We performed a coincidence measurement of two nucleons emitted from the<br />
nonmesonic weak decay (NMWD) of ^{5}_{\Lambda}He formed via the<br />
^{6}Li(\pi^+,K^+) reaction. The energies of two nucleons and the pair number<br />
distributions in the opening angle between them were measured. In both np and<br />
nn pairs, we observed a clean back-to-back correlation coming from the two-body<br />
decay of \Lambda p --&gt; n p and \Lambda n --&gt; n n, respectively. The ratio of<br />
the nucleon pair numbers was N_{nn}/N_{np}=0.45 \pm 0.11(stat)\pm 0.03(syst) in<br />
the kinematic region of cos(theta_{NN}) &lt; -0.8. Since each decay mode was<br />
exclusively detected, the measured ratio should be close to the ratio of<br />
\Gamma(\Lambda p --&gt; np)/\Gamma(\Lambda n --&gt; nn).<br />
The ratio is consistent with recent theoretical calculations based on the<br />
heavy meson/direct quark exchange picture.