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We performed a high resolution study of $0^{+}$ states in $^{134}$Ba usingthe $^{136}$Ba($p,t$) two-neutron transfer reaction. Our experiment shows asignificant portion of the $L = 0$ pair-transfer strength concentrated atexcited $0^+$ levels in $^{134}$Ba. Potential implications in the context of$^{136}$Xe $\to$ $^{136}$Ba neutrinoless double beta decay matrix elementcalculations are briefly discussed.

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