Abstract
This chapter addresses energy-loss straggling of ions with v > v0. The topic is divided up into uncorrelated or linear straggling, correlated straggling (bunching and packing) and charge-exchange straggling. The theory of linear straggling is developed in straight analogy with the stopping cross section. Bunching takes into account the spatial confinement of electrons in the atoms, while packing takes into account the spatial arrangement of atoms in molecules and solids. Charge-exchange straggling accounts for the dependence of elementary energy-loss processes ons the ion charge. Significant gas-solid differences are pointed out in pertinent theory as well as experiment.
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References
Besenbacher F., Andersen H.H., Hvelplund P. and Knudsen H. (1981): Straggling in energy loss of swift hydrogen and helium ions in gases. Mat Fys Medd Dan Vid Selsk 40 no. 9, 1–42
Besenbacher F., Andersen J.U. and Bonderup E. (1980): Straggling in energy loss of energetic hydrogen and helium ions. Nucl Instrum Methods 168, 1–15
Bohr N. (1915): On the decrease of velocity of swiftly moving electrified particles in passing through matter. Philos Mag 30, 581–612
Bohr N. (1948): The penetration of atomic particles through matter. Mat Fys Medd Dan Vid Selsk bf18 no. 8, 1–144
Bonderup E. and Hvelplund P. (1971): Stopping power and energy straggling for swift protons. Phys Rev A 4, 562–589
Chu W.K. (1976): Calculation of energy straggling for protons and helium ions. Phys Rev A 13, 2057–2060
Cuevas J., Garcia-Munos M., Torres P. and Allison S.K. (1964): Partial atomic and ionic stopping powers of gaseous hydrogen for helium and hydrogen beams. Phys Rev 135, A335–345
Fano U. (1963): Penetration of protons, alpha particles, and mesons. Ann Rev Nucl Sci 13, 1–66
Glazov L. and Sigmund P. (1997): Energy-loss spectra of charged particles in the presence of charge exchange. Nucl Instrum Methods B 125, 110–115
Glazov L. and Sigmund P. (2000): Energy-loss spectra of charged particles in the presence of charge exchange: addendum on \(^6\)Li spectra. Nucl Instrum Methods B 170, 39–44
Grande P.L. and Schiwietz G. (1991): Impact-parameter dependence of electronic energy loss and straggling of incident bare ions on H and He atoms by using the coupled-channel method. Phys Rev A 44, 2984–2992
Grande P.L. and Schiwietz G. (2009): Convolution approximation for the energy loss, ionization probability and straggling of fast ions. Nucl Instrum Methods B 267, 859–865
Herman F. and Skillman S. (1963): Atomic structure calculations. Prentice Hall, New Jersey
ICRU (2005): Stopping of ions heavier than helium, vol. 73 of ICRU Report. Oxford University Press, Oxford
Lindhard J. and Scharff M. (1953): Energy loss in matter by fast particles of low charge. Mat Fys Medd Dan Vid Selsk 27 no. 15, 1–31
Lindhard J. and Sørensen A.H. (1996): On the relativistic theory of stopping of heavy ions. Phys Rev A 53, 2443–2456
Malherbe J.B. and Alberts H.W. (1982): Energy-loss straggling in C and Ge of p, D and alpha particles in the energy region 0.2 to 2.4 MeV. Nucl Instrum Methods 192, 559–563
Ogawa H., Katayama I., Sugai I., Haruyama Y., Saito M., Yoshida K. and Tosaki M. (1996): Energy loss of high velocity \(^6\)Li\(^{2+}\) ions in carbon foils in charge state non-equilibrium region. Nucl Instrum Methods B 115, 66–69
Osmani O. and Sigmund P. (2011): Charge-state evolution of swift heavy-ion beams explored by matrix method. Nucl Instrum Methods B 269, 813–816
Rozet J.P., Stephan C. and Vernhet D. (1996): ETACHA: a program for calculating charge states at GANIL energies. Nucl Instrum Methods B 107, 67–70
Sørensen A.H. (2002): Stopping of relativistic hydrogen- and heliumlike heavy ions. Nucl Instrum Methods B 195, 106–117
Sigmund P. (1976): Energy loss of charged particles to molecular gas targets. Phys Rev A 14, 996–1005
Sigmund P. (1978): Statistics of particle penetration. Mat Fys Medd Dan Vid Selsk 40 no. 5, 1–36
Sigmund P. (1992): Statistical theory of charged-particle stopping and straggling in the presence of charge exchange. Nucl Instrum Methods B 69, 113–122
Sigmund P. (2006): Particle penetration and radiation effects, vol. 151 of Springer Series in Solid-State Sciences. Springer, Berlin
Sigmund P., Osmani O. and Schinner A. (2011): Charge-exchange straggling in equilibrium. Nucl Instrum Methods B 269, 804–809
Sigmund P. and Schinner A. (2003): Barkas effect, shell correction, screening and correlation in collisional energy-loss straggling of an ion beam. Europ Phys J D 23, 201–209
Sigmund P. and Schinner A. (2010): Impact-parameter-dependent stopping of swift ions. 3. Bunching and packing in energy-loss straggling. Europ Phys J D 58, 105–116
Sørensen A.H. (2010): Private communication. Unpublished
Sun G., Döbeli M., Müller A.M., Stocker M., Suter M. and Wacker L. (2007): Energy loss and straggling of heavy ions in silicon nitride in the low MeV energy range. Nucl Instrum Methods B 256, 586–590
Vockenhuber C., Jensen J., Julin J., Kettunen H., Laitinen M., Rossi M., Sajavaara T., Osmani O., Schinner A., Sigmund P. et al. (2013): Energy-loss straggling of 2–10 MeV/u Kr ions in gases. Europ Phys J D 67, 145
Weick H., Geissel H., Scheidenberger C., Attallah F., Baumann T., Cortina D., Hausmann M., Lommel B., Münzenberg G., Nankov N. et al. (2000): Slowing down of relativistic few-electron heavy ions. Nucl Instrum Methods B 164–165, 168–179
Yang Q., O’Connor D.J. and Wang Z. (1991): Empirical formulae for energy loss straggling of ions in matter. Nucl Instrum Methods B 61, 149
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Sigmund, P. (2014). Straggling. 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_5
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DOI: https://doi.org/10.1007/978-3-319-05564-0_5
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