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.
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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
“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
K. Takatsuka, V. McKoy, Phys. Rev. A 24, 2473 (1981)
K. Takatsuka, V. McKoy, Phys. Rev. A 30, 1734 (1984)
H. Tanaka, L. Boesten, K. Onda, O. Ohashi, J. Phys. Soc. Jpn 63, 485 (1994)
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),
R. Hofstadter, Rev. Mod. Phys. 28, 214 (1956)
C. Winstead, V. McKoy, Phys. Rev. A 73, 012711 (2006)
R.R. Lucchese, F.A. Gianturco, N. Sanna, Chem. Phys. Lett. 305, 413 (1999)
W. Krätschmer, L.D. Lamb, K. Fostiropoulos, D.R. Huffman, Nat. 347, 354 (1990)
H.W. Kroto, J.R. Heath, S.C. OBrian, R.F. Curl, R.E. Smalley, Nat. 318, 162 (1985)
P.R. Buseck, S.J. Tsipursky, R. Hettich, Sci. 257, 215 (1992)
J. Cami, J. Bernard-Salas, E. Peeters, S.E. Malek, Sci. 329, 1180 (2010)
NASA, Mission News, JPL News Release 2010-243, JPL Caltech, July, 22, (2010)
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)
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)
M.L. Heger, Lick Obs. Bull. 10, 146 (1922)
E.K. Campbell, J.P. Maier, Astrophys. J. 858, A36 (2018)
J.W. Keller, M.A. Coplan, Chem. Phys. Lett. 193, 89 (1992)
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)
G. Bulliard, M. Allan, S. Leach, Chem. Phys. Lett. 209, 434 (1993)
R. Abouaf, J. Pommier, S. Cvejanovic, Chem. Phys. Lett. 213, 503 (1993)
O. Elhamidi, J. Pommier, R. Abouaf, J. Phys. B: At. Mol. Opt. Phys. 30, 4633 (1997)
M. Lezius, P. Scheier, T.D. Märk, Chem. Phys. Lett. 203, 232 (1993)
T. Jaffke, E. Illenberger, M. Lezius, S. Matejcik, D. Smith, T.D. Märk, Phys. Lett. 226, 213 (1994)
J. Huang, H.S. Carman, R.N. Compton, J. Phys. Chem. 99, 171 (1995)
Z. Felfli, K. Suggsa, N. Nicholas, A.Z. Msezane, Int. J. Mol. Sci. 21, 3159 (2020). (therein other references are well cited)
J. Berkowitz, J. Chem. Phys. 111, 1446 (1999). (therein earlier references in the 1990s)
L.R. Hargreaves, B. Lohman, C. Winstead, V. McKoy, Phys. Rev. A 82, 062716 (2010)
L.G. Gerchikov, P.V. Efimov, V.M. Mikoushkin, A.V. Solovyov, Phys. Rev. Lett. 81, 2707 (1998)
Y.S. Gordeev, V.M. Mikoushkin, A.V. Solovyov, Mol. Mater. 13, 1 (2000)
F.A. Gianturco, R.R. Lucchese, N. Sanna, J. Phys. B: At. Mol. Opt. Phys. 32, 2181 (1999)
F.A. Gianturco, R.R. Lucchese, J. Chem. Phys. 111, 6739 (1999)
M.Y. Amusia, L.V. Chernysheva, V.K. Dolmatov, J. Phys. B: At. Mol. Opt. Phys. 52, 085201 (2019)
H. Tanaka, L. Boesten, D. Matsunaga, T. Kudo, J. Phys. B At. Mol. Opt. Phys. 21, 125 (1988)
A.F. Hebard, R.C. Hadden, R.M. Fleming, A.R. Kortan, Appl. Phys. Lett. 59, 2109 (1991)
A. Popović, G. Dražič, J. Marsel, Rapid Commun. In. Mass Spectrom. 8, 985 (1994)
L. Boesten, H. Tanaka, At. Data Nucl. Data Tables 52, 25 (1992)
D.C. Cartwright, G. Csanak, S. Trajmar, D.F. Register, Phys. Rev. A 45, 1602 (1992)
S.K. Srivastava, A. Chutjian, S. Trajmar, J. Chem. Phys. 63, 2659 (1975)
S. Trajmar, D. F. Register, Electron Molecule Collisions, Eds. K. Takayanagi and I. Shimamura, (Plenum, New York, 1984)
K.A. Dubey, J. Jose, Eur. Phys. J. Plus 136, 713 (2021)
S. Trajmar, D.F. Register, A. Chutjian, Phys. Rep. 97, 219 (1983)
M.J. Brunger, S.J. Buckman, Phys. Rep. 357, 215 (2002)
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)
Y. Fujikawa, K. Sakai, A. Koma, Surface Science 176, 357 (1996)
G. Grenterblum, J.J. Pireaux, P.A. Thiry, R. Caudano, J.P. Vigneron, Ph. Lambin, A.A. Lucas, Phys. Rev. Lett. 67, 2171 (1991)
