Skip to main content
SpringerLink
Log in

Interatomic Potentials, Scattering and Nuclear Stopping

  • Chapter
  • First Online:
Particle Penetration and Radiation Effects Volume 2

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 179))

  • 1404 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

    Google Scholar 

  • Abrahamson A.A. (1963a): Repulsive Interaction Potentials Between Rare-Gas Atoms. Heteronuclear Two-Center Systems. Phys Rev 133, A990–A1004

    Google Scholar 

  • Abrahamson A.A. (1963b): Repulsive Interaction Potentials Between Rare-Gas Atoms. Homonuclear Two-Center Systems. Phys Rev 130, 693–707

    Google Scholar 

  • 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

    Google Scholar 

  • Abramowitz M. and Stegun I.A. (1964): Handbook of mathematical functions. Dover, New York

    Google Scholar 

  • 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

    Google Scholar 

  • 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)]

    Google Scholar 

  • Amdur I. and Mason E.A. (1956): Scattering of high velocity neutral particles.IX. Ne-A; A-Ne. J Chem Phys 25, 632–634

    Google Scholar 

  • Biersack J.P. and Ziegler J.F. (1982): Refined Universal Potentials in Atomic Collisions. Nucl Instrum Methods 194, 93–100

    Google Scholar 

  • Bister M., Anttila A. and Keinonen J. (1975): Method for determination of nuclear and electronic stopping power parameters. Phys Lett A 53, 471–472

    Google Scholar 

  • Bohr N. (1948): The penetration of atomic particles through matter. Mat Fys Medd Dan Vid Selsk 18 no. 8, 1–144

    Google Scholar 

  • Born M. and Mayer J.E. (1932): Zur Gittertheorie der Ionenkristalle. Physica B 75, 1–18

    Google Scholar 

  • Daw M.S. (1989): Model of metallic cohesion: The embedded-atom method. Phys Rev B 39, 7441

    Google Scholar 

  • Daw M.S. and Baskes M.I. (1983): Semiempirical, quantum-mechanical calculation of hydrogen embrittlement in metals. Phys Rev Lett 50, 1285

    Google Scholar 

  • 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

    Google Scholar 

  • Dedkov G.V. (1984): On the Theory of the Interatomic Interaction Potential at High Projectile Velocities. Radiat Eff Lett 86, 127–132

    Google Scholar 

  • Dedkov G.V. (1989): Interatomic Interaction Potentials in the Electron Gas Approximation: Static Case. Nucl Instrum Methods B 36, 14–22

    Google Scholar 

  • Dedkov G.V. (1995): The interatomic interaction potentials in radiation physics. phys stat sol A 149, 453–514

    Google Scholar 

  • 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]

    Google Scholar 

  • 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

    Google Scholar 

  • Fermi E. and Amaldi E. (1934): Le orbite degli elementi. Mem Accad Italia 6, 119–149

    Google Scholar 

  • Firsov O.B. (1953): Opredelenie sil, deistvuyushchikh mezhdu atomami, pri pomoshchi differentsialnogo effektivnogo secheniya uprugogo rasseyaniya. Zh Eksp Teor Fiz 24, 279

    Google Scholar 

  • 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)]

    Google Scholar 

  • 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)]

    Google Scholar 

  • Firsov O.B. (1958): Scattering of ions by atoms. Zh Eksp Teor Fiz 34, 447. [Engl. transl. Soviet Physics Jetp 7, 308–311 (1958)]

    Google Scholar 

  • 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-

    Google Scholar 

  • Gombas P. (1949): Die Statistische Theorie des Atoms. Springer, Vienna

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Hartree D.R. and Hartree W. (1938): Self-Consistent Field with Exchange for Potassium and Argon. Rev Mod Phys 166, 450–464

    Google Scholar 

  • 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

    Google Scholar 

  • Herman F. and Skillman S. (1963): Atomic structure calculations. Prentice Hall, New Jersey

    Google Scholar 

  • 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

    Google Scholar 

  • Hoyt F.C. (1939): The determination of force fields from scattering in the classical theory. Phys Rev 55, 664–665

    Google Scholar 

  • 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

    Google Scholar 

  • Jensen H. (1932): Die Ladungsverteilung in Ionen und die Gitterkonstante des Rubidiumbromids nach der statistischen Methode. Z Physik 77, 722

    Google Scholar 

  • Kaminker D.M. and Fedorenko N.V. (1955): Single Scatter of Argon Ions During Stripping in a Gas. Zh Tekh Fiz 25, 2239–2255

    Google Scholar 

  • Khodyrev V.A. (2000): On the origin of the Bloch correction in stopping. J Phys B 33, 5045–5056

