Abstract
This chapter focuses on interatomic potentials of interest in single and multiple scattering of heavy charged particles and the associated energy loss. In the keV energy range and above it is commonly assumed that binary elastic scattering on central potentials makes up an adequate description. Limitations of this description are mentioned. Classical scattering for screened-Coulomb interaction is outlined, and special attention is given to scaling properties, in particular for Thomas-Fermi-type interaction. Power-law scattering is mentioned as a convenient tool for rough estimates. Comparisons between different theoretical estimates as well as between measured and calculated cross sections are presented, and attempts to directly invert a measured cross section into the underlying potential are reported. The chapter concludes with explicit results for nuclear stopping and straggling including pertinent experiments.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
- Interatomic Potential
- Screen Function
- Interatomic Interaction Potential
- Screen Radius
- Stop Cross Section
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Aberth W., Lorents D.C., Marchi R.P. and Smith F.T. (1965): Effect of nuclear symmetry in ion-atom scattering. Phys Rev Lett 14, 776–778
Abrahamson A.A. (1963a): Repulsive Interaction Potentials Between Rare-Gas Atoms. Heteronuclear Two-Center Systems. Phys Rev 133, A990–A1004
Abrahamson A.A. (1963b): Repulsive Interaction Potentials Between Rare-Gas Atoms. Homonuclear Two-Center Systems. Phys Rev 130, 693–707
Abrahamson A.A., Hatcher R.D. and Vineyard G.H. (1961): Interatomic Repulsive Potentials at Very Small and Intermediate Separations. Phys Rev 121, 159–171
Abramowitz M. and Stegun I.A. (1964): Handbook of mathematical functions. Dover, New York
Adams J.B. and Foiles S.M. (1990): Development of an embedded-atom potential for a bcc metal: Vanadium. Phys Rev B 41, 3316–3328
Afrosimov V.V., Gordeev Y.S., Nikulin V.K., Polyanski A.M., and Shergin A.P. (1972): Singularities in scattering of atomic particles in collisions involving the excitation of inner electron shells. Zh Exp Teor Fiz 62, 848–862. [Engl. Transl. in, Sov. Phys. JETP 35, 449–456 (1972)]
Amdur I. and Mason E.A. (1956): Scattering of high velocity neutral particles.IX. Ne-A; A-Ne. J Chem Phys 25, 632–634
Biersack J.P. and Ziegler J.F. (1982): Refined Universal Potentials in Atomic Collisions. Nucl Instrum Methods 194, 93–100
Bister M., Anttila A. and Keinonen J. (1975): Method for determination of nuclear and electronic stopping power parameters. Phys Lett A 53, 471–472
Bohr N. (1948): The penetration of atomic particles through matter. Mat Fys Medd Dan Vid Selsk 18 no. 8, 1–144
Born M. and Mayer J.E. (1932): Zur Gittertheorie der Ionenkristalle. Physica B 75, 1–18
Daw M.S. (1989): Model of metallic cohesion: The embedded-atom method. Phys Rev B 39, 7441
Daw M.S. and Baskes M.I. (1983): Semiempirical, quantum-mechanical calculation of hydrogen embrittlement in metals. Phys Rev Lett 50, 1285
Daw M.S. and Baskes M.I. (1984): Embedded-atom method - derivation and application to impurities, surfaces, and other defects in metals. Phys Rev B 29, 6443–6453
Dedkov G.V. (1984): On the Theory of the Interatomic Interaction Potential at High Projectile Velocities. Radiat Eff Lett 86, 127–132
Dedkov G.V. (1989): Interatomic Interaction Potentials in the Electron Gas Approximation: Static Case. Nucl Instrum Methods B 36, 14–22
Dedkov G.V. (1995): The interatomic interaction potentials in radiation physics. phys stat sol A 149, 453–514
Demkov Y.N., Ostrovskii V.N., and Berezina N.B. (1971): Uniqueness of the Firsov inversion method and focusing potentials. Zh Eks Teor Fiz 60, 1604–1610. [Engl. Transl. in, Sov. Phys. JETP 33, 867–870]
Everhart E., Carbone R.J. and Stone G. (1955): Differential cross-section measurements for large-angle collisions of helium, neon and argon ions with argon atoms at energies to 100 keV. Phys Rev 98, 1045–1049
Fermi E. and Amaldi E. (1934): Le orbite degli elementi. Mem Accad Italia 6, 119–149
Firsov O.B. (1953): Opredelenie sil, deistvuyushchikh mezhdu atomami, pri pomoshchi differentsialnogo effektivnogo secheniya uprugogo rasseyaniya. Zh Eksp Teor Fiz 24, 279
Firsov O.B. (1957a): Calculation of the interaction potential of atoms. Zh Eksp Teor Fiz 33, 696. [Engl. transl. Sov. Phys. JETP 6, 5340–537 (1958)]
Firsov O.B. (1957b): Interaction energy of atoms for small nuclear separations. Zh Eksp Teor Fiz 32, 1464–1469. [Engl. transl. Sov. Phys. JETP 5, 1192–1196(1957)]
Firsov O.B. (1958): Scattering of ions by atoms. Zh Eksp Teor Fiz 34, 447. [Engl. transl. Soviet Physics Jetp 7, 308–311 (1958)]
Gilbert T.L. and Wahl A.C. (1967): Single-Configuration Wavefunctions and Potential Curves for Ground States of He\(_2\), Ne\(_2\) and Ar\(_2\). J Chem Phys 47, 3425-
Gombas P. (1949): Die Statistische Theorie des Atoms. Springer, Vienna
Grahmann H. and Kalbitzer S. (1976): Nuclear and electronic stopping powers of low energy ions with \(Z\le 10\) in silicon. Nucl Instrum Methods 132, 119–123
Günther K. (1964): Über die Existenz eines Maximalprinzips als äquivalente Formulierung des Thomas-Fermi-Dirac-Modells und das TFD-Wechselwirkungspotential v on Atomen. Ann Physik 14, 296–309
Hartree D.R. and Hartree W. (1938): Self-Consistent Field with Exchange for Potassium and Argon. Rev Mod Phys 166, 450–464
Hartung H., Fricke B., Sepp W.D., Sengler W. and Kolb D. (1985): Theoretical evidence for quasi-molecular structure at small internuclear distances in elastic ion-atom scattering. J Phys B 18, L433–L437
Herman F. and Skillman S. (1963): Atomic structure calculations. Prentice Hall, New Jersey
Högberg G. and Skoog R. (1972): Non-evidence for \(Z_1\) oscillations of the nuclear ion-atom interaction in an amorphous target. Radiat Eff 13, 197–202
Hoyt F.C. (1939): The determination of force fields from scattering in the classical theory. Phys Rev 55, 664–665
Hvelplund P. (1975): Energy loss and straggling of 100–500 keV \(_{90}\)Th, \(_{82}\)Pb, \(_{80}\)Hg, and \(_{64}\)Gd in H\(_2\). Phys Rev A 11, 1921–1927
Jensen H. (1932): Die Ladungsverteilung in Ionen und die Gitterkonstante des Rubidiumbromids nach der statistischen Methode. Z Physik 77, 722
Kaminker D.M. and Fedorenko N.V. (1955): Single Scatter of Argon Ions During Stripping in a Gas. Zh Tekh Fiz 25, 2239–2255
Khodyrev V.A. (2000): On the origin of the Bloch correction in stopping. J Phys B 33, 5045–5056
Kim Y.S. and Gordon R.G. (1974): Ionrare Gas Interactions on the Repulsive Part of the Potential Curves. J Chem Phys 60, 4323–4331
Klein O. (1932): Zur Berechnung yon Potentialkurven für zweiatomige Moleküle mit Hilfe von Spektraltermen. Z Physik 76, 226–235
Kuzmin V. (2006): Range Parameters of Heavy Ions in Carbon Calculated with First-Principles Potentials. Nucl Instrum Methods B 249, 13–17
Lane G.H. and Everhart E. (1960): Ion-atom potential functions obtained from keV scattering data. Phys Rev 120, 2064-
Lennard-Jones J.E. (1924): On the determination of molecular fields. Proc Roy Soc A 106, 463–477
Lenz W. (1932): Über die Anwendbarkeit der statistischen Methode auf Ionengitter. Z Physik 77, 713
Lindhard J. (1965): Influence of crystal lattice on motion of energetic charged particles. Mat Fys Medd Dan Vid Selsk 34 no. 14, 1–64
Lindhard J., Nielsen V. and Scharff M. (1968): Approximation method in classical scattering by screened Coulomb fields. Mat Fys Medd Dan Vid Selsk 36 no. 10, 1–32
Lindhard J., Scharff M. and Schiøtt H.E. (1963): Range concepts and heavy ion ranges. Mat Fys Medd Dan Vid Selsk 33 no. 14, 1
Lockwood G.J., Helbig H.F. and Everhart E. (1963): Measurements of Resonant Electron Capture in \({\rm {He}}^{+}\) on He Collisions. Phys Rev 132, 2078–2082
Loftager P., Besenbacher F., Jensen O.S. and Sørensen V.S. (1979): Experimental study of effective interaction potentials. Phys Rev A 20, 1443
Loftager P. and Hermann G. (1968): Influence of \(Q\) values in atomic single collisions on observed scattering cross sections and som \(Q\) values. Phys Rev Lett 21, 1623–1626
Martini V. (1976): Stopping cross-section measurements with heavy ions in keV energy-range in gases by time-of-flight spectroscopy. Nucl Instrum Methods 139, 163–167
Molière G. (1947): Theorie der Streuung schneller geladener Teilchen I. Einzelstreuung am abgeschirmten Coulomb-Feld. Z Naturforsch 2a, 133–145
Nielsen K.O. (1956): The range of atomic particles with energies about 50 keV. In M.L. Smith, editor, Electromagnetically Enriched Isotopes and Mass Spectrometry. AERE Harwell, Butterworth Sci. Pub., London
