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Probabilities of Radiative Transitions

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Plasma Atomic Physics

Abstract

In this chapter, we consider the probability of photoprocesses including bound–bound, bound–free, and free–free electronic transitions. This concerns atomic radiation transitions in the discrete energy spectrum, radiative recombination, Bremsstrahlung including polarization channel, photoionization, photodetachment of negative ions, and phase control of photoprocesses by ultrashort laser pulses. Considerable attention has been paid to various types of broadening of the spectral lines of atomic radiative transitions, including plasma broadening mechanisms. The rotational approximation of the Kramers electrodynamics is presented which is suitable for describing both free–free and free–bound electronic transitions in the high frequency limit. The photoionization of atoms is described both within the framework of a rigorous quantum mechanical approach and with the help of a number of approximate methods. Analytical generalized photoionization cross section formulas from K-, L-, M-, N-, and O-shell that include also possible inner-shell photoionization are presented. Finally, generalized scaled formulas for radiation recombination rates into all states with principal quantum numbers n = 1–9 and orbital quantum numbers l = 0–8 are given that can be applied for a large variety of practical cases.

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References

  • M.Y. Amusia, Atomic Photoeffect (Springer, Berlin, 1990)

    Google Scholar 

  • D.R. Bates, A. Damgaard, The calculation of the absolute strengths of spectral lines. Phil. Trans. 242, 101 (1949)

    ADS  Google Scholar 

  • H.A. Bethe, E.E. Salpeter, Quantum Mechanics of One- and Two Electron Atoms (Springer, Berlin, 1977)

    Book  Google Scholar 

  • W. Brandt, S. Lundqvist, Atomic oscillations in the statistical approximation. Phys. Rev. 139, A612 (1965)

    Article  ADS  Google Scholar 

  • R.D. Cowan, The Theory of Atomic Structure and Spectra (University of California Press, Berkeley, 1981)

    Google Scholar 

  • V.A. Davydkin, B.A. Zon, Radiation and polarization characteristics of Rydberg atomic states. Opt. Spectrosk. 51, 13 (1981)

    ADS  Google Scholar 

  • R.A. Gantsev, N.F. Kazakova, V.P. Krainov, Radiation transition rates in hydrogen-like plasmas, in Plasma Chemistry, vol. 12, ed. by B.M. Smirnov (Energoatomizdat, Moscow, 1985), p. 96

    Google Scholar 

  • H. Gao, D.R. DeWitt, R. Schuch, W. Zong, S. Asp, M. Pajek, Observation of enhanced electron-ion recombination rates at very low energies. Phys. Rev. Lett. 75, 4381 (1995)

    Article  ADS  Google Scholar 

  • H. Gao, R. Schuch, W. Zong, E. Justinianoz, D.R. DeWitt, H. Lebius, W. Spies, Energy and charge dependence of the rate of electron–ion recombination in cold magnetized plasmas. J. Phys. B 30, L499–L506 (1997)

    Article  ADS  Google Scholar 

  • V.I. Gervids, V.I. Kogan, Penetration and screening effects in electron bremsstrahlung on ions. JETP Lett. 22, 142 (1975)

    ADS  Google Scholar 

  • V.I. Gervids, V.I. Kogan, Electron bremsstrahlung in a static potential, in Polarization Bremsstrahlung of Particles and Atoms, eds. by V.N. Tsytovich, I.M. Oiringel (Plenum, New York, 1991)

    Google Scholar 

  • S.P. Goreslavsky, N.B. Delone, V.P. Krainov, Probabilities of radiative transitions between highly excited atomic states. JETP 55, 1032 (1982)

    Google Scholar 

  • H.R. Griem, Spectral Line Broadening by Plasmas (Academic Press, New York, 1974)

    Google Scholar 

  • H.R. Griem, Principles of Plasma Spectroscopy (Cambridge University Press, New York, 1997)

    Book  Google Scholar 

  • C. Heerlein, G. Zwicknagel, C. Toepffer, Radiative recombination enhancement of bare ions in storage rings with electron cooling. Phys. Rev. Lett. 89, 83202 (2002) and erratum Phys. Rev. Lett. 93, 209901(E) (2004a)

    Google Scholar 

  • C. Heerlein, G. Zwicknagel, C. Toepffer, Reply to Hörndl et al. PRL 93, 209301 (2004). Phys. Rev. Lett. 93, 209302 (2004b)

    Google Scholar 

  • A. Hoffknecht, C. Brandau, T. Bartsch, C. Böhme, H. Knopp, S. Schippers, A. Müller, C. Kozhuharov, K. Beckert, F. Bosch, B. Franzke, A. Krämer, P.H. Mokler, F. Nolden, M. Steck, Th Stöhlker, Z. Stachura, Recombination of bare Bi83+ ions with electron. Phys. Rev. A 63, 012702 (2001)

    Article  ADS  Google Scholar 

  • M. Hörndl, S. Yoshida, K. Tokési, J. Burgdörfer, Comment on radiative recombination enhancement of bare ions in storage rings with electron cooling. Phys. Rev. Lett. 93, 209301 (2004)

