The asymmetry parameter alpha_p^NM for a proton exclusively emitted in the Lambda p -> np process was, for the first time, measured in the non-mesonic weak decay of a polarized 5_La,bda_He hypernucleus by selecting the proton-neutron pairs emitted in the back-to-back kinematics. The highly polarized 5_Lambda_He was abundantly produced with the (pi+,K+) reaction at 1.05GeV/c in the scattering angular range of +-15$ degrees. The obtained value alpha_p^NM=0.31+-0.22, as well as that for inclusive protons, alpha_p^NM=0.11+-0.08+-0.04, largely contradicts recent theoretical values of around -0.6, although these calculations well reproduce the branching ratios of non-mesonic weak decay.
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