Abstract
The development of channeling and blocking since the foundation of the field was laid by Jens Lindhard in his classical paper in 1965 is discussed, and the question is asked whether this theory has passed the test of time. Have important aspects of the theory been challenged? Where has the theory needed modification or extension? Are there still open questions to be solved? A basic theoretical issue is the applicability of classical mechanics in the description. Lindhard showed that for particles heavy compared with the electron classical orbital pictures may always be applied. However, for electrons and positrons there are strong quantal features, like Bragg interference. The quantal description introduced by Lindhard and co-workers has been used as the basis for a comprehensive treatment of the channeling of MeV electrons and positrons and of channeling radiation. At very high energies, GeV and TeV, the motion becomes classical, due to the relativistic increase of the field seen by the particles in the reference frame following their longitudinal motion. Channeling radiation in this regime is still an active field of research. For channeling and blocking of ions, the concept of statistical equilibrium plays a central part in Lindhard’s theory. The application of this concept has met with two important challenges, the first based on computer simulations and the second on experiments with the transmission of heavy ions through thin crystals. In both cases the challenges have been met and new insight has been gained but there are still problems to be solved. Channeling and blocking of ions have found very many interesting applications, and a few problems and opportunities worth pursuing are suggested.
Updated and slightly edited from J. U. Andersen’s contribution to Ion Beam Science. Solved and Unsolved Problems. Part II. P. Sigmund, editor. Published in Mat. Fys. Medd. Dan. Vid. Selsk. 52:2, 655–698 (2006). Reprinted with kind permission of the Royal Danish Academy of Sciences and Letters.
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References
Alguard M.J., Swent R.L., Pantell R.H., Datz S., Barrett J.H., Berman B.L. and Bloom S.D. (1980): Radiation from channeled leptons. Nucl Instrum Methods 170, 7–13
Andersen J.U., Andersen S.K., and Augustyniak W.M. (1977): Electron channeling. Mat Fys Medd Dan Vid Selsk 39 no. 10, 1–58. http://www.sdu.dk/Bibliotek/matfys
Andersen J.U., Augustyniak W.M. and Uggerhøj E. (1971): Channeling of Positrons. Phys Rev B 3, 705–711
Andersen J.U., Bonderup E., Lægsgaard E., Marsh B.B. and Sørensen A.H. (1982): Axial channeling radiation from MeV electrons. Nucl Instrum Methods 194, 209–224
Andersen J.U., Bonderup E., Lægsgaard E. and Sørensen A.H. (1983a): Incoherent scattering of electrons and linewidth of planar-channeling radiation. Physica Scripta 28, 308–330
Andersen J.U., Bonderup E. and Pantell R.H. (1983b): Channeling radiation. Ann Rev Nucl Part Sci 33, 453–504
Andersen J.U., Chevallier J., Ball G.C., Davies W.G., Forster J.S., Geiger J.S., Davies J.A., Geissel H. and Kanter E.P. (1996): Dielectronic recombination and energy loss for He-like \(^{79}\)Br ions channeled in a thin single crystal of Si. Phys Rev A 54, 624–635
Andersen J.U., Chevallier J., Forster J.S., Karamian S.A., Vane C.R., Beene J.R., Galindo-Uribarri A., del Campo J.G., Gross C.J., Krause H.F. et al. (2008): Attosecond lifetimes in heavy-ion induced fission measured by crystal blocking. Phys Rev C 78, 064609
Andersen J.U. and Feldman L.C. (1970): Comparison of average-potential models and binary-collision models of axial channeling and blocking. Phys Rev B 1, 2063–2069
Andersen J.U., Lægsgaard E., Nielsen K.O., Gibson W.M., Forster J.S., Mitchell I.V. and Ward D. (1976): Time evolution of heavy-ion-induced fission studied by crystal blocking. Phys Rev Lett 36, 1539–1542
