Abstract
Particle penetration phenomena are intrinsically statistical in nature. It is extremely unlikely that two particles penetrating a material medium at different times will undergo the same sequence of collision events. This applies even to ideal experiments with a well-collimated, monochromatic particle beam hitting a highly homogeneous target material with a uniform thickness. The energies and directions of motion of penetrating particles, as well as their charge and excitation states, will differ shortly after they hit the target. The same is true for the radiation effects they generate, such as excitation, ionization, and relocation of target atoms, and nuclear or chemical reactions. In brief, whatever quantity you find appropriate to measure, you will find fluctuations, and these fluctuations will not go to zero if you increase the number of particles in the beam.
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References
Abramowitz, M. & Stegun, I.A, 1965, Handbook of Mathematical Functions, Dover Publ.
Amsel, G., 1982, Nucl. Instrum. Methods 194: 1.
Andersen, H.H., Bottiger, J., Knudsen, H., Moller Petersen, P., & Wohlenberg, T., 1974, Phys. Rev. A10: 1568.
Anne, R., Herault, J., Bimbot, R., Gauvion, H., Bastin, G., & Hubert, F., 1988, Nucl. Instrum. Methods B34: 295.
Ascolani, H. & Arista, N.R., 1986, Phys. Rev. A33: 2352.
Ashley, J.C., Ritchie, R.H., & Brandt, W., 1972, Phys. Rev. B5: 2393.
Baily, N.A., Steigerwaldt, J.E., & Hilbert, J.W., 1970, Phys. Rev. B2: 577.
Bak, J.F., Burenkov, A., Petersen, J.B.B., Uggerhøj, E., Møller, S.P., & Siffert, P., 1987, Nucl. Phys. B288: 681.
Barrett, J.H., Appleton, B.R., & Holland, O.W., 1980, Phys. Rev. B22: 4180.
Bateman, H., 1911, Philos. Mag. 21: 745.
Belkacem, A., & Sigmund, P., 1990, Nucl. Instrum. Methods B48: 29.
Berger, M.J., 1963, Meth. Comp. Phys. 1: 135.
Besenbacher, F., Heinemeier, J., Hvelplund, P., & Knudsen, H., 1977, 1978, Phys. Lett. 61A; 75.
Besenbacher, F., Heinemeier, J., Hvelplund, P., & Knudsen, H., Phys. Rev. A18: 2470.
Besenbacher, F., Andersen, J.U., & Bonderup, E., 1980, Nucl. Instrum. Methods 168: 1.
Besenbacher, F., Andersen, H.H., Hvelplund, P., & Knudsen, H., 1981, Mat. Fys. Medd. Dan. Vid. Selsk. 40: no. 9.
Bethe, H. 1930, Ann. Physik 5: 325.
Betz, H.D., 1972, Rev. Mod. Phys. 44: 465.
Betz, H.D., 1990, this school.
Bichsei, H., 1970, Phys. Rev. B1 2854.
Bichsei, H., 1988, Rev. Mod. Phys. 60: 663.
Bichsei, H. & Saxon, R. P., 1975, Phys. Rev. 11: 1286.
Biersack, J.P. & Haggmark, L.G., 1980, Nucl. Instrum. Methods 174: 257.
Bloch, F., 1933, Ann. Physik 16: 285.
Blomberg, A., Aberg, T., & Goscinski, O., 1986, J. Phys. B19 1063.
Blunck, O. & Leisegang, S., 1950, Z. Physik 128: 500.
Bohr, A. 1948, Mat. Fys. Medd. Dan. Vid. Selsk. 24: no. 19.
Bohr, N., 1913, Philos. Mag. 25: 10.
Bohr, N., 1915, Philos. Mag. 30: 581.
Bohr, N., 1948, Mat. Fys. Medd. Dan. Vid. Selsk. 18: no. 8.
Bohr, N. & Lindhard, J., 1954, Mat. Fys. Medd. Dan. Vid. Selsk. 28: no. 7.
Bonderup, E., 1967, Mat. Fys. Medd. Dan. Vid. Selsk. 35: no. 17.
Bonderup, E., 1981, Penetration of Charged Particles through Matter, Aarhus University.
Bonderup, E., & Hvelplund, P., 1971, Phys. Rev. A4 562.
Bothe, W., 1921, Z. Physik 4, 161, 300; 5, 63.
Capuj, N.E., Eckardt, J.C., Lantschner, G.H., & Arista, N.R., 1987, Phys. Rev. 36: 3715.
