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

Abstract

We derive general analytical expressions for the evaluation of the intrinsic asymmetry parameter in nonmesonic hypernuclear weak decay, within an independent particle shell model framework. Present formalism is valid for even-even, even-odd and odd-odd core hypernucleus. A standard strangeness-changing weak transition potential with exchange of the complete meson octet (π, η, K, ρ, ω, K*) is assumed. Very simple analytical formulas are obtained within the s-wave approximation when we restrict to the π and π+K exchange models, providing an useful and manageable tool to understand the origin of the discrepancies between theoretical and experimental results. Numerical values for ⁴_ΛHe, ⁵_ΛHe, ¹¹_ΛB, ¹²_ΛC, ¹⁶_ΛO, ¹⁷_ΛO and ²⁸_ΛSi hypernuclei are exhibited. Present formalism could be used to understand why new contributions to the exchange potential allow to obtain good agreement with data, as indicated in very recent works. The necessity of a consistent inclusion of: i) different modifications of the exchange potential (two-pion exchange, a₁ meson, ΔT = 3/2 terms coming from vector mesons, etc); ii) final state interactions on primary nucleons inside the residual nucleus and also correlations between the free emitted ones; and iii) configuration mixing in the final system, is remarked.