Relativistic energy operator of magnetic interactions of electrons

Heavy multielectron atoms and multicharged ions with (αZ)² ~ c^v2₂ ≥ 0,01 

are relativistic systems. Studying their energy spectra requires considering the magnetic interactions of electrons and operation in the j-representation since the orbital quantum number in these cases becomes a bad quantum number. We use the relativistic quantum mechanical approach on the basis of coupled relativistic Dirac-type functions (functions-bispinors with larger and smaller components) to calculate the relativistic matrix elements of the energy operator of electron magnetic interactions in the Breit approximation in the case of one shell with any number of equivalent electrons. The function of the coupled moments of the shell of equivalent electrons is obtained using the Clebsch-Gordan coefficients and coefficients of fractional parentage. The Breit operator is responsible for the magnetic interactions of electrons. It has been transformed into a convenient form for studying the matrix elements of the operator regarding the functions of the coupled moments in the j-representation. It is possible to simplify the formulas for matrix elements when using the Casimir operators of the symplectic group Sp(2j+1).

1. Dirak, P. A. M. Sobranie nauchnyh trudov. T. 2. Kvantovaya teoriya (nauchnye stat'i 1924–1947). – Moskva : FIZMATLIT, 2003. – 848 s. – (Klassiki nauki). – ISBN 5-9221-0381-4 (T. II).

2. Beresteckij, V. B. Relyativistskaya kvantovaya teoriya : ch. 1 / V. B. Beresteckij, B. M. Lifshic,L. P. Pitaevskij. – Moskva : Nauka, 1968, – 480 s.

3. Ahiezer, A. I. Kvantovaya elektrodinamika / A. I. Ahiezer, V. B. Beresteckij. – Moskva : Nauka, 1981. – 428 s..

4. Breit, G. The Effect of Retardations on the Interactions of Two Electrons / G. Breit // Phys. Rev.– 1929. – V. 34. – P. 553.

5. Breit, G. The Fine Structure of HE as a Test of the Spin Interactions Two Electrons / G. Breit // Phys. Rev. – 1930. – V. 36. – P. 383.

6. Breit, G. Dirac’s Equation and the Spin-Spin Interactions of Two Electrons / G. Breit // Phys. Rev. – 1932. – V. 39. – P. 616.

7. Ralchenko, Yu. Spectroscopy of diagnostically important magnetic-dipole lines in highly charged 3dn ions of tungsten / Yu. Ralchenko, I. N. Draganić, D. Osin [et. al.] // Phys. Rev. A. – 2011. – Vol. 83. – No 032517.

8. Osin, D. EUV magnetic-dipole lines from highly-charged high-Z ions with an open 3d shell / D. Osin, J. D. Gillaspy, J. Reader, Yu Ralchenko // Eur. Phys. J. D. – 2012. – Vol. 66. – № 286. – Pp. 1–10.

9. Zhao, Z. L. Multi-configuration Dirac–Hartree–Fock calculations of forbidden transitions within the 3dk ground configurations of highly charged ions (Z=72–83) / Z. L. Zhao, K. Wang, S. Li [et. al.] // At. Data Nucl. Data Tables. – 2018. – Vol. 119, 314.

10. Froese Fisher C. Core Effects on Transition Energies for 3dk Configurations in Tungsten Ions / C. Froese Fisher, G. Gaigalas, P. Jönsson P. // Atoms. – 2017. – Vol. 5. – № 7. – Pp. 1–34.

11. Hawryluk, D. Principal physics developments evaluated in the ITER design review / R. Hawryluk,D. Campbell, G. Janeschitz [et al.] // Nucl. Fusion. – 2009. – Vol. 49. – № 0650129. – Pp. 1–15.

12. Arvanitaki, A. Searching for dilaton dark matter with atomic clocks /A. Arvanitaki, J. Huang, K. Van Tilburg // Phys. Rev. D. – 2015. – Vol. 91. – № 015015. – Pp. 1–17.

13. Roberts, B. M. Search for domain wall dark matter with atomic clocks on board global positioning system satellites / B. M. Roberts, G. Blewitt, C. Dailey //Nat. Commun. – 2017. – Vol. 8. – № 1195. – Pp. 1–9.

14. Ficek, F. Constraints on exotic spin-dependent interactions between electrons from heliumfine-structure spectroscopy / F. Ficek, D. F. J. Kimball, M. G. Kozlov [et. al.] // Phys. Rev. A. – 2017. – Vol. 95. – № 032505. – Pp. 1–9.

15. Safronova, M. S. Atomic properties of actinide ions with particle-hole configurations / M. S. Safronova U. I. Safronova M. G. // Phys. Rev. A. – 2018. – Vol. 97. – № 012511. – Pp. 1–5.

16. Kychkin, I. S. Osnovy relyativistskoj teorii mnogoelektronnyh atomov i ionov / I. S. Kychkin.– Moskva : Fizmatlit, 1994. – 273 s.