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)
R.L. Cappelletti, J.R.D. Copley, W.A. Kamitakahara, J.R.F. Li, D.R. Lannin, Phys. Rev. Lett. 66, 3261 (1991)
E.W. Schlag, R.D. Levine, J. Chem. Phys. 96, 10608 (1992)
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
C.Z. Li, Z.L. Miškovič, F.Q. Goodman, Y.N. Wang, J. App. Phys. 113, 184301 (2013)
A.V. Zayats, I.I. Smolyaninov, A.A. Maradudin, Phys. Rep. 408, 131 (2005)
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)
R. Kuzuo, M. Terauchi, M. Tanaka, Y. Saito, H. Shinohara, Jap. J. of Appl. Phys. 30, L1817 (1991)
M. Terauchi, N.K. Gakkaishi, J. Crystallogr. Soc. Jpn. 44, 277 (2002). (in Japanese)
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
W.S.M. Werner, V. Astašauskas, P. Ziegler, A. Bellissimo, G. Stefani, L. Linhart, F. Libisch, Phys. Rev. Lett. 125, 196603 (2020)
R.F. Egerton, Electron energy loss spectroscopy in the electron microscope (Plenum Press, New York, 1986)
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)
M. Inokuti, Radiat. Eff. Defects Solids 117, 143 (1991)
U. Fano, Phys. Rev. 118, 451 (1960)
R.F. Yoo, B. Ruscic, J. Berkowitz, J. Chem. Phys. 96, 911 (1992)
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)
I.V. Hertel, H. Steger, J. de Vries, B. Weisser, C. Menzel, B. Kamke, W. Kamke, Phys. Rev. Lett. 68, 784 (1992)
H. Deutsch, K. Becker, J. Pittner, V. Banacic-Koutecky, S. Matt, T.D. Märk, J. Phys. B: At. Mol. Opt. Phys. 29, 5175 (1996)
D.L. Strout, R.L. Murry, C. Xu, W.C. Eckhoff, G.K. Odom, G.E. Scuseria, Chem. Phys. Lett. 214, 576 (1993)
J. Onoe, T. Nakayama, M. Aono, T. Hara, Appl. Phys. Lett. 82, 595 (2003)
N. Aoki, Molecular Technology: Energy Innovation, Eds: H. Yamamoto, T. Kato, Chapter 1 (Wiley-VCH Verlag GmbH & Co. KGaA, 2018)
M. Nakaya, S. Watanabe, J. Onoe, Carbon 152, 882 (2019)
H. Yasumatsu, T. Kondow, H. Kitagawa, K. Tabayashi, K. Shobatake, J. Chem. Phys. 104, 899 (1996)
H. Kato, M. Hoshino, H. Tanaka, P. Limao-Vieira, O. Ingólfsson, L. Campbell, M.J. Brunger, J. Chem. Phys. 134, 134308 (2001)
B.B. Brady, E.J. Beiting, J. Chem. Phys. 97, 3855 (1992)
S. Dai, L.M. Toth, G.D. Cut, H. Metcaff, J. Chem. Phys. 101, 4470 (1994)
Q. Gong, Y. Sun, Z. Huang, X. Zhu, Z.N. Gu, D. Qiang, J. Phys. B: At. Mol. Opt. Phys. 27, L199 (1994)
Q. Gong, Y. Sun, Z. Huang, X. Zhu, Z.N. Gu, D. Qiang, J. Phys. B: At. Mol. Opt. Phys. 29, 4981 (1996)
A.L. Smith, J. Phys. B: At. Mol. Opt. Phys. 29, 4975 (1996)
P.F. Coheur, M. Career, R. Colin, J. Phys. B: At. Mol. Opt. Phys. 29, 4987 (1996)
Y.-K. Kim, J. Chem. Phys. 126, 064306 (2001)
L. Vriens, Phys. Rev. 160, 100 (1967)
H. Tanaka, M.J. Brunger, L. Campbell, H. Kato, M. Hoshino, A.R.P. Rau, Rev. Mod. Phys. 88, 025004 (2016)
B.P. Marinković, R. Panajotović, D. Šević, R.P. McEachran, G. Garciá, F. Blanco, M.J. Brunger, Phys. Rev. A 99, 062702 (2019)
B. Predojević, D. Šević, B.P. Marinković, R.P. McEachran, F. Blanco, G. Garciá, M.J. Brunger, Phys. Rev. A 101, 032704 (2020)
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)
B.P. Marinković, S.D. Tošić, D. Šević, R.P. McEachran, F. Blanco, G. Garciá, M.J. Brunger, Phys. Rev. A 104, 022808 (2021)
C. Winstead, V. McKoy, Adv. At. Mol. Opt. Phys. 43, 117 (2000)
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.
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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
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DOI: https://doi.org/10.1140/epjd/s10053-021-00295-1