• A. S. Chernyshev Одеський національний університет імені І. І. Мечникова
  • O. L. Mykhailov Odessa State Environmental University
  • A. V. Tsudik Odessa State Environmental University
  • I. S. Cherkasova Odessa State Environmental University


Ключові слова:

relativistic theory, radiative transitions, francium


The combined relativistic energy approach and relativistic many-body perturbation theory with the zeroth order Dirac-Kohn-Sham one-particle approximation are used for estimating the energies and the E1 radiative transitions amplitudes (oscillator strengths) for the low-excited states of the francium. The comparison with available theoretical and experimental (compilated) data is performed. The important point is linked with an accurate accounting for the complex exchange-correlation (polarization) effect contributions and using the optimized one-quasiparticle representation in the relativistic many-body perturbation theory zeroth order that significantly provides a physically reasonable agreement between theory and precise experiment.


Grant, I. Relativistic Quantum Theory of Atoms and Molecules. Oxford, 2007.

Glushkov, A., Khetselius, O., Svinaren-ko, A., Buyadzhi, V. Spectroscopy of autoionization states of heavy atoms and multiply charged ions. Odessa: 2015.

Buyadzhi, V. Laser multiphoton spectroscopy of atom embedded in Debye plasmas: multiphoton resonances and transitions. Photoelectronics. 2015, 24, 128-133.

Khetselius, O.Yu. Relativistic perturbation theory calculation of the hyperfine structure parameters for some heavy-element isotopes. Int. J. Quant. Chem. 2009, 109, 3330–3335.

Chernyakova, Y., Ignatenko, A., Vitavetskaya, L.A. Sensing the tokamak plasma parameters by means high resolution x-ray theoretical spectroscopy method: new scheme. Sensor Electr. and Microsyst. Techn. 2004, 1, 20-24.

Dzuba, V.A., Flambaum, V.V., Sushkov, O.P. Calculation of energy levels, E1 transition amplitudes, and parity violation in Fr Phys. Rev. A. 1995, 51, 3454.

Marinescu, M., Vrinceanu, D., Sadeghpour, H. Radiative transitions and van der Waals coefficients for francium. Phys. Rev. A. 1998, 58, R4259.

Safronova, U., Johnson, W., Derevianko, A. Relativistic many-body calculations of energy levels, hyperfine constants, electric-dipole matrix elements, and static polarizabilities for alkali-metal atoms. Phys. Rev. A. 1999, 60, 4476.

Ivanov, L.N., Ivanova, E.P., Aglitsky, E. Modern trends in the spectroscopy of multicharged ions. Phys. Rep. 1988, 166.

Svinarenko, A., Khetselius, O., Buyadzhi, V., Florko, T., Zaichko,P., Ponomarenko, E. Spectroscopy of Rydberg atoms in a Black-body radiation field: Relativistic theory of excitation and ionization. J. Phys.: Conf. Ser. 2014, 548, 012048.

Glushkov, A.V., Ivanov, L.N. Radiation decay of atomic states: atomic residue polarization and gauge noninvariant contributions. Phys. Lett. A 1992, 170, 33-36.

Glushkov A.V., Ivanov, L.N. DC strong-field Stark effect: consistent quantum-mechanical approach. J. Phys. B: At. Mol. Opt. Phys. 1993, 26, L379-386.

Glushkov, A. Spectroscopy of atom and nucleus in a strong laser field: Stark effect and multiphoton resonances. J. Phys.: Conf. Ser. 2014, 548, 012020

Glushkov, A. Spectroscopy of coope-rative muon-gamma-nuclear processes: Energy and spectral parameters J. Phys.: Conf. Ser. 2012, 397, 012011.

Khetselius, O.Yu. Quantum Geometry: New approach to quantization of quasistationary states of Dirac equation for superheavy ion and calculating hyperfine structure parameters. Proc. Int. Geometry Center. 2012, 5(3-4), 39-45.

