s-Wave Approximation for Asymmetry in Nonmesonic Decay of Finite Hypernuclei

We establish the bridge between the commonly used Nabetani-Ogaito-Sato-Kishimoto (NOSK) formula for the asymmetry parameter $a_\Lambda$ in the $\vec\Lambda p \to np$ emission of polarized hypernuclei, and the shell model (SM) formalism for finite hypernuclei. We demonstrate that the s-wave approximation leads to a SM formula for $a_\Lambda$ that is as simple as the NOSK one, and that reproduces the exact results for $^5_\Lambda$He and $^{12}_\Lambda$C better than initially expected. The simplicity achieved here is indeed remarkable. The new formalism makes the theoretical evaluation of $a_\Lambda$ more transparent, and explains clearly why the one-meson exchange model is unable to account for the experimental data of $^5_\Lambda$He.