Issues

 / 

2015

 / 

August

  

Physics of our days


Coulomb problem for a Z>Zcr

 a,  a,  a,  a,  b,  c
a National Research Nuclear University MEPhI, Kashirskoe shosse 31, Moscow, 115409, Russian Federation
b Institute of Spectroscopy, Russian Academy of Sciences, ul. Fizicheskaya 5, Troitsk, Moscow, 108840, Russian Federation
c Russian Federation State Scientific Center A.I. Alikhanov Institute ofTheoretical and Experimental Physics, ul. Bolshaya Cheremushkinskaya 25, Moscow, 117259, Russian Federation

A closed form equation is derived for the critical nucleus charge, i.e. for the value Z=Zcr at which the discrete level with the Dirac quantum number touches the lower continuum of Dirac equation solutions. For a Coulomb potential cut off rectangularly at a small distance r0 = Rħ/(mc), R ⪡ 1, the critical nucleus charge values are obtained for several values of κ and R. It is shown that the partial scattering matrix of the elastic positron-nucleus scattering, Sκ = exp (2iδκp)), is also unitary for Z>Zcr. For this range, the scattering phase δκp) is calculated as a function of the positron energy Ep = εpmc2, as are the positions and widths of quasidiscrete levels corresponding to the scattering matrix poles. The implication is that the single-particle approximation for the Dirac equation is valid not only for ZZcr and that there is no spontaneous creation of e+e pairs from vacuum.

Fulltext is available at IOP
Keywords: the Coulomb problem, pointlike nucleus, boundary conditions, critical charge, scattering phase, Breit—Wigner resonance
PACS: 03.65.Pm, 12.20.−m, 73.22.Pr (all)
DOI: 10.3367/UFNe.0185.201508d.0845
URL: https://ufn.ru/en/articles/2015/8/d/
Citation: Kuleshov V M, Mur V D, Narozhnyi N B, Fedotov A M, Lozovik Yu E, Popov V S "Coulomb problem for a Z>Zcr" Phys. Usp. 58 785–791 (2015)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 16th, June 2015, 23rd, June 2015

:   ,   ,   ,   ,   ,    « Z>Zcr» 185 845–852 (2015); DOI: 10.3367/UFNr.0185.201508d.0845

References (46) Cited by (24) ↓ Similar articles (5)

  1. Krylov K S, Mur V D, Fedotov A M Eur. Phys. J. C 80 (3) (2020)
  2. Xia Ch-Ju, Xue Sh-Sh et al Phys. Rev. D 101 (10) (2020)
  3. Grashin P, Sveshnikov K Annals Of Physics 415 168094 (2020)
  4. Breev A I, Ferreira R et al J. Exp. Theor. Phys. 130 711 (2020)
  5. Sveshnikov K A, Voronina Yu S et al Theor Math Phys 199 533 (2019)
  6. Sveshnikov K A, Voronina Yu S et al Theor Math Phys 198 331 (2019)
  7. Krylov K S, Mur V D J. Phys.: Conf. Ser. 1238 012042 (2019)
  8. Popov V S, Popruzhenko S V Phys. Atom. Nuclei 82 1583 (2019)
  9. Voronina Yu, Komissarov I, Sveshnikov K Annals Of Physics 404 132 (2019)
  10. Garanin S F, Kravets E M Physics Letters A 383 27 (2019)
  11. Godunov S I, Glazyrin S I et al EPJ Web Conf. 182 02047 (2018)
  12. Davydov A, Sveshnikov K, Voronina Yu Int. J. Mod. Phys. A 33 1850004 (2018)
  13. Rochev V E Eur. Phys. J. C 78 (11) (2018)
  14. Davydov A, Sveshnikov K, Voronina Yu Int. J. Mod. Phys. A 33 1850005 (2018)
  15. Godunov S, Machet B et al EPJ Web Conf. 191 02018 (2018)
  16. Kuleshov V M, Mur V D, Narozhny I N B J. Phys.: Conf. Ser. 788 012044 (2017)
  17. Kuleshov V M, Mur V D et al J. Exp. Theor. Phys. 125 1144 (2017)
  18. Kuleshov V M, Mur V D et al J. Phys.: Conf. Ser. 941 012048 (2017)
  19. Voronina Yu S, Davydov A S, Sveshnikov K A Theor Math Phys 193 1647 (2017)
  20. Godunov S I, Machet B, Vysotsky M I Eur. Phys. J. C 77 (11) (2017)
  21. Voronina Yu, Davydov A, Sveshnikov K Phys. Part. Nuclei Lett. 14 698 (2017)
  22. Davydov A, Sveshnikov K, Voronina Yu Int. J. Mod. Phys. A 32 1750054 (2017)
  23. Ershov D K Russ Phys J 60 741 (2017)
  24. Voronov B L, Voronov B L i dr Teoreticheskaya Matematicheskaya Fizika 187 213 (2016) [Voronov B L, Gitman D M et al Theor Math Phys 187 633 (2016)]

© 1918–2020 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions