Skip to main content

Advertisement

Log in

Elastic and inelastic scattering of low-energy electrons from gas-phase \(\hbox {C}_{\mathbf {60}}\): elastic scattering angular distributions and coexisting solid-state features revisited

  • Regular Article – Atomic and Molecular Collisions
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

We revisit the crossed-beam experimental results for the elastic scattering of low-energy electrons from gas-phase \(\hbox {C}_{60}\), with an emphasis on comparison with the results from ab initio calculations. The relevance of Vincent McKoy’s work, the SMC method, in this respect is demonstrated by our re-normalized data. This is evidenced in the DCS-energy (eV) and DCS-scattering angle (\(\theta )\) space, i.e., in 3D distributions, as the more comprehensive and distinctive features of electron scattering from this typically high-symmetry and large molecule of \(\hbox {C}_{60}\). An earlier inconsistency between the experimental data and theoretical absolute DCS values is solved, by re-normalizing the cross sections. Absolute scales are also placed on the inelastic scattering DCS of vibrational and electronic excitations, with the latter being compared with photoabsorption cross sections. In addition, some coexisting solid-state phase features, which emerged in the free molecules of \(\hbox {C}_{60}\), are summarized using low-energy electron spectroscopy.

Graphic Abstract

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Data Availability Statement

The manuscript has no associated data, or the data will not be deposited. [Authors’ comment: Tables of our re-normalized elastic data, vibrational and electronic excitation data are available from the corresponding author on reasonable request.]

Notes

  1. Study of Electron Collisions with Interstellar Molecules and Interstellar Fine Particles proposed to NASA, but the latter subject was not accomplished because the particle size distribution could not be specified for the fine particles in those days.

References

  1. K. Takatsuka, V. McKoy, Phys. Rev. A 24, 2473 (1981)

    Article  ADS  Google Scholar 

  2. K. Takatsuka, V. McKoy, Phys. Rev. A 30, 1734 (1984)

    Article  ADS  Google Scholar 

  3. H. Tanaka, L. Boesten, K. Onda, O. Ohashi, J. Phys. Soc. Jpn 63, 485 (1994)

    Article  ADS  Google Scholar 

  4. H. Tanaka, L. Boesten, O. Ohashi, M. Kawasaki, The 1992 Fall Meeting of The Physical Society of Japan (Sep. 1992, University of Tokyo), 26pZK7 (in Japanese),

  5. R. Hofstadter, Rev. Mod. Phys. 28, 214 (1956)

  6. C. Winstead, V. McKoy, Phys. Rev. A 73, 012711 (2006)

    Article  ADS  Google Scholar 

  7. R.R. Lucchese, F.A. Gianturco, N. Sanna, Chem. Phys. Lett. 305, 413 (1999)

    Article  ADS  Google Scholar 

  8. W. Krätschmer, L.D. Lamb, K. Fostiropoulos, D.R. Huffman, Nat. 347, 354 (1990)

    Article  ADS  Google Scholar 

  9. H.W. Kroto, J.R. Heath, S.C. OBrian, R.F. Curl, R.E. Smalley, Nat. 318, 162 (1985)

  10. P.R. Buseck, S.J. Tsipursky, R. Hettich, Sci. 257, 215 (1992)

    Article  ADS  Google Scholar 

  11. J. Cami, J. Bernard-Salas, E. Peeters, S.E. Malek, Sci. 329, 1180 (2010)

    Article  ADS  Google Scholar 

  12. NASA, Mission News, JPL News Release 2010-243, JPL Caltech, July, 22, (2010)

  13. NASA’s Spitzer Space Telescope has at last found buckyballs in space, as illustrated by this artist’s conception showing the carbon balls coming out from the type of object where they were discovered. https://www.nasa.gov/feature/goddard/2019/soccer-balls-in-space, accessed on Aug. Sept. 2, (2021)