    Google Scholar 

  • 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

    Google Scholar 

  • Klein O. (1932): Zur Berechnung yon Potentialkurven für zweiatomige Moleküle mit Hilfe von Spektraltermen. Z Physik 76, 226–235

    Google Scholar 

  • Kuzmin V. (2006): Range Parameters of Heavy Ions in Carbon Calculated with First-Principles Potentials. Nucl Instrum Methods B 249, 13–17

    Google Scholar 

  • Lane G.H. and Everhart E. (1960): Ion-atom potential functions obtained from keV scattering data. Phys Rev 120, 2064-

    Google Scholar 

  • Lennard-Jones J.E. (1924): On the determination of molecular fields. Proc Roy Soc A 106, 463–477

    Google Scholar 

  • Lenz W. (1932): Über die Anwendbarkeit der statistischen Methode auf Ionengitter. Z Physik 77, 713

    Google Scholar 

  • Lindhard J. (1965): Influence of crystal lattice on motion of energetic charged particles. Mat Fys Medd Dan Vid Selsk 34 no. 14, 1–64

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Loftager P., Besenbacher F., Jensen O.S. and Sørensen V.S. (1979): Experimental study of effective interaction potentials. Phys Rev A 20, 1443

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Molière G. (1947): Theorie der Streuung schneller geladener Teilchen I. Einzelstreuung am abgeschirmten Coulomb-Feld. Z Naturforsch 2a, 133–145

    Google Scholar 

  • 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

    Google Scholar 

  • 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)]

    Google Scholar 

  • Nørskov J.K. (1977): Electronic structure of H and He in metal vacancies. Sol St Comm 24, 691–693

    Google Scholar 

  • 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

    Google Scholar 

  • Nørskov J.K. and Lang N.D. (1980): Effective-medium theory of chemical binding: Application to chemisorption. Phys Rev B 21, 2131–2136

    Google Scholar 

  • Oen O.S. (1983): Universal shadow cone expressions for an atom in an ion-beam. Surf Sci 131, L407–L411

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Ormrod J.H., MacDonald J.R. and Duckworth H.E. (1965): Some low-energy atomic stopping cross sections. Can J Physics 43, 275–284

    Google Scholar 

  • Robinson M.T. (1970): Table of classical scattering integrals. Tech. Rep. ORNL-4556, Oak Ridge National Laboratory

    Google Scholar 

  • 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

    Google Scholar 

  • Sidenius G. (1963). In M.R.C. McDowell, editor, Proceedings of the 3rd International Conference on Atomic Collisions, 709. North Holland, Amsterdam

    Google Scholar 

  • 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

    Google Scholar 

  • Sigmund P. (1997): Charge-dependent electronic stopping of swift nonrelativistic heavy ions. Phys Rev A 56, 3781–3793

    Google Scholar 

  • Srivastava K.P. (1958): Unlike molecular interactions and properties of gas mixtures. J Chem Phys 28, 543–549

    Google Scholar 

  • Stillinger F.H. and Weber T.A. (1985): Computer simulation of local order in condensed phases of silicon. Phys Rev B 31, 5262–5271

    Google Scholar 

  • Stott M.J. and Zaremba E. (1980): Quasiatoms: An approach to atoms in nonuniform electron systems. Phys Rev B 22, 1564–1583

    Google Scholar 

  • Tersoff J. (1986): New empirical model for the structural properties of silicon. Phys Rev Lett 56, 632–635

    Google Scholar 

  • Wedepohl P.T. (1967): Influence of Electron Distribution on Atomic Interaction Potentials. Proc Phys Soc 92, 79–93

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Winterbon K.B. (1972): Heavy-ion range profiles and associated damage distributions. Radiat Eff 13, 215–226

    Google Scholar 

  • 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

    Google Scholar 

  • Witte H. and Wölfel E. (1958): Electron Distributions in NaCl, LiF, CaF\(_2\), and Al. Rev Mod Phys 30, 51–55

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Ziemba F.P. and Everhart E. (1959): Resonance Phenomena in Large-Angle Helium Ion-Helium Atom Collisions. Phys Rev Lett 2, 299–301

    Google Scholar 

  • Zinoviev A.N. (2011): Interaction potentials for modeling of ion-surface scattering. Nucl Instrum Methods B 269, 829–833

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Deptartment of Physics, Chemistry and Pharmacy, University of Southern Denmark, Odense M., Denmark

    Peter Sigmund

Authors
  1. Peter Sigmund
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Peter Sigmund .

Rights and permissions

Reprints 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

Publish with us

Policies and ethics

Search

Navigation