Chandrasekhar, S., 1943, Rev. Mod. Phys. 15: 1.
Chu, W.K., 1976, Phys. Rev. A13 2057.
Chu & Powers, 1972, Phys. Lett. 40A: 23.
Clouvas, A., Gaillard, M.J., dePinho, A.G., Poizat, J.C., & Remillieux, J., 1984, Phys. Lett. 103A: 419.
Cowern, N.E.B., Sofield, C.J., Freeman, J.M., & Mason, J.P., 1979, Phys. Rev. A19 111.
Crawford, O.H., 1980, Phys. Rev. Lett. 44: 185.
Dixmier, M., L’Hoir, A., & Amsel, G., 1982, Nucl. Instrum. Methods 197: 537.
Echenique, P., 1990, this school.
Esbensen, H. & Sigmund, P., 1990, Ann. Phys. (New York), July issue.
Fano, U., 1963, Ann. Rev. Nucl. Sci. 13: 1.
Faibis, A., Koenig, W., Kanter, E.P., Vager, Z., 1986, Nucl. Instrum. Methods B13 673.
Feldman, L.C., 1990, this school.
Feller, W., 1957, 1966, An Introduction to Probability Theory and its Applications, Vols. I & II, Wiley, New York.
Firsov, O.B., 1959, Zh. Eksp. Teor. Fiz. 36: 1517.
Firsov, O.B., Sov. Phys. JETP 9: 1076.
Flamm, L., 1914, 1915, Sitzungsber. Akad. Wiss. Wien, Math. Nat. Wiss. K1.123: 1393; 124: 597.
Gaillard, M.J., Gemmell, D.S., Goldring, G., Levine, I., Pietsch, W.J., Poizat, J.C., Ratkowski, A.J., Remillieux, J., Vager, Z., Zabransky, B.J., 1978, Phys. Rev. A17 1797.
Geissei, H., Lennard, W.N., Andrews, H.R., Ward, D., & Phillips, D., 1984,Phys. Lett. 106A: 371.
Geissei, H., Lennard, W.N., Andrews, H.R., Jackson, D.P., Mitchell, I.V., Philips, D., & Ward, D., 1985, Nucl. Instrum. Methods B12 38.
Gerjuoy, E., 1966, Phys. Rev. 148: 54.
Glauber, R.R., 1955, Phys. Rev. 100: 242.
Goscinski, O., Aberg, T., & Peltonen, M., 1982, Phys. Lett. 90A: 464.
Goudsmit, S. & Saunderson, J.L., 1940, Phys. Rev. 84: 1092.
Gras-Marti, A., 1985, Nucl. Instrum. Methods B9: 1.
Gryzinski, M., 1965, Phys. Rev. 138: A305, A322, A366.
Hansen, F.Y., Knudsen, T.S., & Carneiro, K., 1975, J.Chem. Phys. 62: 1556.
Harberger, J.H., Johnson, R.E., & Boring, J.W., 1974, Phys. Rev. A9 1161, 1172.
Herzfeld, K.F., 1912, Phys. Z. 13: 347.
Huang, W., Urbassek, H.M., & Sigmund, P., 1985, Philos. Mag. A52 753.
Hvelplund, 1968, prize essay, Aarhus University.
Hvelplund, P., 1975, Phys. Rev. A11 1921.
Inokuti, M., 1971, Rev. Mod. Phys. 43: 297.
Inokuti, M., Itikawa, Y., & Turner, J.E., 1978, Rev. Mod. Phys. 50: 23.
Inokuti, M., Dehmer, J.L., Baer, T., & Hansen, J.D., 1981, Phys. Rev. A23 95.
Ishiwari, R., Shiomi, N., & Sakamoto, N., 1982, 1983, 1984, Phys. Rev. A25 2524; 27: 810; 30: 82.
Ishiwari, R., Shiomi-Tsuda, N., Sakamoto, N. & Ogawa, H., 1990, Nucl. Instrum. Methods B48 65.
Jackson, J.D., 1975, Classical Electrodynamics, Wiley, New York.
Jakas, M.M. & Baragiola, R.A., 1980, Phys. Rev. Lett. 44: 425.
Jakas, M.M., Lantschner, G.H., Eckardt, J.C., & Ponce, V.H., 1983, 1984, phys. stat. sol. (b) 117: K131.
Jakas, M.M., Lantschner, G.H., Eckardt, J.C., & Ponce, V.H., Phys. Rev. A29 1838.