  14. M.A. Cordiner, H. Linnartz, N.L.J. Cox, J. Cami, F. Najarro, C.R. Proffitt, R. Lallement, P. Ehrenfreund, B.H. Foing, T.R. Gull, Astrophys. J. Lett. 875, L28 (2019)

    Article  ADS  Google Scholar 

  15. M.L. Heger, Lick Obs. Bull. 10, 146 (1922)

    ADS  Google Scholar 

  16. E.K. Campbell, J.P. Maier, Astrophys. J. 858, A36 (2018)

    Article  ADS  Google Scholar 

  17. J.W. Keller, M.A. Coplan, Chem. Phys. Lett. 193, 89 (1992)

    Article  ADS  Google Scholar 

  18. A.W. Burose, T. Dresch, A.M. Ding: XVI International Symposium on Mole. Beams Asilomar, June 7-12, 1992, 243, Z. Phys. D: At. Mol. Clusters, 26, S294 (1993)

  19. G. Bulliard, M. Allan, S. Leach, Chem. Phys. Lett. 209, 434 (1993)

    Article  ADS  Google Scholar 

  20. R. Abouaf, J. Pommier, S. Cvejanovic, Chem. Phys. Lett. 213, 503 (1993)

    Article  ADS  Google Scholar 

  21. O. Elhamidi, J. Pommier, R. Abouaf, J. Phys. B: At. Mol. Opt. Phys. 30, 4633 (1997)

    Article  ADS  Google Scholar 

  22. M. Lezius, P. Scheier, T.D. Märk, Chem. Phys. Lett. 203, 232 (1993)

    Article  ADS  Google Scholar 

  23. T. Jaffke, E. Illenberger, M. Lezius, S. Matejcik, D. Smith, T.D. Märk, Phys. Lett. 226, 213 (1994)

    Google Scholar 

  24. J. Huang, H.S. Carman, R.N. Compton, J. Phys. Chem. 99, 171 (1995)

    Google Scholar 

  25. Z. Felfli, K. Suggsa, N. Nicholas, A.Z. Msezane, Int. J. Mol. Sci. 21, 3159 (2020). (therein other references are well cited)

