Asymmetry parameter for nonmesonic hypernuclear decay

Abstract

We give general expressions for the vector asymmetry in the angular distribution of protons in the nonmesonic weak decay of polarized hypernuclei. From these we derive an explicit expression for the calculation of the asymmetry parameter, a_Λ, which is applicable to the specific cases of ⁵_ΛHe and ¹²_ΛC described within the extreme shell model. In contrast to the approximate formula widely used in the literature, it includes the effects of three-body kinematics in the final states of the decay and correctly treats the contribution of transitions originating from single-proton states beyond the s-shell. This expression is then used for the corresponding numerical computation of a_Λ within 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_Λ ranging from -0.62 to -0.24, in qualitative agreement with other theoretical estimates but in contradiction with some recent experimental determinations.