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

Abstract

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 ${}_{\Lambda }^5$He and ${}_{\Lambda }^{12}$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 ${}_{\Lambda }^5$He.

Comments: 9 pages. to be published in Physical Review C