We have measured both yields of neutron-proton and neutron-neutron pairs emitted from the non-mesonic weak decay process of 5_Lambda-He and 12_Lambda-C hypernuclei produced via the (pi^+,K^+) reaction for the first time. We observed clean back-to-back correlation of the np- and nn-pairs in the coincidence spectra for both hypernuclei. The ratio of those back-to-back pair yields, Nnn / Nnp, must be close to the ratio of neutron- and proton-induced decay widths of the decay, Gn(Lambda n -> nn)/Gp(Lambda p -> np). The obtained ratios for each hypernuclei support recent calculations based on short-range interactions.
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