Laser Spectroscopy of Neutron-Rich <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi>Hg</mml:mi></mml:mrow><mml:mprescripts /><mml:none /><mml:mrow><mml:mn>207</mml:mn><mml:mo>,</mml:mo><mml:mn>208</mml:mn></mml:mrow></mml:mmultiscripts></mml:mrow></mml:math> Isotopes: Illuminating the Kink and Odd-Even Staggering in Charge Radii across the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</…

The mean-square charge radii of $^{207,208}$Hg ($Z=80, N=127,128$) have been studied for the first time and those $^{202,203,206}$Hg ($N=122,123,126$) remeasured by application in-source resonance-ionization laser spectroscopy at ISOLDE (CERN). characteristic \textit{kink} in $N=126$ neutron shell closure has revealed, providing information on its behavior below $Z=82$ proton closure. A theoretical analysis performed within relativistic Hartree-Bogoliubov non-relativistic Hartree-Fock-Bogoliubov approaches, considering both new mercury results existing lead data. Contrary to previous interpretations, it is demonstrated that kink odd-even staggering (OES) vicinity can be described predominately mean-field level, pairing does not need play a crucial role their origin. OES mechanism suggested, related occupation different orbitals odd- even-$A$ nuclei, facilitated particle-vibration coupling odd-$A$ nuclei.