31. S. Hagmannn, I. Ali, H.-J. Lüdde, E. Wagner, http://www/jrm.phys.ksu.edu/Resource/Pubs/Progress/a-1-5.pdf

  32. S. Hagmannn, I. Ali, http://www/jrm.phys.ksu.edu/Resource/Pubs/Progress/a-1-4.pdf

  33. Fiol J., Suaréz S., Fregenal D., González A.D., Fainstein P.D.: Phys. Rev. 67, 050702 (2003)

    Google Scholar 

  34. Shah M.B., McGrath C., Illescas C., Pons B., Riera A., Luna H., Crothers D.S.F., O’Rourke S.F.C., Gilbody H.B.: Phys. Rev. A 67, 010704 (2003)

    Google Scholar 

  35. Schmidt-Böcking H., Schmidt L., Weber Th., Mergel V., Jagutzki O., Czasch A., Hagmann S., Dorner R., Demkov Y., Jahnke T., Prior M., Cocke C.L., Osipov T., Landers A.: Rad. Phys. Chem. 71, 627–632 (2004)

    Google Scholar 

  36. Barrachina R.O., Sarkadi L.: Nucl. Instr. Meth. Phys. Res. B 233, 260–265 (2005)

    CAS  Google Scholar 

  37. Barrachina R.O., Sarkadi L.: Phys. Rev. A. 71, 062712 (2005)

    Google Scholar 

  38. Afaneh F., Schmidt L.Ph.H., Schöffler M., Stiebing K.E., Al-Jundi J., Dorner R.: J. Phys. B: At. Mol. Opt. Phys. 40, 1745–1753 (2007)