Nikulin V.K. (1971): Calculation of repulsive atomic-interaction potentials from statistical theory. Zh Tekh Fiz 41, 33–40. [Engl. transl.: Sov. Phys. Techn. Phys. 16, 21–27 (1971)]
Nørskov J.K. (1977): Electronic structure of H and He in metal vacancies. Sol St Comm 24, 691–693
Nørskov J.K. (1982): Covalent effects in the effective-medium theory of chemical binding: Hydrogen heats of solution in the 3d metals. Phys Rev B 26, 2875–2885
Nørskov J.K. and Lang N.D. (1980): Effective-medium theory of chemical binding: Application to chemisorption. Phys Rev B 21, 2131–2136
Oen O.S. (1983): Universal shadow cone expressions for an atom in an ion-beam. Surf Sci 131, L407–L411
Oetzmann H., Feuerstein A., Grahmann H. and Kalbitzer S. (1975): Range parameters of heavy-ions in amorphous targets at LSS-energies of \(0.0006\le \epsilon \le 0.3\). Phys Lett A 55, 170–172
Olsen J.O., Andersen T., Barat M., Courbin-Gaussorgues C., Sidis V., Pommier J., Agusti J., Andersen N. and Russek A. (1979): Excitation and charge transfer in low-energy Na\(^+\)-Ne collisions. Phys Rev A 19, 1457–1484
Ormrod J.H. and Duckworth H.E. (1963): Stopping cross sections in carbon for low-energy atoms with \(Z\le 12\). Can J Physics 41, 1424–1442
Ormrod J.H., MacDonald J.R. and Duckworth H.E. (1965): Some low-energy atomic stopping cross sections. Can J Physics 43, 275–284
Robinson M.T. (1970): Table of classical scattering integrals. Tech. Rep. ORNL-4556, Oak Ridge National Laboratory
Shane K.C., Laumer H. and Seaman G.G. (1976): Energy loss of low-energy \(^{40}\)Ca ions in C. J Appl Phys 47, 2286–2288
Sidenius G. (1963). In M.R.C. McDowell, editor, Proceedings of the 3rd International Conference on Atomic Collisions, 709. North Holland, Amsterdam
Sidenius G. (1974): Systematic stopping cross section measurements with low energy ions in gases. Mat Fys Medd Dan Vid Selsk 39 no. 4, 1–32
Sigmund P. (1997): Charge-dependent electronic stopping of swift nonrelativistic heavy ions. Phys Rev A 56, 3781–3793
Srivastava K.P. (1958): Unlike molecular interactions and properties of gas mixtures. J Chem Phys 28, 543–549
Stillinger F.H. and Weber T.A. (1985): Computer simulation of local order in condensed phases of silicon. Phys Rev B 31, 5262–5271
Stott M.J. and Zaremba E. (1980): Quasiatoms: An approach to atoms in nonuniform electron systems. Phys Rev B 22, 1564–1583
Tersoff J. (1986): New empirical model for the structural properties of silicon. Phys Rev Lett 56, 632–635
Wedepohl P.T. (1967): Influence of Electron Distribution on Atomic Interaction Potentials. Proc Phys Soc 92, 79–93
Wilson W.D. and Bisson C.L. (1971): Inert Gases in Solids: Interatomic Potentials and their Influence on Rare-Gasmobility. Phys Rev B 3, 3984–3992
Wilson W.D., Haggmark L.G. and Biersack J.P. (1977): Calculations of nuclear stopping, ranges and straggling in the low-energy region. Phys Rev B 15, 2458–2468
Winterbon K.B. (1972): Heavy-ion range profiles and associated damage distributions. Radiat Eff 13, 215–226
Winterbon K.B., Sigmund P. and Sanders J.B. (1970): Spatial distribution of energy deposited by atomic particles in elastic collisions. Mat Fys Medd Dan Vid Selsk 37 no. 14, 1–73
Witte H. and Wölfel E. (1958): Electron Distributions in NaCl, LiF, CaF\(_2\), and Al. Rev Mod Phys 30, 51–55
Yamamura Y. and Takeuchi W. (1984): Large-angle surface scattering of low-energy ions in the 2-atom scattering model. Radiat Eff 82, 73–84
Ziegler J.F., Biersack J.P. and Littmark U. (1985): The stopping and range of ions in solids, vol. 1 of The stopping and ranges of ions in matter. Pergamon, New York
Ziemba F.P. and Everhart E. (1959): Resonance Phenomena in Large-Angle Helium Ion-Helium Atom Collisions. Phys Rev Lett 2, 299–301
Zinoviev A.N. (2011): Interaction potentials for modeling of ion-surface scattering. Nucl Instrum Methods B 269, 829–833
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Sigmund, P. (2014). Interatomic Potentials, Scattering and Nuclear Stopping. 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_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-05564-0_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-05563-3
Online ISBN: 978-3-319-05564-0
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)