Isotope-shift analysis with the $4f^{14}6s^{2}~^1S_0- 4f^{13}5d6s^{2}(J=2)$ transition in ytterbium

Measurements of isotope shifts have recently been attracting considerable attention due to their potentials in searching for new forces. We report on the isotope shifts of the $4f^{14}6s^{2}~^1S_0- 4f^{13}5d6s^{2}(J=2)$ transition at 431 nm in Yb, based on absolute frequency measurements with an accuracy of $\sim10$ kHz. With these data, the hyperfine constants for $^{173}$Yb are determined. To analyze these data further, electronic structure of ytterbium is theoretically calculated. The nuclear charge radii are estimated together with some previously reported isotope-shift data for other transitions. An analysis of the King plot for the $4f^{14}6s^{2}~^1S_0- 4f^{13}5d6s^{2}(J=2)$ transition shows a good consistency with other transitions, resulting in a constraint on the existence of new bosons mediating the force between an electron and a neutron. The analysis motivates further precision measurements on isotope shifts of the narrow-linewidth transitions in ytterbium, not only for the even-mass isotopes but also for the odd-mass isotopes.