    CAS  Google Scholar 

  39. Martínez S., Bernardi G., Focke P., Suárez S., Fregenal D.: J. Phys. B: At. Mol. Opt. Phys. 41, 145204 (2008)

    Google Scholar 

  40. Sarkadi L., Orbán A.: Phys. Rev. Lett. 100, 133201 (2008)

    Google Scholar 

  41. Sarkadi L., Orbán A.: Nucl. Instr. Meth. Phys. Res. B. 267, 270–274 (2009)

    CAS  Google Scholar 

  42. Pedersen E.H., Larsen L.: J. Phys. B: At. Mol. Opt. Phys. 12, 4085–4098 (1999)

    Google Scholar 

  43. Gulyás L., Fainstein P.D., Shirai T.: J. Phys. B: At. Mol. Opt. Phys. 34, 1473–1483 (2001)

    Google Scholar 

  44. Rudd M.E., Kim Y.-K., Madisson D.H., Gray T.J.: Rev. Mod. Phys. 64, 441–490 (1992)

    CAS  Google Scholar 

  45. Stolterfoht N., DuBois R.D., Rivarola R.D.: Electron Emission in Heavy Ion-Atom Collisions. Springer, Berlin (1997)

    Google Scholar 

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

    CAS  Google Scholar 

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

    CAS  Google Scholar 

  48. O’Rourke S.F.C., McSherry D.M., Crothers D.S.F.: Adv. Chem. Phys. 121, 311–356 (2002)

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    CAS  Google Scholar 

  52. Rosenberg L.: Phys. Rev. D 8, 1833–1843 (1973)

    Google Scholar 

  53. Messiah A.: Quantum Mechanics, pp. 377 . Wiley, New York (1966)

    Google Scholar 

  54. Garibotti C.R., Miraglia J.E.: Phys. Rev. 21, 572–580 (1980)

    CAS  Google Scholar 

  55. Garibotti C.R., Miraglia J.E.: J. Phys. B 14, 863–868 (1981)

    CAS  Google Scholar 

  56. Garibotti C.R., Miraglia J.E.: Phys. Rev. A. 25, 1440–1444 (1982)

    CAS  Google Scholar 

  57. Vainstein L., Presnyakov L., Sobelman I.: J. Exp. Theor. Phys. JETP. 18, 1383–1385 (1964)

    Google Scholar 

  58. Vainstein L., Presnyakov L., Sobelman I.: Zh. Eksper. Teor. Fiz. 45, 2015–2021 (1964)

    Google Scholar 

  59. Presnyakov L.: J. Exp. Theor. Phys. JETP. 20, 760–761 (1965)

    Google Scholar 

  60. Presnyakov L.: Zh. Eksper. Teor. Fiz. 47, 1134–1135 (1964)

    CAS  Google Scholar 

  61. Dewangan D.P., Bransden B.H.: J. Phys. B 15, 4561–4576 (1982)

    CAS  Google Scholar 

  62. Brauner M., Briggs J.S., Klar H.: J. Phys. B 22, 2265–2287 (1989)

    CAS  Google Scholar 

  63. Brauner M., Briggs J.S., Klar H., Broad J.T., Rösel T., Jung K., Erhradt H.: J. Phys. B 24, 657–673 (1991)

    CAS  Google Scholar 

  64. Berakdar J., Briggs J.S., Klar H.: Z. Phys. D 24, 351–364 (1992)

    CAS  Google Scholar 

  65. Maulbetsch F., Briggs J.S.: Phys. Rev. Lett. 68, 2004–2006 (1992)

    CAS  Google Scholar 

  66. Maulbetsch F., Briggs J.S.: J. Phys. B 26, 1679–1696 (1993)

    CAS  Google Scholar 

  67. Berakdar J.: Phys. Rev. Lett. 72, 3799–3802 (1994)

    CAS  Google Scholar 

  68. Berakdar J.: Phys. Rev. A 54, 1480–1486 (1996)

    CAS  Google Scholar 

  69. Jones S., Madison D.H.: Phys. Rev. Lett. 81, 2886–2889 (2000)

    Google Scholar 

  70. Jones S., Madison D.H.: Phys. Rev. A 62, 042701 (2000)

    Google Scholar 

  71. L.J. Dubé, D.P. Dewangan, in 19th International Conference on the Physics of Electronic and Atomic Collisions, Book of Abstracts, (Whistler, Canada, 1995), p. 62