Assmann W., Huber H., Karamian S.A., Grüner F., Mieskes H.D., Andersen J.U., Posselt M. and Schmidt B. (1999): Transverse cooling or heating of channeled ions by electron capture and loss. Phys Rev Lett 83, 1759
Barrett J.H. (1973a): Breakdown of the statistical-equilibrium hypothesis in channeling. Phys Rev Lett 31, 1542
Barrett J.H. (1973b): Monte Carlo channeling calculations. Phys Rev B 3, 1527–1547
Baurichter A., Biino C., Clément M., Doble N., Elsener K., Fidecaro G., Freund A., Gatignon L., Grafteröm P., Gyr M. et al. (2000): Channeling of high-energy particles in bent crystals - Experiments at the CERN SPS. Nucl Instrum Methods B 164–165, 27–43
Bonderup E., Esbensen H., Andersen J.U. and Schiøtt H.E. (1972): Calculations on axial dechanneling. Radiat Eff 12, 261–266
Briggs J. and Pathak A. (1973): Momentum transfer cross sections and the \(Z_1\) oscillations in stopping power. J Phys C 6, L153–L157
Cohen C. and Dauvergne D. (2004): High energy ion channeling. Principles and typical applications. Nucl Instrum Methods 225, 40–71
Datz S., Berman B.L., Dahling B.A., Hynes M.V., Park H., Kephart J.O., Klein R.K. and Pantell R.H. (1986): On the dependence of electron planar channeling radiation upon lattice vibration amplitude. Nucl Instrum Methods B 13, 19–22
Davies J.A. (1983): The channeling phenomenon—and some of its applications. Physica Scripta 28, 294–302
Domeij B. and Björkqvist K. (1965): Anisotropic emission of \(\alpha \)-particles from a monocrystalline source. Phys Lett 14, 127
Doyle P.A. and Turner P.S. (1968): Relativistic Hartree-Fock X-ray and electron scattering factors. Acta Cryst A 24, 390–397
Drouart A., Charvet J.L., Dayras R., Nalpas L., Volant C., Chbihi A., Rodriguez C.E., Frankland J.D., Morjean M., Chevallier M. et al. (2005): Evidence of \(Z=120\) compound nucleus formation from lifetime measurements in the \(^{238}\)U\(+\)Ni reaction at 6. 62 MeV/nucleon. In Proc. Int. Symposium on Exotic Nuclei, Peterhof 2004, 192–197. World Scientific
Eriksson L., Davies J.A. and Jespersgaard P. (1967): Range measurements in oriented tungsten single crystals (0.1–1.0 MeV). I. Electronic and nuclear stopping powers. Phys Rev 161, 219–234
Esbensen H., Fich O., Golovchenko J.A., Madsen S., Nielsen H., Schiøtt H.E., Uggerhøj E., Vraast-Thomsen C., Charpak G., Majewski S. et al. (1978): Random and channeled energy loss in thin germanium and silicon crystals for positive and negative 2–15-GeV/c pions, kaons, and protons. Phys Rev B 18, 1039–1054
Esbensen H. and Golovchenko J.A. (1976): Energy loss of fast channeled particles. Nucl Phys A 298, 382–396
Feldman L.C., Mayer J.W. and Picraux S.T. (1982): Materials Analysis by Ion Channeling. Academic Press, New York
Finnemann J. (1968): En redegørelse for resultaterne af beregninger over spredning af elektroner med lav energi på afskærmede Coulombfelter. Master’s thesis, Aarhus University
Gärtner K., Hehl K. and Schlotzhauer G. (1984): Axial dechanneling : II. Point defects. Nucl Instrum Methods B 4, 55–62
Gemmell D.S. (1974): Channeling and related effects in motion of charged particles through crystals. Rev Mod Phys 46, 129–227
Gibson W.M. (1975): Blocking measurements of nuclear decay times. Ann Rev Nucl Sci 25, 465–508
Grüner F., Assmann W., Bell F., Schubert M., Andersen J.U., Karamian S., Bergmaier A., Dollinger G., Gorgens L., Günther W. et al. (2003): Transverse cooling and heating in ion channeling. Phys Rev B 68, 174104
Guanere M., Sillou D., Spighel M., Cue N., Gaillard M.J., Kirsch R.G., Poizat J.C., Remmillieux J., Berman B.L., Cattillon P. et al. (1982): Sharp-line and broad-continuum radiation from electrons channeled in diamond. Nucl Instrum Methods 194, 225–228
Hau L.V. and Andersen J.U. (1993a): Channeling radiation beyond the continuum model: The phonon ‘Lamb shift’ and higher-order corrections. Phys Rev A 47, 4007–4032
Hau L.V. and Andersen J.U. (1993b): Line shifts of channeling raditation from MeV electrons. Radiat Eff 25, 75–80
