The non-mesonic weak decay of polarized Lambda-hypernuclei is studied for the first time by taking into account, with a Monte Carlo intranuclear cascade code, the nucleon final state interactions. A one-meson-exchange model is employed to describe the Lambda N-> n N processes in a finite nucleus framework. The relationship between the intrinsic Lambda asymmetry parameter a_Lambda and the asymmetry a^M_Lambda accessible in experiments is discussed. A strong dependence of a^M_Lambda on nucleon final state interactions and detection threshold is obtained. Our results for a^M_Lambda are consistent with ^{11}_Lambda B and ^{12}_Lambda C data but disagree with observations in ^5_Lambda He.
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