  72. O’Rourke S.F.C., Crothers D.S.F.: J. Phys. B 30, 2443–2454 (1997)

    Google Scholar 

  73. Gulyás L., Fainstein P.D.: J. Phys. B 31, 3297–3305 (1998)

    Google Scholar 

  74. Ciappina M.F., Cravero W.R., Garibotti C.R.: J. Phys. B 36, 3775–3786 (2003)

    CAS  Google Scholar 

  75. Ciappina M.F., Cravero W.R.: Braz. J. Phys. B 36, 524–528 (2006)

    CAS  Google Scholar 

  76. Geltman S.: Proc. Phys. Soc. 75, 67–76 (1960)

    CAS  Google Scholar 

  77. McDowell M.R.C., Williamson J.H.: Phys. Lett. 4, 159–161 (1963)

    CAS  Google Scholar 

  78. Belly O., Schwartz S.B.: J. Phys. B 2, 159–161 (1969)

    Google Scholar 

  79. Gayet R., Janev R., Salin A.: J. Phys. B 6, 993–1002 (1973)

    CAS  Google Scholar 

  80. Bell K.L., Kingston A.E., Madden P.J.: J. Phys. B 11, 3977–3982 (1978)

    CAS  Google Scholar 

  81. Sidis V., Kubach C., Fussen D.: Phys. Rev. A 27, 2431–2446 (1983)

    CAS  Google Scholar 

  82. Fussen D., Claeys W.: J. Phys. B 17, L89–L93 (1984)

    CAS  Google Scholar 

  83. Ermolaev A.M.: J. Phys. B 21, 81–101 (1988)

    CAS  Google Scholar 

  84. Ermolaev A.M., Joachain C.J.: Phys. Rev. A 62, 012710 (2000)

    Google Scholar 

  85. Lucey S., Whelan C.T., Allan R.J., Walters H.R.J.: J. Phys. B 29, L489–L495 (1996)

    CAS  Google Scholar 

  86. Kazansky A.K., Taulbjerg K.: J. Phys. B 29, 4465–4475 (1996)

    CAS  Google Scholar 

  87. Peart B., Walton D.S., Dolder K.T.: J. Phys. B 3, 1346–1356 (1970)

    CAS  Google Scholar 

  88. Walton D.S., Peart B., Dolder K.T.: J. Phys. B 4, 1343–1348 (1971)

    CAS  Google Scholar 

  89. Peart B., Grey R., Dolder K.T.: J. Phys. B 9, 3047–3053 (1976)

    CAS  Google Scholar 

  90. Dolder K., Peart B.: Rep. Progr. Phys. 48, 1283–1332 (1985)

    CAS  Google Scholar 

  91. Andersen L.H., Mathur D., Schmidt H.T., Vejby-Christensen J.: Phys. Rev. Lett. 74, 892–895 (1995)

    CAS  Google Scholar 

  92. Fritioff K., Sandström J., Andersson P., Hanstorp D., Hellberg F., Thomas R., Geppert W., Larsson M., Österdahl F., Collins G.F., Pegg D.J., Danared H., Källberg A., Gibson N.D.: Phys. Rev. A 69, 042707 (2004)

    Google Scholar 

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

    Google Scholar 

  94. Belkić Dž., Mančev I., Mergel V.: Phys. Rev. A 55, 378–395 (1997)

    Google Scholar 

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

    CAS  Google Scholar 

  96. C.J. Joachain, M. Terao, Private Communication (1991)

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

    CAS  Google Scholar 

  98. Drake G.W.F.: Nucl. Inst. Meth. Phys. Res. B 31, 7–13 (1988)

    Google Scholar 

  99. Gradshteyn I.S., Ryzhik I.M.: Tables of Integrals, Series and Products. Academic Press, New York (1980)

    Google Scholar 

  100. Dollard J.D.: J. Math. Phys. 5, 729–738 (1964)

    Google Scholar 

  101. Melchert F., Krüdener S., Huber K., Salzborn E.: J. Phys. B 32, L139–L144 (1999)

    CAS  Google Scholar 

  102. Rotenberg M., Stein J.: Phys. Rev. 182, 1–7 (1969)

    CAS  Google Scholar 

  103. Yu S.S., Logan B.G., Barnard J.J., Bieniosek F.M., Briggs R.J., Cohen R.H., Coleman J.E., Davidson R.C., Friedman A., Gilson E.P., Grisham L.R., Grote D.P., Henestroza E., Kaganovich I.D., Kireeff Covo M., Kishek R.A., Kwan J.W., Lee E.P., Leitner M.A., Lund S.M., Molvik A.W., Olson C.L., Qin H., Roy P.K., Sefkow A., Seidl P.A., Startsev E.A., Vay J-L., Waldron W.L., Welch D.R.: Nucl. Fusion. 47, 721–727 (2007)

    CAS  Google Scholar 

  104. Kraft G.: Prog. Part. Nucl. Phys. 45, S473–S544 (2000)

    Google Scholar 

  105. Kraft G.: Nucl. Instr. Meth. Phys. Res. A 454, 1–10 (2000)

    CAS  Google Scholar 

  106. Krämer M., Jäkel O., Kraft G., Schardt D., Weber U.: Phys. Med. Biol. 45, 3299–3317 (2000)

    Google Scholar 

  107. Krämer M., Scholz M.: Phys. Med. Biol. 45, 3319–3330 (2000)

    Google Scholar 

  108. Amaldi U., Kraft G.: Rep. Prog. Phys. 68, 1861–1882 (2005)

    CAS  Google Scholar 

  109. Nakano T., Suzuki Y., Ohno T., Kato S., Suzuki M., Morita S., Sato S., Oka K., Tsujii H.: Clin. Cancer Res. 12, 2185–2190 (2006)

