  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.
