Specialization : 510402 Quantum mechanics
Curriculum : 32 Quantum mechanics of atoms, molecules and solids
Supervisor of the curriculum: Prof. Dr. Yu. Yu. Dmitriev
Department of quantum mechanics
Scientific adviser: Prof. Dr. I. I. Tupitsyn
Reviewer: Candidate of Science, Yu. S. Kozhedub
Transition energies and isotope shifts in heavy atoms with the inner-shell vacancies and in highly charged ions
Natalia A. Zubova
This work consists of two stages. The first stage of the work is carried out high-precision calculations of energies of X-Ray lines and calculations of energies atoms and ions with two vacancies in the inner shells. The calculations starts with the Dirac-Fock method and include
Breit, electron-correlation [1] and quantum electrodynamics correlations. The nuclear charge distribution is taken into account within the Fermi model. The approximation in which the energy is averaged over the all atomic terms of the nonrelativistic valence configuration is employed. The relevance of such calculations associated with such works as, for example,
[2],[3], which presents the results of high-precision calculations of X-Ray lines. The end of this stage of work the comparison the results of calculations of X-Ray lines with available experimental data is performed [4].
In the second stage of this work the studying and the calculation of the isotope shifts in heavy atoms and multi-charged ions is described. Through a comparative analysis of theoretical and experimental values of isotope shifts we can get additional information about charge density distribution, determine the RMS radii of cores, test the quantum electrodynamics, and so on.
Initially the nuclear size effect due to changes parameters of the nuclear density from one isotope to another is considered. This effect was calculated using the Dirac-Fock-Sturm and include all necessary corrections, as described above. Calculations were performed for both the heavy atoms, and for the multi-charged ions. In the case of heavy atoms, which is uranium, this effect is about 2000 meV for the case of Kα -line.
The theory of the isotope shift must include the nuclear size, nuclear recoil and nuclear polarization effects. To meet the experimental accuracy for ions the nuclear recoil contribution
(mass shift) has to be calculated within the full relativistic theory which implies using the relativistic recoil operator [V.M.Shabaev, Phys. Rev. A 57, 59 (1998)]. To perform the calculations we use the perturbation theory in the parameter 1/Z (zeroth and first order) for the case of Li-like ions, where Z is the nuclear charge number.
Numerical calculations of these contributions were carried out with hydrogen-like Dirac wave functions. The Dirac equation was solved using the dual kinetic balance (DKB) method with the basis functions constructed from B-splines [V. M. Shabaev, I. I. Tupitsyn, V. A.
Yerokhin, G. Plunien, and G. Soff, Phys. Rev. Lett. 93, 130405 (2004)]
References:
1. V. Bratsev, G. Deyneka, and I. Tupitsyn, Bull. Acad. Sci. USSR, Phys. Ser. (English
Tra nsl.), 41, 173 (1977)
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2. T. Mooney, E. Lindroth, P. Indelicato, E. G. Kessler, Jr., and R. D. Deslattes, Precision measurements of K and L transitions in xenon: Expirement and theory for the K, L, and M levels, Phys. Rev. A 45, 1531-1543 (1992)
3. P. Indelicato, E. Lindroth, Relativistic effects, correlation, and QED corrections on Kα transitions in medium to very heavy atoms, Phys. Rev. A 46, 2426-2436 (1992)
4. R. D. Deslattes, E. G. Kessler, Jr., P. Indeicato, L. de Billy, E. Lindroth, J. Anton,
X-Ray transition energies: New approach to a comprehensive evaluation, Rev. Mod.
Phys. 75, 35-99 (2003)
The list of publication
1. S.Eliseev, C. Roux, K. Blaum, M. Block, C. Droese, F. Herfurth, H.-J. Kluge, M. I.
Krivoruchenko, Yu. N. Novikov, E. Minaya Ramirez, L. Schweikhard, V. M. Shabaev,
F. Simkovic, I. I. Tupitsyn, K. Zuber, and N. A. Zubova: Resonant Enhancement of
Neutrinoless Double-Electron Capture in 152 Gd , Phys. Rev. Lett. 106, 052504 (2011)
2. S. Eliseev, M. Goncharov, K. Blaum, M. Block, C. Droese, F. Herfurth, E. Minaya
Ramirez, Yu. N. Novikov, L. Schweikhard, V. M. Shabaev, I. I. Tupitsyn, K. Zuber, and
N. A. Zubova: Multiple-resonance phenomenon in neutrinoless double-electron capture,
Phys. Rev. C 84, 012501(R) (2011)
3. C. Droese, K. Blaum, M. Block, S. Eliseev, F. Herfurth, E. Minaya Ramirez, Yu.N.
Novikov, L. Schweikhard, V.M. Shabaev, I.I. Tupitsyn, S. Wycech, K. Zuber, N.A.
Zubova, Probing the nuclide 180 W for neutrinoless double-electron capture exploration,
Nuclear Physics A, Volume 875, 1 February 2012
4. S. Eliseev, C. Roux, K. Blaum, M. Block, C. Droese, F. Herfurth, M. Kretzschmar, M.
I. Krivoruchenko, E. Minaya Ramirez, Yu. N. Novikov, L. Schweikhard, V. M. Shabaev,
F. Simkovic, I. I. Tupitsyn, K. Zuber, and N. A. Zubova, Octupolar-Excitation Penning-
Trap Mass Spectrometry for Q-Value Measurement of Double-Electron Capture in
164 Er , Phys. Rev. Lett. 107, 152501 (2011)
5. A. L. Popov, O. G. Vendik and N. A. Zubova, Magnetic field intensity in near field zone of loop antenna for RFID systems, TECHNICAL PHYSICS LETTERS, Volume
36, Number 10 (2010), 882-884
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