    CAS  Google Scholar 

  110. Schulz-Ertner D., Jäkel O., Schlegel W.: Semin. Radiat. Oncol. 16, 249–259 (2006)

    Google Scholar 

  111. Schulz-Ertner D., Tsujii H.: J. Clin. Oncol. 25, 953–964 (2007)

    Google Scholar 

  112. Porta A., Agosteo S., Campi F., Caresana M.: Rad. Protect. Dosim. 132, 29–41 (2008)

    CAS  Google Scholar 

  113. Bortfeld T.: Med. Phys. 24, 2024–2033 (1997)

    CAS  Google Scholar 

  114. Hollmark M., Uhrdin J., Belkić Dž., Gudowska I., Brahme A.: Phys. Med. Biol. 49, 3247–3265 (2004)

    CAS  Google Scholar 

  115. Hollmark M., Gudowska I., Belkić Dž., Brahme A., Sobolevsky N.: Phys. Med. Biol. 53, 3477–3491 (2008)

    CAS  Google Scholar 

  116. Dž. Belkić, SHIELD-HIT: an optimal Monte Carlo code for simulations of transport of protons and heavier ions in tissue, Invited lecture, in: Int. Conf. Comp. Math. Meth. Sci. Eng., Uppsala, Sweden, June 4–8, 2004, Proceedings (2004), ed. by E. Brändas, J. Vigo-Aguiar, pp. 10–16

  117. Gudowska I., Sobolevsky N., Andreo P., Belkić Dž., Brahme A.: Phys. Med. Biol. 49, 1933–1958 (2004)

    Google Scholar 

  118. Geithner O., Andreo P., Sobolevsky N., Hartmann G., Jäkel O.: Phys. Med. Biol. 51, 2279–2292 (2006)

    CAS  Google Scholar 

  119. Andreo P.: Phys. Med. Biol. 55, N205–N215 (2009)

    Google Scholar 

  120. Boyle P., Ferlay J.: Ann. Oncol. 16, 481–488 (2005)

    CAS  Google Scholar 

  121. Technical Report Series, No. 461, Vienna (2008)

  122. Glimelius B., Montelius A.: Radiother. Oncol. 83, 105–109 (2007)

    Google Scholar 

  123. Lodge M., Pijls-Johannesma M., Stirk L., Munro A.J., Ruysscher D.D., Jefferson T.: Radiother. Oncol. 83, 110–122 (2007)

    Google Scholar 

  124. Olsen D.R., Bruland Ø.S., Frykholm G., Norderhaug I.N.: Radiother. Oncol. 83, 123–132 (2007)

    Google Scholar 

  125. Jäkel O., Land B., Combs S.E., Schulz-Ertner D., Debus J.: Radiother. Oncol. 83, 133–138 (2007)

    Google Scholar 

  126. Brada M., Pijls-Johannesma M., Ruysscher D.D.: J. Clin. Oncol. 25, 965–970 (2007)

    Google Scholar 

  127. Tepper J.E.: J. Clin. Oncol. 26, 2436–2437 (2008)

    Google Scholar 

  128. Suit H., Kooy H., Trofimov A., Farr J., Munzenrider J., DeLaney T., Loeffler J., Clasie B., Safai S., Paganetti H.: Radiother. Oncol. 86, 148–153 (2008)

    Google Scholar 

  129. Goitein M., Cox J.D.: J. Clin. Oncol. 26, 175–176 (2008)

    Google Scholar 

  130. Schulz R.J., Kagan A.R.: Int. J. Rad. Oncol. Biol. Phys. 72, 1307–1309 (2008)

    Google Scholar 

  131. Suit H., Kooy H.: Int. J. Rad. Oncol. Biol. Phys. 72, 1309–1310 (2008)

    Google Scholar 

  132. Belkić K.: Molecular Imaging Through Magnetic Resonance in Clinical Oncology. Cambridge International Science Publishing, Cambridge, UK (2003)

    Google Scholar 

  133. Bortfeld T.: Phys. Med. Biol. 51, R363–R379 (2006)

    Google Scholar 

  134. Enghardt W., Crespo P., Fiedler F., Hinz R., Pawelke J., Pönisch F.: Nucl. Instr. Meth. Phys. Res. A 525, 284–288 (2004)

    CAS  Google Scholar 

  135. Enghardt W., Parodi K., Crespo P., Fiedler F., Pawelke J., Pönisch F.: Radiother. Oncol. 73, S96–S98 (2004)

    Google Scholar 

  136. Pönisch F., Parodi K., Hasch B.G., Enghardt W.: Phys. Med. Biol. 49, 5217–5232 (2004)

    Google Scholar 

  137. Parodi K., Paganetti H., Cascio H., Flanz J.B., Bonab A.A., Alpert N.M., Lohmann K., Bortfeld T.: Med. Phys. 34, 419–453 (2007)

