Abstract
The nuclear quadrupole moment (Q) of ^{109}Sn was determined by means of hyperfine structure (hfs) many-body parametrization method. The hyperfine structure splittings for isotopes ^{117-131}Sn recently measured by Yordanov et al. (Commun Phys 3:1, 2020) were used in multiconfiguration semi-empirical calculations. The contributions from the second-order perturbation theory to the magnetic dipole hyperfine structure, concerning electrostatically correlated hyperfine interactions, were taken into consideration for even and odd configurations simultaneously. Contributions from the second-order perturbation theory to the electric quadrupole hyperfine structure, concerning spin–orbit correlated hyperfine interactions, were included for the first time.
Highlights
The nuclear quadrupole moments (Q) constitute an important feature of nuclei which allow one determination of the deviation of the nuclear charge distribution from a spherical shape
We have developed a software package dedicated for comprehensive semi-empirical analysis of the fine and hyperfine structure, as well as transition probabilities, for complex atoms
Since the experimental data of the magnetic–dipole hyperfine structure constants A are available only for the levels of the lowest 5s25p2 configuration, we considered a limited system of 7 even-parity configurations: 5s25p2, 5s25pn p (n = 6–8), 5s25pn f (n = 4–6)
Summary
The nuclear quadrupole moments (Q) constitute an important feature of nuclei which allow one determination of the deviation of the nuclear charge distribution from a spherical shape. We have an opportunity to use the latest data on the hfs splittings of Sn electronic levels [1] and our results of the semi-empirical fine-structure calculations [18] for the purpose of many-body hyperfine structure parametrization and determine an independent value of the nuclear quadrupole moment of 109Sn. In Sect. 2, we describe in detail the calculations of the fine structure for both odd and even configurations of atomic tin, using our method for semi-empirical analysis of complex electronic systems in multiconfiguration approximation up to the second order of the perturbation theory. The results of semi-empirical calculations for even and odd configuration systems of the tin atom, used for determination of the nuclear quadrupole moment of 109Sn, are presented in Sect. In Appendix, explicit formulae for spin–orbit correlated hyperfine interactions are presented
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