  26. J. Berkowitz, J. Chem. Phys. 111, 1446 (1999). (therein earlier references in the 1990s)

  27. L.R. Hargreaves, B. Lohman, C. Winstead, V. McKoy, Phys. Rev. A 82, 062716 (2010)

    Article  ADS  Google Scholar 

  28. L.G. Gerchikov, P.V. Efimov, V.M. Mikoushkin, A.V. Solovyov, Phys. Rev. Lett. 81, 2707 (1998)

    Article  ADS  Google Scholar 

  29. Y.S. Gordeev, V.M. Mikoushkin, A.V. Solovyov, Mol. Mater. 13, 1 (2000)

    Google Scholar 

  30. F.A. Gianturco, R.R. Lucchese, N. Sanna, J. Phys. B: At. Mol. Opt. Phys. 32, 2181 (1999)

    Article  ADS  Google Scholar 

  31. F.A. Gianturco, R.R. Lucchese, J. Chem. Phys. 111, 6739 (1999)

    Article  ADS  Google Scholar 

  32. M.Y. Amusia, L.V. Chernysheva, V.K. Dolmatov, J. Phys. B: At. Mol. Opt. Phys. 52, 085201 (2019)

    Article  ADS  Google Scholar 

  33. H. Tanaka, L. Boesten, D. Matsunaga, T. Kudo, J. Phys. B At. Mol. Opt. Phys. 21, 125 (1988)

    Article  Google Scholar 

  34. A.F. Hebard, R.C. Hadden, R.M. Fleming, A.R. Kortan, Appl. Phys. Lett. 59, 2109 (1991)

    Article  ADS  Google Scholar 

  35. A. Popović, G. Dražič, J. Marsel, Rapid Commun. In. Mass Spectrom. 8, 985 (1994)

    Article  ADS  Google Scholar 

  36. L. Boesten, H. Tanaka, At. Data Nucl. Data Tables 52, 25 (1992)

    Article  ADS  Google Scholar 

  37. D.C. Cartwright, G. Csanak, S. Trajmar, D.F. Register, Phys. Rev. A 45, 1602 (1992)

    Article  ADS  Google Scholar 

  38. S.K. Srivastava, A. Chutjian, S. Trajmar, J. Chem. Phys. 63, 2659 (1975)

    Article  ADS  Google Scholar 

  39. S. Trajmar, D. F. Register, Electron Molecule Collisions, Eds. K. Takayanagi and I. Shimamura, (Plenum, New York, 1984)

  40. K.A. Dubey, J. Jose, Eur. Phys. J. Plus 136, 713 (2021)

    Article  Google Scholar 

  41. S. Trajmar, D.F. Register, A. Chutjian, Phys. Rep. 97, 219 (1983)

    Article  ADS  Google Scholar 

  42. M.J. Brunger, S.J. Buckman, Phys. Rep. 357, 215 (2002)

    Article  ADS  Google Scholar 

  43. M. Inokuti, in Nuclear and Atomic Data for Radiotherapy and Related Radiobiology, Proceedings of an Advisory Group Meeting on Nuclear and Atomic Data for Radiotherapy and Related Radiobiology, organized by IAEA in cooperation with Radiobiology Institute TNO and held Rijswick, Netherlands, 16-20 Sep. 1985, pp. 357-65 (IAEA, Vienna, 1987)

  44. Y. Fujikawa, K. Sakai, A. Koma, Surface Science 176, 357 (1996)

    Google Scholar 

  45. G. Grenterblum, J.J. Pireaux, P.A. Thiry, R. Caudano, J.P. Vigneron, Ph. Lambin, A.A. Lucas, Phys. Rev. Lett. 67, 2171 (1991)

    Article  ADS  Google Scholar 

  46. D.S. Bethune, O. Meijer, W.C. Tang, H.J. Rosen, W.G. Golden, H. Seki, A.A. Brown, M.S. de Vries, Chem. Phys. Lett. 179, 181 (1991)

    Article  ADS  Google Scholar 

  47. R.L. Cappelletti, J.R.D. Copley, W.A. Kamitakahara, J.R.F. Li, D.R. Lannin, Phys. Rev. Lett. 66, 3261 (1991)

    Article  ADS  Google Scholar 

  48. E.W. Schlag, R.D. Levine, J. Chem. Phys. 96, 10608 (1992)

    Article  Google Scholar 

  49. D. A. Gurnett, W. S. Kurth, Nature Astronomy 3, 1024 (2019). Note that the plasma density in the outer heliosphere is typically about \(\text{0.002/cm}^{3}\). But the first electron density measured by the Voyager 2 plasma wave instrument in the interstellar medium, \(0.039/\text{cm }^{3} \pm 15{\%}\), was on 30 January 2019 at a heliocentric radial distance of 119.7 au

  50. C.Z. Li, Z.L. Miškovič, F.Q. Goodman, Y.N. Wang, J. App. Phys. 113, 184301 (2013)

    Article  ADS  Google Scholar 

  51. A.V. Zayats, I.I. Smolyaninov, A.A. Maradudin, Phys. Rep. 408, 131 (2005)

    Article  ADS  Google Scholar 

  52. A.V. Verkhovtsev, A.V. Korol, A.V. Solovyov, P. Bolognesi, A. Ruocco, L. Avaldi, J. Phys. B. At. Mol. Opt. Phys. 45, 14100 (2012)