Jakas, M.M. & Ponce, V.H., 1984, J. Phys. D17 1303.
Kampen, N.G.v., 1981, Stochastic Processes in Physics and Chemistry, North Holland, Amsterdam
Kanter, E.P., 1983, Phys. Rev. A28 1401.
Kölbig, K.S., & Schorr, B., 1984, Comp. Phys. Commun. 31: 97.
Kumbartzki, G.J., Neuburger, H., & Polster, W., 1985, Nucl. Instrum. Methods B12 315.
Kührt, E., & Wedel1, R., 1981, 1983, Phys. Lett. 86A: 54. 96A: 347.
Landau, L., 1944, J.Phys. USSR 8 201.
Lantschner, G.H., Eckardt, J.C., Jakas, M.M., Capuj, N.E., & Ascolani, H., 1987, Phys. Rev. A36 4667.
Lassen, N.O., 1951, Mat. Fys. Medd. Dan. Vid. Selsk. 26: no. 5; no. 12.
Lennard, W.N., Geissei, H., Phillips, D., & Jackson, D.P., 1986, Phys. Rev. Lett. 57: 318.
Lindhard, J., 1954, Mat. Fys. Medd. Dan. Vid. Selsk. 28: no. 8.
Lindhard, J., 1965, Mat. Fys. Medd. Dan. Vid. Selsk. 34: no.14.
Lindhard, J., 1970 in Atomic Collision Phenomena in Solids, D.W. Palmer et al., eds., North Holland, Amsterdam, p. 675.
Lindhard, 1976, Nucl. Instrum. Methods 132: 1.
Lindhard, J.,1984, unpublished private communication.
Lindhard, 1985, Phys. Sci. 32: 72.
Lindhard, J., 1990, this school; no written version has been submitted to the proceedings; the elementary parts of J.Lindhardts lectures have been written up by Bonderup (1981).
Lindhard, J., Scharff, M., & Schiøtt, H.E., 1963, Mat. Fys. Medd. Dan. Vid. Selsk. 33: no. 14.
Lindhard, J. & Nielsen, V., 1971, Mat. Fys. Medd. Dan. Vid. Selsk. 38: no.9.
Lindhard, J., Nielsen, V., & Scharff, M., 1968, Mat. Fys. Medd. Dan. Vid. Selsk. 34: no. 14.
Lindhard, J. & Scharff, M., 1953, Mat. Fys. Medd. Dan. Vid. Selsk. 27: no. 15.
Lindhard, J. & Winther, A., 1964, Mat. Fys. Medd. Dan. Vid. Selsk. 34: no. 4.
Livingston, M.S. & Bethe, H.A., 1937, Rev. Mod. Phys. 9: 245.
Loftager, P., Besenbacher, F., Jensen, O.S., & Sørensen, V.S., 1979, Phys. Rev. A20 1443.
Lucas, A., 1990. this school.
Malherbe, J.B. & Alberts, H.W., 1982, Nucl. Instrum. Methods 192: 559.
Marwick, A.D. & Sigmund, P., 1975, Nucl. Instrum. Methods 126: 317.
McGuire, E.J., 1971, Phys. Rev. A28 2096.
Meitner, L., & Freitag, K., 1926, Z. Physik 37: 481.
Mertens, P., 1986, Nucl. Instrum. Methods B13: 91.
Mertens, P. & Krist, Th., 1986, Nucl. Instrum. Methods B13 95.
Meyer, L., 1971, Phys. stat. sol. (b) 44: 253.
Meyer, L., Klein, M., & Wedell, R., 1977, phys. stat. sol. (b) 83: 451.
Mikkelsen, H.H., 1990, to appear in Nucl. Instrum. Methods B.
Mikkelsen, H.H., & Mortensen, E.H., 1990, Nucl. Instrum. Methods B48 39.
Mikkelsen, H.H. & Sigmund, P., 1989, Phys. Rev. A40 101.
Mikkelsen, H.H. & Sigmund, P., 1987, Nucl. Instrum. Methods B27: 266.
Moak, C.D., & Brown, M.D., 1966, Phys. Rev. 149: 244.
Molière, G., 1947, 1948, Z. Naturforsch. 2A: 133; 3a: 78.
Moyal, J.E., 1955, Philos. Mag. 46, 263.
Oddershede, J., & Sabin, J.R., 1984, Atomic Data & Nucl. Data Tables 31: 275.
Olson, R.E., 1989, Phys. Rev. A39 5572.