    CAS  Google Scholar 

  138. Wilson R.R.: Radiology 47, 487–491 (1946)

    CAS  Google Scholar 

  139. Wilson R.R.: Phys. Rev. 71, 385–386 (1947)

    CAS  Google Scholar 

  140. Tobias C.A., Anger H.O., Lawrence J.H.: Am. J. Roentg. Rad. Ther. Nucl. Med. 67, 1–27 (1952)

    CAS  Google Scholar 

  141. C.A. Tobias, J.E. Roberts, J.H. Lawrence, B.V. Low-Beer, H.O. Anger, J.L. Born, R. McCombs, C. Huggins, in Peaceful Uses of Atomic Energy, Proceedings of International Conference, Geneva (1955), pp. 95–106

  142. Malis L.I., Loevinger R., Kruger L., Rose J.L.: Science 126, 302–303 (1957)

    CAS  Google Scholar 

  143. Lawrence J.H., Tobias C.A., Born J.L., McCombs R., Roberts J.L., Anger H.O., Low-Beer B.V., Huggins C.: Cancer Res. 18, 121–134 (1958)

    CAS  Google Scholar 

  144. Larsson B., Leksell L., Rexed B., Sourander P., Mair W., Andersson B.: Nature 182, 1222–1223 (1958)

    CAS  Google Scholar 

  145. Larsson B., Kihlman B.A.: Int. J. Rad. Biol. 2, 8–19 (1960)

    CAS  Google Scholar 

  146. Brahme A., Nilsson J., Belkić Dž.: Acta Oncol. 40, 725–734 (2001)

    CAS  Google Scholar 

  147. Belkić Dž.: Adv. Quantum Chem. 51, 157–233 (2006)

    Google Scholar 

  148. Belkić Dž., Belkić K.: J. Math. Chem. 43, 395–425 (2008)

    Google Scholar 

  149. Belkić Dž., Belkić K.: J. Math. Chem. 45, 563–597 (2009)

    Google Scholar 

  150. Belkić Dž., Belkić K.: J. Math. Chem. 45, 790–818 (2009)

    Google Scholar 

  151. Belkić Dž., Belkić K.: J. Math. Chem. 45, 819–858 (2009)

    Google Scholar 

  152. Belkić Dž.: Adv. Quantum Chem. 56, 95–179 (2009)

    Google Scholar 

  153. Stopping powers and ranges for protons and alpha particles, ICRU Report 49: International Commission of Radiation Units and Measurements (Barthesda, MD, USA, 1993)

  154. Stopping powers and ions heavier than helium, ICRU Report 73: International Commission of Radiation Units and Measurements (Oxford University Press, 2005)

  155. Bragg W.H.: Phil. Mag. 8, 719–725 (1904)

    CAS  Google Scholar 

  156. Bragg W.H., Kleeman R.D.: Phil. Mag. 8, 726–738 (1904)

    CAS  Google Scholar 

  157. Bragg W.H., Kleeman R.D.: Phil. Mag. 10, 318–340 (1905)

    CAS  Google Scholar 

  158. Lomax A.: Phys. Med. Biol. 44, 185–205 (1999)

    CAS  Google Scholar 

  159. Cella L., Lomax A., Miralbell R.: Phys. Medica 17(Supplement 1), S100–S102 (2001)

    Google Scholar 

  160. Lomax A.J., Boehringer T., Coray A., Egger E., Goitein G., Grossmann M., Juelke P., Lin S., Pedroni E., Rohrer B., Roser W., Rossi B., Siegenthaler B., Stadelmann O., Stauble H., Vetter C., Wisser L.: Med. Phys. 28, 317–324 (2001)

