Setting Limits on Double $\beta$ Decay of $^{136}$Xe to the Excited State of $^{136}$Ba using EXO-200

When a single $\beta$ decay is energetically forbidden, it is possible for certain even-even nuclei to undergo the very rare process of two neutrino double $\beta$ decay ($2\nu\beta\beta$). Further, the $2\nu\beta\beta$ decay to the excited state of a daughter nucleus has been directly observed for $^{150}$Nd and $^{100}$Mo with half lives on the order of 10$^{20}$ years, several orders of magnitude longer than the age of the universe. A better understanding of this type of decay could put constraints on current models for nuclear matrix elements. Using data from EXO-200, a 110-kg liquid xenon time projection chamber designed to search for the neutrinoless double $\beta$ decay ($0\nu\beta\beta$) of $^{136}$Xe, we search for the $2\nu\beta\beta$ decay of $^{136}$Xe to the first 0$^+$ excited state of $^{136}$Ba, a process expected to have a half life on the order of 10$^{25}$ years.