E2andE4reduced matrix elements ofGd154,156,158,160andHf176,178,180

Coulomb excitation by ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ ions was studied to deduce the electric quadrupole and hexadecapole reduced transition matrix elements of deformed gadolinium and hafnium nuclei. Our values of $〈0^{+}\parallel M\left(E2\right)\parallel 2^{+}〉$ for ${}_{}{}^{154,156,158,160}{}_{}{}^{}\mathrm{Gd}$ are 1.962(20), 2.136(7), 2.230(12), and 2.269(14) eb. For ${}_{}{}^{176,178,180}{}_{}{}^{}\mathrm{Hf}$ they are 2.281, 2.204, and 2.176 eb. The values of $〈0^{+}\parallel M\left(E4\right)\parallel 4^{+}〉$ for ${}_{}{}^{156,158,160}{}_{}{}^{}\mathrm{Gd}$ are 0.42 ± 0.08, $0.34_{}^{+0.20\mathrm{}}{}_{-0.22\mathrm{}}{}^{}$, and $0.35_{}^{+0.09\mathrm{}}{}_{-0.07\mathrm{}}{}^{}$ e${\mathrm{b}}^2$. For ${}_{}{}^{176,178,180}{}_{}{}^{}\mathrm{Hf}$ they are 0.26 ± 0.12, $0.23_{}^{+0.11\mathrm{}}{}_{-0.20\mathrm{}}{}^{}$, and $0.21_{}^{+0.11\mathrm{}}{}_{-0.16\mathrm{}}{}^{}$ e${\mathrm{b}}^2$, if positive values are taken, and -0.76 ± 0.15, -0.67 ± 0.20, and -0.65 ± 0.16 e${\mathrm{b}}^2$ if they are negative. We compare our measurements with other experimental values and with theoretical predictions of quadrupole and hexadecapole moments.