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 , which is applicable to the specific cases of 5 He and 12 C 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 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 ranging from −0.62 to −0.24, in qualitative agreement with other theoretical estimates but in contradiction with some recent experimental determinations.

Asymmetry parameter for the nonmesonic decay of 5<FONT FACE=Symbol>L</font>He

“…We have recently derived [5] an expression for an exact fi nite-nucleus shell-model calculation of a Λ in terms of the appropriate matrix elements of the transition potential, V , which is constructed in a one-meson-exchange (OME) model based on the ground pseudoscalar and vector meson octets (π, η, K, ρ, ω, K * ) [6] and including two effects that have been systematically neglected in the literature, namely, the kinematical effects due to the difference between the lambda and nucleon masses and the fi rst-order nonlocality corrections [7]. We have also shown [5] that, if one constrains the two emitted nucleons to fly apart with opposite momenta, this expression reduces to the approximate formula usually adopted in the literature (Eq.…”

Intrinsic asymmetry parameter in nonmesonic hypernuclear decay: analytical proof of the independence on hypernucleus within an independent particle shell model

“…(15) from [23]) and ν F specifying the remaining quantum numbers in the final state besides the nuclear spin. The factors are defined as…”

“…[23]. Additionally, the bridge between nuclear matter and finite hypernucleus formalisms has been established in Ref.…”

“…Having in mind that the A Λ Z hypernucleus is considered as a Λ particle coupled to an A − 1 core, we need to distinguish between the cases with even-even, even-odd and odd-odd cores. The formalism introduced in [23] has been established only for even-even and even-odd core hypernucleus, and was applied specifically to 5 Λ He and 12 Λ C. Based in the actual status of NMHD problem it would be very useful to establish, within the SM framework, conclusions valid for all types of hypernuclei about theoretical predictions for asymmetry parameter. In particular, they could clearly give a guide to find the origin of discrepancies with experimental data.…”

“…In particular, they could clearly give a guide to find the origin of discrepancies with experimental data. Motivated by this fact, we extend in the present work the formalism from [23] to the odd-odd core case, and obtain a very simple analytical expression for a Λ valid for all kind of hypernucleus. The aim of the present is not to solve the puzzle, but to explicitly remark the limitations of our formalism, and have certain control on it, to include consistently in the future the missing ingredients and decide which ones to add in order to obtain agreement with experiments.…”