    Article  ADS  Google Scholar 

  • M. Hörndl, S. Yoshida, A. Wolf, G. Gwinner, J. Burgdörfer, Enhancement of low energy electron-ion recombination in a magnetic field: Influence of transient field effects. Phys. Rev. Lett. 95, 243201 (2005)

    Article  ADS  Google Scholar 

  • J. Jackson, Classical Electrodynamics, 3rd edn. (Wiley, New York, 2007)

    MATH  Google Scholar 

  • L. Kim, R.H. Pratt, Direct radiative recombination of electrons with atomic ions: cross sections and rate coefficients, Phys. Rev. A 27, 2913 (1983)

    Google Scholar 

  • V.I. Kogan, A.B. Kukushkin, Radiation emission by quasiclassical electrons in an atomic potential. JETP 60, 665 (1984)

    Google Scholar 

  • V.I. Kogan, A.B. Kukushkin, V.S. Lisitsa, Kramers electrodynamics and electron-atomic radiative-collisional processes. Phys. Rep. 213, 1 (1992)

    Article  ADS  Google Scholar 

  • H.A. Kramers, On the theory of X-ray absorption and of the continuous X-ray spectrum. Phil. Mag. 46, 836 (1923)

    Article  Google Scholar 

  • A.B. Kukushkin, V.S. Lisitsa, Radiative cascades between Rydberg atomic states. JETP 61, 937 (1985)

    Google Scholar 

  • L.D. Landau, E.M. Lifschitz, Quantum Mechanics: Nonrelativistic Theory (Pergamon, Oxford, 1977)

    Google Scholar 

  • L.D. Landau, E.M. Lifschitz, The Classical Theory of Fields (Pergamon, Oxford, 2003)

    Google Scholar 

  • L.D. Landau, E.M. Lifschitz, Mechanics (Pergamon, Oxford, 2005)

    Google Scholar 

  • P.F. Naccache, Matrix elements and correspondence principles. J. Phys. B: At. Mol. Opt. Phys. 5, 1308 (1972)

    Article  ADS  Google Scholar 

  • F.B. Rosmej, V.A. Astapenko, V.S. Lisitsa, Effects of ultrashort laser pulse durations on Fano resonances in atomic spectra. Phys. Rev. A 90, 043421 (2014)

    Article  ADS  Google Scholar 

  • F.B. Rosmej, V.A. Astapenko, V.S. Lisitsa, Scaling laws for ionization of atomic states by ultra-short electromagnetic pulses. J. Phys. B 49, 025602 (2016)

    Article  ADS  Google Scholar 

  • F.B. Rosmej, V.A. Astapenko, V.S. Lisitsa, XUV and X-ray elastic scattering of attosecond electromagnetic pulses on atoms. J. Phys. B: At. Mol. Opt. Phys. 50, 235601 (2017)

    Google Scholar 

  • F.B. Rosmej, V.A. Vainshtein, V.A. Astapenko, V.S. Lisitsa, Statistical and quantum photoionization cross sections in plasmas: analytical approaches for any configurations including inner shells, Matter and Radiation at Extremes (Review) 5, 064202 (2020). Open access: https://aip.scitation.org/doi/10.1063/5.0022751

  • F.B. Rosmej, V.A. Astapenko, E. Khramov, XFEL and HHG interaction with matter: effects of ultrashort pulses and random spikes, Letter to Matter and Radiation at Extremes 6, 034001 (2021). Open access: https://doi.org/10.1063/5.0046040

  • F.B. Rosmej, V.A. Vainshtein, V.A. Astapenko, V.S. Lisitsa, Semi-empirical analytical radiative recombination rates into nl = 1s9l states for hydrogen and non H-like ions, in preparation for Matter and Radiation at Extremes (2022)

    Google Scholar 

  • J.M. Rost, Analytical total photo cross section for atoms. J. Phys. B. 28, L601 (1995)

    Article  ADS  Google Scholar 

  • I.I. Sobelman, Introduction to the Theory of Atomic Spectra (Pergamon, Oxford, 1972)

    Google Scholar 

  • I.I. Sobelman, Theory of Atomic Spectra (Alpha Science Int. Limited, Oxford, UK, 2006)

    Google Scholar 

  • I.I. Sobelman, L.A. Vainshtein, E.A. Yukov, Excitation of Atoms and Broadening of Spectral Lines, 2nd edn. (Springer, Berlin, 1995)

    Book  Google Scholar 

  • A. Sommerfeld, Atombau and Spektrallinien: Band I und II (Harri Deutsch, Frankfurt, 1978)

    Google Scholar 

  • A. Unsöld, Physik der Sternatmosphären (Springer, Berlin, 1955)

    Book  Google Scholar 

Download references

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Correspondence to Frank B. Rosmej .

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Rosmej, F.B., Astapenko, V.A., Lisitsa, V.S. (2021). Probabilities of Radiative Transitions. In: Plasma Atomic Physics. Springer Series on Atomic, Optical, and Plasma Physics, vol 104. Springer, Cham. https://doi.org/10.1007/978-3-030-05968-2_3

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