Asymmetry parameter for nonmesonic hypernuclear decay

Abstract

We derive general explicit expressions for a shell-model calculation of the intrinsic asymmetry parameter, $a_{\Lambda }$, in nonmesonic weak hypernuclear decay. They include the effects of three-body kinematics in the final states of the decay and correctly treat the contribution of transitions originating from single-proton states beyond the s-shell. The expressions are particularized to the cases of ${}_{\Lambda }^5$He and ${}_{\Lambda }^{12}$C and used for the calculation of $a_{\Lambda }$ in several one-meson-exchange models. Besides the strictly local approximation usually adopted for the transition potential, we also consider the addition of the first-order nonlocality terms. We find values for $a_{\Lambda }$ ranging from -0.62 to -0.24, in qualitative agreement with other theoretical estimates but in contradiction with some recent experimental determinations.

Comments: RevTex, 10 pages, 1 figure, submitted for publication. v2: 16 pages, 1 correction made, more detail and 4 appendices added, numerical results and conclusions unchanged