Olson, R.E., Radiat. Eff. 110: 1.
Poisson, D.S., 1837, Recherches sur la probabilité des jugements en matière criminelle et en matière civile, Bachelier, Paris.
Pronko, P.P., Appleton, B.R., Holland, O.W., & Wilson, S.R., 1979, Phys. Rev. Lett. 43: 779.
Robinson, M.T., & Torrens, I.M., 1974, Phys. Rev. B9 5008.
Schiwietz, G., 1990, this school.
Schmaus, D. & L’Hoir, A., 1982, Nucl. Instrum. Methods 194: 75.
Schmaus, D., L’Hoir, A., & Cohen, C., 1982, Nucl. Instrum. Methods 194: 81.
Schweidler, E.v., 1910, Phys. Z. 11, 614.
Scott, W.T., 1963, Rev. Mod. Phys. 35: 231.
Sidenius, G., Andersen, N., Sigmund, P., Besenbacher, F., Heinemeier, J., Hvelplund, P., Knudsen, H., 1976, Nucl. Instrum. Methods 134: 597.
Sigmund, P., 1975, in Radiation Damage Processes in Materials, ed. by C.H.S. Dupuy, Noordhof, Leiden, p.3.
Sigmund, P., 1976, Phys. Rev. A14 996.
Sigmund, P., 1977, Mat. Fys. Medd. Dan. Vid. Selsk. 39: no. 11.
Sigmund, P., 1978, Mat. Fys. Medd. Dan. Vid. Selsk. 40: no. 5.
Sigmund, P., 1982, Phys. Rev. A26 2497.
Sigmund, P., 1983, Phys. Scr. 28, 257 (1983)
Sigmund, P., 1989, presented at the International Conference on Atomic Collisions in Solids, Aarhus, unpublished.
Sigmund, P. & Fu, D.J., 1982, Phys. Rev. A25 1450.
Sigmund, P. & Gras-Marti, A., 1981, Nucl. Instrum. Methods 182/183: 25.
Sigmund, P. & Haagerup, 1986, Phys. Rev. A34 892.
Sigmund, P., Heinemeier, J., Besenbacher, F., Hvelplund, P., & Knudsen, H., Nucl. Instrum. Methods 150: 221.
Sigmund, P. & Johannessen, K., 1985, Nucl. Instrum. Methods B6 486.
Sigmund, P. & Winterbon, K.B., 1974, 1975, Nucl. Instrum. Methods 119: 541; 125: 491.
Sigmund, P. & Winterbon, K.B., 1985, Nucl. Instrum. Methods B12 1.
Smoluchowski, M.v., 1904, Festschrift Ludwig Boltzmann, p. 626.
Sofield, C.J., Cowern, N.E.B., & Freeman, J.M., 1981, Nucl. Instrum. Methods 191: 462.
Symon, K.R., 1948, Thesis, Harvard Univ., unpublished.
Thomson, J.J., 1912, Philos. Mag. 23: 449.
Tougaard, S., 1990a, this school.
Tougaard, S., 1990b, J. Elect. Spect. Related Phen. 52: 243.
Tougaard, S. & Sigmund, P., 1982, Phys. Rev. B25 4452.
Tschalär, C., 1968, Nucl. Instrum. Methods 61: 141; 64: 237.
Vavilov, P.V., 1957, Zh. Eksp. Teor. Fiz. 32: 920.
Vavilov, P.V., Sov. Phys. JETP 5: 749.
Vollmer, O., 1974, Nucl. Instrum. Methods 121: 373.
Williams, E.J., 1929, 1931a, 1931b, 1933, 1939, Proc. Roy. Soc. A125 420;130: 328; 135: 108; 139: 163; 169: 531.
Williams, E.J., 1940, Phys. Rev. 58: 292.
Williams, E.J., 1945, Rev. Mod. Phys. 17: 217.
Winterbon, K.B., 1968, Can. J. Phys. 46: 2429.
Winterbon, K.B., 1977, Nucl. Instrum. Methods 144: 311.
Winterbon, K.B., 1983, Radiat. Eff. 79: 251.
Winterbon, K.B., 1987, 1989, Nucl. Instrum. Methods B21 1; 43: 146.
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Sigmund, P. (1991). Statistics of Charged-Particle Penetration. In: Gras-Marti, A., Urbassek, H.M., Arista, N.R., Flores, F. (eds) Interaction of Charged Particles with Solids and Surfaces. Nato ASI Series, vol 271. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-8026-9_3
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