Abstract
Charge radii of Tl, Pb and Bi isotopic chains and magnetic moments of the \(1/2^{+}\) Tl \({}^{g}\) ground state and \(11/2^{-}\) Tl \({}^{m}\) isomeric state in thallium isotopic chain are calculated simultaneously within the self-consistent Theory of Finite Fermi Systems (TFFS) based on the Energy Density Functional DF3-a by Fayans et al. The calculated ground-state charge radii \(R_{\textrm{ch}}\) of Tl, Pb and Bi isotopic chains reveal distinctive kink at the \(N=126\) shell closure which has a similar magnitude, as in the neighboring mercury, lead and bismuth isotopic chains. The experimental kink indicator \(\xi\) in Tl isotopes is well described by the present calculation. Taking into account the meson exchange in the external field operator and in the effective spin dependent \(NN\) -interaction, as well as the regular effects of \(np{-}nh\) configurations and non-regular phonon-coupling (PC) corrections enables an improved description of the ground state magnetic moments in the long isotopic chain of thallium isotopes. The calculated \(1/2^{+}\) Tl \({}^{g}\) ground state magnetic moments agree fairly well with the isotopic trend reproducing the ‘‘asymmetric’’ jump at \(N=126\) revealed by the recent ISOLDE (CERN) experiments. For \(N=82{-}126\) , a ‘‘parabolic’’ \(N\) -dependence of the \(11/2^{-}\) Tl \({}^{m}\) isomeric state magnetic moments is shown and experimental data for \({}^{207}\) Tl \({}^{m}\) is described without phonon-coupling corrections.
