Exchange terms in the two--nucleon induced non--mesonic weak decay of $\Lambda$--hypernuclei

TL;DR

This paper investigates the impact of Pauli exchange terms on the decay rates of $ ext{Lambda}$-hypernuclei, revealing that exchange effects significantly alter the decay width calculations, which is crucial for accurate theoretical and experimental analysis.

Contribution

It introduces a detailed calculation of exchange terms in the two-nucleon induced decay of hypernuclei using a nuclear matter approach with a comprehensive meson exchange potential.

Findings

Exchange terms reduce two-nucleon decay rate by 18%

Exchange effects increase one-nucleon decay rate by the same amount

Accurate decay width determination requires considering exchange contributions

Abstract

The contribution of Pauli exchange terms to the two--nucleon induced non--mesonic weak decay of $^{12}_\Lambda$C hypernuclei, $\Lambda NN\to nNN$ ($N=n$ or $p$), is studied within a nuclear matter formalism implemented in a local density approximation. We have adopted a weak transition potential including the exchange of the complete octets of pseudoscalar and vector mesons as well as a residual strong interaction modeled on the Bonn potential. The introduction of exchange terms turns out to reduce the two--nucleon induced non--mesonic rate by 18% and, jointly with an increase in the one--nucleon induced rate by the same magnitude, reveals to be significant for an accurate determination of the full set of hypernuclear non--mesonic decay widths in theoretical and experimental analyses.