Hau L.V., Lægsgaard E. and Andersen J.U. (1990): Thermal vibrations in Si studied by channeling-radiation spectroscopy. Nucl Instrum Methods B 48, 244–247
Hofsäss H. (1996): Emission channeling. Hyperfine Interactions 97–98, 247–283
Karamian S.A., Forster J.S., Andersen J.U., Assmann W., Broude C., Chevallier J., Geiger J.S., Grüner F., Khodyrev V.A., Malaguti F. et al. (2003): Fission lifetimes of Th nuclei measured by crystal blocking. Europ Phys J A 17, 49–56
Kennedy E.F., Nielsen B.B. and Andersen J.U. (1992): Planar channeling dips in backscattering yield. Nucl Instrum Methods B 67, 236–240
Krause H.F. and Datz S. (1996): Channeling heavy ions through crystalline lattices. Adv At Mol Opt Phys 37, 139–180
Kumakhov M.A. (1976): On the theory of electromagnetic radiation of charged particles in a crystal. Phys Lett A 57, 17–18
Lervig P., Lindhard J. and Nielsen V. (1967): Quantal treatment of directional effects for energetic charged particles in crystal lattices. Nucl Phys A 96, 481
Lindhard J. (1965): Influence of crystal lattice on motion of energetic charged particles. Mat Fys Medd Dan Vid Selsk 34 no. 14, 1–64
Malyshevsky V.S. (2005): Transverse cooling or heating of channeled ions by electron capture and loss. Phys Rev B 72, 094109
Moak C.D., Datz S., Crawford O.H., Krause H.F., Dittner P.F., del Campo J.G., Biggerstaff J.A., Miller P.D., Hvelplund P. and Knudsen H. (1979): Resonant coherent excitation of channeled ions. Phys Rev A 19, 977–993
Nakai Y., Ikeda T., Kanai Y., Kambara T., Fukinishi N., Komaki K., Kondo C., Azuma T. and Yamazaki Y. (2005): Resonant coherent excitation of 2s electron of Li-like Fe ions to the \(n=3\) states. Nucl Instrum Methods B 230, 90–95
Nielsen B.B., Andersen J.U. and Pearton S.J. (1988): Lattice location of deuterium interacting with the boron acceptor in silicon. Phys Rev Lett 60, 321–324
Okorokov V.V. (1965): The coherent excitation of nuclei moving through a crystal. Yad Fiz 2, 1009. Engl. Translation. Sov. J. Nucl. Phys. 2, 719 (1966)
Pedersen M.J., Andersen J.U. and Augustyniak W.M. (1972): Channeling of positrons. Radiat Eff 12, 47–52
Rasmussen F.B. and Nielsen B.B. (1994): Microstructure of the nitrogen pair in crystalline silicon studied by ion channeling. Phys Rev B 49, 16353–16360
Robinson M.T. and Oen O.S. (1963): Computer studies of the slowing down of atoms in crystals. Phys Rev 132, 2385–2398
Sørensen A.H. and Uggerhøj E. (1987): Channeling and channeling radiation. Nature 325, 311–318
Tsyganov E.N. (1976a): Estimates of cooling and bending processes for charged particle penetration through a monocrystal. Fermilab TM 684
Tsyganov E.N. (1976b): Some aspects of the mechanism of a charge particle penetration through a monocrystal. Fermilab TM 682
Tulinov A.F., Kulikauskas V.S. and Malov M.M. (1965): Proton scattering from a tungsten single crystal. Phys Lett 18, 304–307
Uggerhøj E. (1966): Orientation dependence of the emission of positrons and electrons from \(^{64}\)Cu embedded in single crystals. Phys Lett 22, 382–383
Uggerhøj E. and Andersen J.U. (1968): Influence of lattice structure on motion of positrons and electrons through single crystals. Can J Physics 46, 543–550
Uggerhøj U.I. (2005): The interaction of relativistic particles with strong crystalline fields. Rev Mod Phys 77, 1131–1171
Uguzzoni A., Andersen J.U. and Ryabov V. (1992): Thermal fluctuations in surface transmission for axial channeling. Nucl Instrum Methods B 67, 231–235
Uguzzoni A., Gärtner K., Lulli G. and Andersen J.U. (2000): The minimum yield in channeling. Nucl Instrum Methods B 164–165, 53–60
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Andersen, J.U. (2014). Channeling and Blocking of Energetic Particles in Crystals. In: Particle Penetration and Radiation Effects Volume 2. Springer Series in Solid-State Sciences, vol 179. Springer, Cham. https://doi.org/10.1007/978-3-319-05564-0_11
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