E2andE4transition moments inYb172,Yb174, andYb176

Electric quadrupole and hexadecapole transition matrix elements in the ground-state rotational bands of ${}_{}{}^{172}{}_{}{}^{}\mathrm{Yb}$, ${}_{}{}^{174}{}_{}{}^{}\mathrm{Yb}$, and ${}_{}{}^{176}{}_{}{}^{}\mathrm{Yb}$ were measured in precise Coulomb excitation experiments with 13 MeV $\alpha$ particles. The results are $〈2^{+}\parallel M\left(E2\mathrm{}\right)\mathrm{}\parallel 0^{+}〉=2.456\mathrm{}\pm 0.012 e\mathrm{b}, 2.439\pm 0.012 e\mathrm{b}, 2.325\pm 0.018 e\mathrm{b}$ and $〈4^{+}\parallel M\left(E4\mathrm{}\right)\mathrm{}\parallel 0^{+}〉={0.22}_{-0.18\mathrm{}}^{+0.12\mathrm{}} e{\mathrm{b}}^2, {0.21}_{-0.18\mathrm{}}^{+0.14\mathrm{}} e{\mathrm{b}}^2, {0.28}_{-0.20\mathrm{}}^{+0.11\mathrm{}} e{\mathrm{b}}^2$ for ${}_{}{}^{172}{}_{}{}^{}\mathrm{Yb}$, ${}_{}{}^{174}{}_{}{}^{}\mathrm{Yb}$, and ${}_{}{}^{176}{}_{}{}^{}\mathrm{Yb}$, respectively. Model-dependent charge deformation parameters, ${\beta }_2$ and ${\beta }_4$, are deduced from the measured transition moments.