gfactor of41+states in theN=82isotonesXe136andBa138

The g factors for the $4_1^{+}$ states in ${}_{}{}^{136}{}_{}{}^{}\mathrm{Xe}$ and ${}_{}{}^{138}{}_{}{}^{}\mathrm{Ba}$ were measured using the method of time-integral perturbed angular correlation. The levels of interest were populated by the decay of mass-separated ${}_{}{}^{136}{}_{}{}^{}\mathrm{I}$ and ${}_{}{}^{138}{}_{}{}^{}\mathrm{Cs}$. g factors of 0.80±0.15 and 0.80±0.14 were measured for the $4_1^{+}$ states in ${}_{}{}^{136}{}_{}{}^{}\mathrm{Xe}$ and ${}_{}{}^{138}{}_{}{}^{}\mathrm{Ba}$, respectively. The above results, along with those for the g factors in the $4_1^{+}$ state in ${}_{}{}^{140}{}_{}{}^{}\mathrm{Ce}$ and the $6_1^{+}$ states in ${}_{}{}^{134}{}_{}{}^{}\mathrm{Te}$ and ${}_{}{}^{138}{}_{}{}^{}\mathrm{Ba}$, are well described by a shell-model calculation in which the effective elemental proton g factors are $g_l^{\mathcal{’}}$=1.12 and $g_s^{\mathcal{’}}$=4.12.