    Google Scholar 

  53. R. Kuzuo, M. Terauchi, M. Tanaka, Y. Saito, H. Shinohara, Jap. J. of Appl. Phys. 30, L1817 (1991)

    Article  ADS  Google Scholar 

  54. M. Terauchi, N.K. Gakkaishi, J. Crystallogr. Soc. Jpn. 44, 277 (2002). (in Japanese)

  55. H. Raether, Excitation of Plasmons and Interband Transitions by Electrons, Springer Tracts in Modern Physics, Vol. 88, (Springer-Verlag, Berlin, Heidelberg, New York, 1980): conventional evaluation criteria for testing the bulk plasmon excitations in solids; one is for the dispersion relation: \(E_{p}(\theta ) \approx E_{p}\)(0) \(+ \mathit{A} \cdot \theta ^{2}\), \(A =(6\cdot E_{f} \cdot E_{0}) / (5\cdot E_{p})\), and another for the differential cross section: \(d\sigma /d\theta \propto \theta _{E} / (\theta _{E}^{2} +\theta ^{2})\), \(\theta _{E} = E_{p} /(2\cdot E_{0})\), where \(E_{p}\) is the plasmon energy, \(E_{f}\) is the Fermi energy, and \(E_{0}\) the impact energy, respectively

  56. W.S.M. Werner, V. Astašauskas, P. Ziegler, A. Bellissimo, G. Stefani, L. Linhart, F. Libisch, Phys. Rev. Lett. 125, 196603 (2020)

    Article  ADS  Google Scholar 

  57. R.F. Egerton, Electron energy loss spectroscopy in the electron microscope (Plenum Press, New York, 1986)

    Google Scholar 

  58. M. B. Robin, Higher Excited States of Polyatomic Molecules, I, II, II, (Academic Press, INC, Orland, San Diego, New York, London, Toronto, Montréal, Sydney, and Tokyo, 1974, 1975, and 1985)

  59. M. Inokuti, Radiat. Eff. Defects Solids 117, 143 (1991)

    Article  ADS  Google Scholar 

  60. U. Fano, Phys. Rev. 118, 451 (1960)

    Article  ADS  MathSciNet  Google Scholar 

  61. R.F. Yoo, B. Ruscic, J. Berkowitz, J. Chem. Phys. 96, 911 (1992)

    Article  ADS  Google Scholar 

  62. J.H. Weaver, J.L. Martins, T. Komeda, Y. Chen, T.R. Ohno, G.H. Kroll, N. Troullier, R.E. Haufler, R.E. Smalley, Phys. Rev. Lett. 66, 1741 (1991)

    Article  ADS  Google Scholar 

  63. I.V. Hertel, H. Steger, J. de Vries, B. Weisser, C. Menzel, B. Kamke, W. Kamke, Phys. Rev. Lett. 68, 784 (1992)

    Article  ADS  Google Scholar 

  64. H. Deutsch, K. Becker, J. Pittner, V. Banacic-Koutecky, S. Matt, T.D. Märk, J. Phys. B: At. Mol. Opt. Phys. 29, 5175 (1996)

    Article  ADS  Google Scholar 

  65. D.L. Strout, R.L. Murry, C. Xu, W.C. Eckhoff, G.K. Odom, G.E. Scuseria, Chem. Phys. Lett. 214, 576 (1993)

    Article  ADS  Google Scholar 

  66. J. Onoe, T. Nakayama, M. Aono, T. Hara, Appl. Phys. Lett. 82, 595 (2003)

    Article  ADS  Google Scholar 

  67. N. Aoki, Molecular Technology: Energy Innovation, Eds: H. Yamamoto, T. Kato, Chapter 1 (Wiley-VCH Verlag GmbH & Co. KGaA, 2018)

  68. M. Nakaya, S. Watanabe, J. Onoe, Carbon 152, 882 (2019)

    Article  Google Scholar 

  69. H. Yasumatsu, T. Kondow, H. Kitagawa, K. Tabayashi, K. Shobatake, J. Chem. Phys. 104, 899 (1996)

    Article  ADS  Google Scholar 

  70. H. Kato, M. Hoshino, H. Tanaka, P. Limao-Vieira, O. Ingólfsson, L. Campbell, M.J. Brunger, J. Chem. Phys. 134, 134308 (2001)

