Semi-empirical determination of the nuclear quadrupole moment of $$^{109}$$Sn

The nuclear quadrupole moment (Q) of $$^{109}$$ 109 Sn was determined by means of hyperfine structure (hfs) many-body parametrization method. The hyperfine structure splittings for isotopes $$^{117-131}$$ 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.