Testing Shell Stabilization at N = 80; $g$ factor of the 2$^{+}_{1}$ state in $^{138}$Ce

The study of observed mixed symmetry states in N = 80 isotones, namely $^{134}$Xe, $^{136}$Ba and $^{138}$Ce manifest a large effect of single-particle structure on the evolution of these collective excitations. The observed fragmentation of $M1$ transition strength between the (2$_{1,ms}^{+}$) state and the ($2_{1,fs}^{+}$) state in $^{138}$Ce and the largely unfragmented strength in $^{134}$Xe and $^{136}$Ba was attributed to the presence of a $\pi g_{7/2}$ subshell closure at $Z=58$. To prove the validity of this proposed concept of shell stabilization, the $g$ factor of the 2$^{+}_{1}$ in $^{138}$Ce was measured. The low-lying excited states in $^{138}$Ce were populated via inverse Coulomb excitation at ATLAS, ANL. To measure the $g$ factor, the recoil into vacuum technique was used and attenuation of the angular distribution of emitted 2$^{+}_{1}\rightarrow0^{+}\gamma$ rays was measured. The results of the ongoing analysis will be presented providing a constraint on the single-particle wavefunctions contributing to the collective states in the N = 80 isotones and guide theory in developing a consistent and predictive picture of the underlying single-particle dynamics.