Experimental study of the reaction $\Xi^{0}n\rightarrow\Lambda\Lambda X$ using $\Xi^{0}$-nucleus scattering

Using $(10087\pm44)\times10^{6}$$J/\psi$ events collected with the BESIII detector operating at the BEPCII storage ring in $2009$, $2012$, $2018$, and $2019$, we perform a search for the reaction $\Xi^0n\rightarrow\Lambda\Lambda X$, where $X$ denotes any additional final particles. Given the highly suppressed phase space for producing extra pions, the $X$ consists of either nothing or a photon, corresponding to the processes $\Xi^0 n \rightarrow \Lambda\Lambda$ and $\Xi^{0}n\rightarrow\Lambda\Sigma^0\rightarrow\Lambda\Lambda\gamma$. The $\Xi^0$ comes from the decay of $J/\psi\rightarrow\Xi^0\bar{\Xi}^0$, while the neutron originates from material of the beam pipe. A signal is observed for the first time with a statistical significance of 6.4$\sigma$. The cross section for the reaction $\Xi^0+{^9\rm{Be}}\rightarrow\Lambda+\Lambda+X$ is measured to be $(43.6\pm10.5_{\text{stat}}\pm11.1_{\text{syst}})$ mb at $P_{\Xi^0}\approx0.818$ GeV/$c$, where the first uncertainty is statistical and the second systematic. No significant $H$-dibaryon signal is observed in the $\Lambda\Lambda$ final state.