Skip to main content
Log in

Normalized Mott Cross Section in Different Approaches

  • PHYSICS OF ELEMENTARY PARTICLES AND ATOMIC NUCLEI. THEORY
  • Published:
Physics of Particles and Nuclei Letters Aims and scope Submit manuscript

Abstract

An intercomparison is carried out for some earlier approaches to the calculation of the normalized Mott cross section, as well as the approach proposed by the authors of the present work. It is demonstrated that applying the proposed method, along with the method of Lijian et al., is preferable for relevant calculations.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1.
Fig. 2.

Similar content being viewed by others

Notes

  1. At energies higher than 10 MeV, the results are very close to those of 10 MeV, according to [18], since β in this case is close to 1.

REFERENCES

  1. P. Sigmund and A. Schinner, “Progress in understanding heavy-ion stopping,” Nucl. Instrum. Methods Phys. Res., Sect. B 382, 15–25 (2016). https://doi.org/10.1016/j.nimb.2015.12.041

    Article  Google Scholar 

  2. P. Sigmund, Particle Penetration and Radiation Effects: General Aspects and Stopping of Swift Point Particles, Vol. 151 of Springer Series in Solid State Sciences (Springer, Berlin, Heidelberg, 2006).

  3. N. Forcellini and E. Artacho, “Floquet theory for the electronic stopping of projectiles in solids,” arXiv: 1908.09783 [cond-mat.mtrl-sci] (2019).

  4. H. A. Bethe and J. Ashkin, Experimental Nuclear Physics, Ed. by E. Segre (Wiley, New York, 1953).

    Google Scholar 

  5. H. Bethe, “Bremsformel für Elektronen relativistischer Geschwindigkeit,” Z. Phys. 76, 293–299 (1932). https://doi.org/10.1007/BF01342532

    Article  ADS  MATH  Google Scholar 

  6. F. Bloch, “Zur Bremsung rasch bewegter Teilchen beim Durchgang durch Materie,” Ann. Phys. 16, 285–320 (1933). https://doi.org/10.1002/andp.19334080303

    Article  MATH  Google Scholar 

  7. N. F. Mott, “The scattering of fast electrons by atomic nuclei,” Proc. R. Soc. London, Ser. A 124, 425–442 (1929). https://doi.org/10.1098/rspa.1929.0127

    Article  ADS  MATH  Google Scholar 

  8. N. F. Mott, “The polarization of electrons by double scattering,” Proc. R. Soc. London, Ser. A 135, 429–458 (1932). https://doi.org/10.1098/rspa.1932.0044

    Article  ADS  MATH  Google Scholar 

  9. P. B. Eby and S. H. Morgan, Jr., “Charge dependence of ionization energy loss for relativistic heavy nuclei,” Phys. Rev. A 6, 2536–2541 (1972). https://doi.org/10.1103/PhysRevA.5.2536

    Article  ADS  Google Scholar 

  10. S. H. Morgan, Jr. and P. B. Eby, “Corrections to the Bethe–Bloch formula for average ionization energy loss of relativistic heavy nucley,” Nucl. Instrum. Methods Phys. Res. 106, 429–435 (1973). https://doi.org/10.1016/0029-554X(73)90303-0

    Article  ADS  Google Scholar 

  11. O. O. Voskresenskaya, A. N. Sissakyan, A. V. Tarasov, and G. T. Torosyan, “Expression for the Mott corrections to the Bethe–Bloch Formula in terms of the Mott partial amplitudes,” JETP Lett. 64, 604–607 (1996). https://doi.org/10.1134/1.567276

    Article  Google Scholar 

  12. E. F. R. S. Rutherford, “The scattering of α and β particles by matter and the structure of the atom,” Philos. Mag. 21, 669–688 (1911). http://dbhs.wvusd.k12.ca.us/Chem-History/Rutherford-1911/Rutherford-1911.htm.

    Article  Google Scholar 

  13. W. Gordon, “Über den Stoß zweier Punktladungen nach der Wellenmechanik,” Z. Phys. 48, 180–191 (1928). https://doi.org/10.1007/BF01351302

    Article  ADS  MATH  Google Scholar 

  14. N. F. Mott, “The solution of the wave equation for the scattering of particles by a coulombian centre of force,” Proc. R. Soc. London, Ser. A 118, 542–549 (1928). https://doi.org/10.1098/rspa.1928.0067

    Article  ADS  MATH  Google Scholar 

  15. G. Temple, “The scattering power of a bare nucleus according to wave mechanics,” Proc. R. Soc. London, Ser. A 121, 673–675 (1928). https://doi.org/10.1098/rspa.1928.0225

    Article  ADS  MATH  Google Scholar 

  16. W. A. McKinley and H. Feshbach, “The Coulomb scattering of relativistic electrons by nuclei,” Phys. Rev. 74, 1759–1763 (1948). https://doi.org/10.1103/PhysRev.74.1759

    Article  ADS  Google Scholar 

  17. W. R. Johnson, T. A. Weber, and C. J. Mullin, “Coulomb scattering of polarized electrons,” Phys. Rev. 121, 933–939 (1961).

    Article  ADS  MathSciNet  Google Scholar 

  18. T. Lijian, H. Qing, and L. Zhengming, “Analytic fitting to the Mott cross section of electrons,” Radiat. Phys. Chem. 45, 235–245 (1995).

    Article  ADS  Google Scholar 

  19. M. J. Boschini, C. Consolandi, M. Gervasi, S. Giani, D. Grandi, V. Ivanchenko, P. Nieminem, S. Pensotti, P. G. Rancoita, and M. Tacconi, “An expression for the Mott cross section of electrons and positrons on nuclei with Z up to 118,” Radiat. Phys. Chem. 90, 39–66 (2013).

    Article  ADS  Google Scholar 

  20. D. R. Yennie, D. G. Ravenhall, and R. N. Wilson, “Phase-shift calculation of high-energy electron scattering,” Phys. Rev. 95, 500–512 (1954).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to O. O. Voskresenskaya.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kats, P.B., Halenka, K.V. & Voskresenskaya, O.O. Normalized Mott Cross Section in Different Approaches. Phys. Part. Nuclei Lett. 18, 277–283 (2021). https://doi.org/10.1134/S1547477121030080

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1547477121030080

Keywords:

Navigation