Investigation of pair-correlated $0^+$ states in $^{134}$Ba via the $^{136}$Ba($p,t$) reaction

We performed a high resolution study of $0^{+}$ states in $^{134}$Ba using the $^{136}$Ba($p,t$) two-neutron transfer reaction. Our experiment shows fewer $0^+$ states than previously reported, with a significant portion of the $L = 0$ pair-transfer strength concentrated at excited $0^+$ levels in $^{134}$Ba. Potential implications in the context of $^{136}$Xe $\to$ $^{136}$Ba neutrinoless double beta decay matrix element calculations are briefly discussed.