    Article  ADS  Google Scholar 

  71. B.B. Brady, E.J. Beiting, J. Chem. Phys. 97, 3855 (1992)

    Article  ADS  Google Scholar 

  72. S. Dai, L.M. Toth, G.D. Cut, H. Metcaff, J. Chem. Phys. 101, 4470 (1994)

    Article  ADS  Google Scholar 

  73. Q. Gong, Y. Sun, Z. Huang, X. Zhu, Z.N. Gu, D. Qiang, J. Phys. B: At. Mol. Opt. Phys. 27, L199 (1994)

    Article  ADS  Google Scholar 

  74. Q. Gong, Y. Sun, Z. Huang, X. Zhu, Z.N. Gu, D. Qiang, J. Phys. B: At. Mol. Opt. Phys. 29, 4981 (1996)

    Article  ADS  Google Scholar 

  75. A.L. Smith, J. Phys. B: At. Mol. Opt. Phys. 29, 4975 (1996)

    Article  ADS  Google Scholar 

  76. P.F. Coheur, M. Career, R. Colin, J. Phys. B: At. Mol. Opt. Phys. 29, 4987 (1996)

    Article  ADS  Google Scholar 

  77. Y.-K. Kim, J. Chem. Phys. 126, 064306 (2001)

    Google Scholar 

  78. L. Vriens, Phys. Rev. 160, 100 (1967)

    Article  ADS  Google Scholar 

  79. H. Tanaka, M.J. Brunger, L. Campbell, H. Kato, M. Hoshino, A.R.P. Rau, Rev. Mod. Phys. 88, 025004 (2016)

    Article  ADS  Google Scholar 

  80. B.P. Marinković, R. Panajotović, D. Šević, R.P. McEachran, G. Garciá, F. Blanco, M.J. Brunger, Phys. Rev. A 99, 062702 (2019)

    Article  ADS  Google Scholar 

  81. B. Predojević, D. Šević, B.P. Marinković, R.P. McEachran, F. Blanco, G. Garciá, M.J. Brunger, Phys. Rev. A 101, 032704 (2020)

    Article  ADS  Google Scholar 

  82. K.R. Hamilton, O. Zatsarinny, K. Bartschat, M.S. Rabasović, D. Šević, B.P. Marinković, S. Dujko, J. Atić, D.V. Fursa, I. Bray, R.P. McEachran, F. Blanco, G. Garciá, P.W. Stokes, R.D. White, M.J. Brunger, Phys. Rev. A 102, 022801 (2020)

    Article  ADS  Google Scholar 

  83. B.P. Marinković, S.D. Tošić, D. Šević, R.P. McEachran, F. Blanco, G. Garciá, M.J. Brunger, Phys. Rev. A 104, 022808 (2021)

    Article  ADS  Google Scholar 

  84. C. Winstead, V. McKoy, Adv. At. Mol. Opt. Phys. 43, 117 (2000)

    ADS  Google Scholar 

Download references

Acknowledgements

One of authors (H.T.) spent his most scientifically fruitful time at JPL, Caltech, 1977–1978 as a NASA Resident Research Associate and learned a lot of electron collision physics under, one of Vincent’s colleagues, Dr. S. Trajmar. We would like to sincerely thank the late Professor V. McKoy and all colleagues from “His” school. Partial financial support from the Australian Research Council, through Grant # DP180101655, is also acknowledged.

Author information

Authors and Affiliations

Authors

Contributions

All authors have contributed equally to the paper.

Corresponding author

Correspondence to M. Hoshino.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tanaka, H., Hoshino, M. & Brunger, M.J. Elastic and inelastic scattering of low-energy electrons from gas-phase \(\hbox {C}_{\mathbf {60}}\): elastic scattering angular distributions and coexisting solid-state features revisited. Eur. Phys. J. D 75, 293 (2021). https://doi.org/10.1140/epjd/s10053-021-00295-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/s10053-021-00295-1

Navigation