Danilov, V., Kruglyak, Y., Pechenaya, V. The electron density-bond order matrix and the spin density in the restricted CI method. Theor. Chim. Act. 1969, 13(4), 288-296.

Kruglyak, Yu. Configuration interaction in the second quantization representation: basics with application up to full CI. ScienceRise. 2014, 4(2), 98-115.

Glushkov, A.V. Relativistic and correlation effects in spectra of atomic systems. Astroprint: Odessa, 2006.

Khetselius, O.Yu. Hyperfine structure of atomic spectra.- Odessa: Astroprint, 2008

Glushkov, A., Buyadzhi, V., Svinarenko, A., Ternovsky, E. Advanced relativistic energy approach in electron-collisional spectroscopy of multicharged ions in plasma. Concepts, Methods, Applications of Quantum Systems in Chemistry and Physics (Springer). 2018, 31, 55-69.

Dubrovskaya, Yu., Khetselius, O.Yu., Vitavetskaya, L., Ternovsky, V., Serga, I. Quantum chemistry and spectroscopy of pionic atomic systems with accounting for relativistic, radiative, and strong interaction effects. Adv. Quantum Chem. 2019, 78, 193-222.

Khetselius, O.Yu., Glushkov, A.V., Dubrovskaya, Yu., Chernyakova, Yu., Ignatenko, A., Serga, I., Vitavetskaya, L. Relativistic quantum chemistry and spectroscopy of exotic atomic systems with accounting for strong interaction effects. In Concepts, Methods and Applications of Quantum Systems in Chem. and Phys. Springer. 2018, 31, 71.

Buyadzhi, V.V., Chernyakova, Yu.G., Antoshkina, O., Tkach, T. Spectroscopy of multicharged ions in plasmas: Oscillator strengths of Be-like ion Fe. Photoelectronics. 2017, 26, 94-102.

Malinovskaya, S.V., Dubrovskaya, Yu.V., Zelentzova, T.N. The atomic chemical environment effect on the b decay probabilities: Relativistic calculation. Herald of Kiev Nat. Univ. Ser.: Phys.-Math. 2004, N4, 427-432.

Bystryantseva, A., Khetselius, O.Yu., Dubrovskaya, Yu., Vitavetskaya, L.A., Berestenk, A.G. Relativistic theory of spectra of heavy pionic atomic systems with account of strong pion-nuclear interaction effects: 93Nb, 173Yb, 181Ta, 197Au. Photoelectronics. 2016, 25, 56-61.

Buyadzhi, V., Zaichko, P., Antoshkina, O., Kulakli, T., Prepelitsa, P., Ternovsky, V., Mansarliysky, V. Computing of radiation parameters for atoms and multicharged ions within relativistic energy approach: Advanced Code. J. Phys.: Conf. Ser. 2017, 905(1), 012003.

Buyadzhi, V., Kuznetsova, A., Buyadzhi, A., Ternovsky, E.V., Tkach, T.В. Advanced quantum approach in radiative and collisional spectroscopy of multicharged ions in plasmas. Adv. in Quant. Chem. 2019, 78, 171-191.

Khetselius, O.Yu., Lopatkin, Yu.M., Dubrovskaya, Yu.V, Svinarenko, A.A. Sensing hyperfine-structure, electroweak interaction and parity non-conservation effect in heavy atoms and nuclei: New nuclear-QED approach. Sensor Electr. and Microsyst. Techn. 2010, 7(2), 11-19.

Glushkov, A.V., Khetselius, O.Yu., Svinarenko, A., Buyadzhi, V. Methods of computational mathematics and mathematical physics TES: Odessa, 2015.

Ignatenko, A.V., Svinarenko, A.A., Prepelitsa, G.P., Perelygina, T.B. Optical bi-stability effect for multi-photon absorption in atomic ensembles in a strong laser field. Photoelectronics. 2009, 18, 103-105.