    CAS  Google Scholar 

  161. Hendee W.R.: Med. Phys. 26, 1185–1187 (1999)

    Google Scholar 

  162. Schulz R.J.: Med. Phys. Lett. Ed. 26, 2515 (1999)

    CAS  Google Scholar 

  163. Lomax A.J.: Med. Phys. Lett. Ed. 27, 622–623 (2000)

    CAS  Google Scholar 

  164. Tsujii H., Bortfeld T.: Radiother. Oncol. 58, S72 (2001)

    Google Scholar 

  165. Chaudhri M.A.: Radiother. Oncol. 58, S22 (2001)

    Google Scholar 

  166. M.A. Chaudhri, 600, 49–51 (2001)

  167. Olivera G.H., Martínez A.E., Rivarola R.D., Fainstein P.D.: Rad. Res. 144, 241–247 (1995)

    CAS  Google Scholar 

  168. Olivera G.H., Fainstein P.D., Rivarola R.D.: Phys. Med. Biol. 41, 1633–1647 (1996)

    CAS  Google Scholar 

  169. Bernardi G.C., Fainstein P.D., Garibotti C.R., Suárez S.: J. Phys. B 23, L139–L143 (1990)

    CAS  Google Scholar 

  170. Dalgarno A., Griffing G.W.: Proc. Phys. Soc. A 232, 423–434 (1955)

    CAS  Google Scholar 

  171. Dalgarno A., Griffing G.W.: Proc. Phys. Soc. A 248, 415–428 (1958)

    CAS  Google Scholar 

  172. Fainstein P.D., Ponce V.H., Martínez A.E.: Phys. Rev. A 47, 3055–3061 (1993)

    CAS  Google Scholar 

  173. Olivera G.H., Martínez A.E., Rivarola R.D.: Phys. Rev. A 49, 603–606 (1994)

    CAS  Google Scholar 

  174. Martínez A.E., Rivarola R.D., Fainstein P.D.: Nucl. Instr. Meth. B 111, 7–11 (1996)

    Google Scholar 

  175. Houamer S., Popov Yu.V., Dal Cappello C., Champion C.: Nucl. Instr. Meth. Phys. Res. B 267, 802–806 (2009)

    CAS  Google Scholar 

  176. Barkas W.H.: Nuclear Research Emulsions. Academic Press, New York (1963)

    Google Scholar 

  177. Porter L.E.: Adv. Quantum Chem. 46, 91–119 (2004)

    CAS  Google Scholar 

  178. Moccia R.: J. Chem. Phys. 40, 2186–2192 (1964)

    CAS  Google Scholar 

  179. Siegbahn K., Nordling C., Johansson G., Hedman J., Hedén P.F., Hamrin K., Gelius U., Bergmark T., Werme L.O., Manne R., Baer Y.: ESCA Applied to Free Molecules. North-Holland, Amsterdam (1969)

    Google Scholar 

  180. Senger B., Rechenmann R.V.: Nucl. Instr. Meth. Phys. Res. B 2, 204–207 (1984)

    Google Scholar 

  181. McCann J.F.: J. Phys. B 18, L569–L573 (1985)

    CAS  Google Scholar 

  182. Deco G.R., Rivarola R.D.: J. Phys. B 19, 1759–1770 (1986)

    CAS  Google Scholar 

  183. Deco G.R., Rivarola R.D.: J. Phys. B 20, 5125–5177 (1987)

    Google Scholar 

  184. Deco G.R., Fainstein P.D., Rivarola R.D.: Nuc. Instr. Meth. B 35, 100–102 (1988)

    Google Scholar 

  185. Dž. Belkić, Review of leading theories for high-energy heavy particle collisions with prospects for applications to medicine, Invited lecture, The 6th Int. Conf. on “Radiation Damage in Biomolecular Systems” (RADAM), Frankfurt, Germany, July 1–5, 2009. Book of Abstracts (Frankfurt Institute for Advanced Studies (FIAS), Goethe University, 2009), ed. by Solov’yov, pp. 48–49 (http://fias.uni-frankfurt.de/radam2009)

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    Dževad Belkić

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Belkić, D. Review of theories on ionization in fast ion-atom collisions with prospects for applications to hadron therapy. J Math Chem 47, 1366–1419 (2010). https://doi.org/10.1007/s10910-010-9662-x

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