Relativistic calculations of the ground state energies and the critical distances for one-electron homonuclear quasi-molecules

Mironova, D. V.; Tupitsyn, I. I.; Shabaev, V. M.; Plunien, G.

doi:10.1016/j.chemphys.2015.01.003

Cited by 21 publications

(27 citation statements)

References 35 publications

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“…To conclude we have shown that the approach, based on the multipole expansions (12), (15) for solving the two-center DE, can be successfully applied for the compact nuclear quasi-molecules (d 100 fm), and allows to investigate the process of diving of discrete levels into the lower continuum in heavy ions collisions not only qualitatively (what could be performed within the monopole approximation), but also quantitatively. Calculated critical distances R cr for the levels 1σ g and 1σ u are in a good agreement with other computations [20,32,33,36,38,39,45]. Moreover, the results R cr for the 1σ u level significantly improve the most relevant values, which have been obtained early within the monopole approximation [39].…”

Section: σGsupporting

confidence: 86%

“…IV for the nuclear charge Z ∼ 87 − 100, as well as the results from the Refs. [32,33,45]. The difference between these results is caused by using various nuclear charge distributions and nuclear radii.…”

Section: Results For the Pure Coulomb Problemmentioning

confidence: 99%

“…The results of extrapolation into the region κ max < 200 coincide with the results of the Refs. [20,26,29,32] within the achievable accuracy of the 4 decimal digits. Thus, the method can be successfully applied for the internuclear distances up to d ∼ 100 fm, which is enough for describing the critical phenomena, however, for larger d the convergence of the method turns out to be too slow.…”

Section: Iii)mentioning

confidence: 85%

“…However, the most important point here is not the magnitude, but the observation that the behavior of the shift due to AMM qualitatively a From Ref. [32] b From Ref. [33] c From Ref.…”

Section: The Levels Shift Due To ∆Uammmentioning

confidence: 99%

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Estimating the radiative part of QED effects in superheavy nuclear quasimolecules

Roenko

Sveshnikov

2018

Phys. Rev. A

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A method for calculating the electronic levels in the compact superheavy nuclear quasi-molecules, based on solving the two-center Dirac equation using the multipole expansion of two-center potential, is developed. For the internuclear distances up to d ∼ 100 fm such technique reveals a quite fast convergence and allows for computing the electronic levels in such systems with accuracy ∼ 10 −6 . The critical distances Rcr between the nuclei for 1σg and 1σu electronic levels in the region Z ≃ 87 − 100 are calculated. By means of the same technique the shifts of electronic levels due to the effective interaction ∆UAMM of the electron's magnetic anomaly with the Coulomb field of the closely spaced heavy nuclei are evaluated as a function of the internuclear distance and the charge of the nuclei, non-perturbatively both in Zα and (partially) in α/π. It is shown, that the levels shifts near the lower continuum decrease with the enlarging size of the system of Coulomb sources both in the absolute units and in units of Z 4 α 5 /πn 3 . The last result is generalized to the whole self-energy contribution to the level shifts and so to the possible behavior of radiative part of QED-effects with virtual photon exchange near the lower continuum in the overcritical region.

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Section: σGsupporting

confidence: 86%

Section: Results For the Pure Coulomb Problemmentioning

confidence: 99%

Section: Iii)mentioning

confidence: 85%

“…However, the most important point here is not the magnitude, but the observation that the behavior of the shift due to AMM qualitatively a From Ref. [32] b From Ref. [33] c From Ref.…”

Section: The Levels Shift Due To ∆Uammmentioning

confidence: 99%

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Estimating the radiative part of QED effects in superheavy nuclear quasimolecules

Roenko

Sveshnikov

2018

Phys. Rev. A

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“…Within the Bohr-Oppenheimer approximation, the one-electron problem is reduced to the Dirac equation with Coulomb potential of two nuclei at a fixed internuclear distance D. This problem was investigated previously by a number of authors, see, e.g., Refs. [15,20,[22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. Majority of these works relied on the partial-wave expansion of the two-center potential in the center-of-mass coordinate system.…”

Section: Introductionmentioning

confidence: 99%

One-electron Energy Spectra of Heavy Highly Charged Quasimolecules

Kotov¹,

Glazov²,

Shabaev³

et al. 2021

Preprint

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The generalized dual-kinetic-balance approach for axially symmetric systems is employed to solve the two-center Dirac problem. The spectra of one-electron homonuclear quasimolecules are calculated and compared with the previous calculations. The analysis of the monopole approximation with two different choices of the origin is performed. Special attention is paid to the lead and xenon dimers, Pb82+–Pb82+–e− and Xe54+–Xe54+–e−, where the energies of the ground and several excited σ-states are presented in the wide range of internuclear distances. The developed method provides the quasicomplete finite basis set and allows for construction of the perturbation theory, including within the bound-state QED.

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Ground‐state energy of uranium diatomic quasimolecules with one and two electrons

et al. 2019

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Ground-state energies of the one-and two-electron uranium dimers are calculated for internuclear distances in the range = 40-1000 fm and compared with the previous calculations. The generalization of the dual-kinetic-balance approach for axially symmetric systems is employed to solve the two-center Dirac equation without the partial-wave expansion for the potential of two nuclei. The one-electron one-loop QED contributions (self-energy and vacuum polarization) to the ground-state energy are evaluated using the monopole approximation for the two-center potential. Interelectronic interaction of the first and second order is taken into account for the two-electron quasimolecule. Within the QED approach one-photon-exchange contribution is calculated in the two-center potential, while the two-photon-exchange contribution is treated in the monopole approximation.

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Relativistic calculations of the ground state energies and the critical distances for one-electron homonuclear quasi-molecules

Cited by 21 publications

References 35 publications

Estimating the radiative part of QED effects in superheavy nuclear quasimolecules

Estimating the radiative part of QED effects in superheavy nuclear quasimolecules

One-electron Energy Spectra of Heavy Highly Charged Quasimolecules

Ground‐state energy of uranium diatomic quasimolecules with one and two electrons

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