Quantum interference terms in nonmesonic weak decay of $\Lambda$-hypernuclei within a RPA formalism

TL;DR

This paper investigates quantum interference effects in the non-mesonic weak decay of $\Lambda$-hypernuclei using a RPA formalism, highlighting the significance of Pauli exchange and the limitations of the approximation in reproducing experimental spectra.

Contribution

It introduces a microscopic RPA-based approach to analyze interference terms and Pauli exchange effects in hypernuclear decay, incorporating FSI via a Bonn potential.

Findings

Pauli exchange terms are significant in decay spectra.

RPA limitations hinder accurate reproduction of experimental data.

Interference effects are complex and not fully conclusive within current approximation.

Abstract

Single and double coincidence nucleon spectra in the $\Lambda$-hypernuclei weak decay are evaluated and discussed using a microscopic formalism. Nuclear matter is employed together with the local density approximation which allows us to analyze the $^{12}_{\Lambda}C$ hypernucleus non-mesonic weak decay. Final state interactions (FSI) are included via the first order (in the nuclear residual interaction) terms to the RPA, where the strong residual interaction is modelled by a Bonn potential. At this level of approximation, these FSI are pure quantum interference terms between the primary decay $(\Lambda N \to NN)$ and $(\Lambda N \to NN \to NN)$, where the strong interaction is responsible for the last piece in the second reaction. Also the Pauli exchange contributions are explicitly evaluated. We show that the inclusion of Pauli exchange terms is important. A comparison with data is made. We conclude that the limitations in phase space in the RPA makes this approximation inadequate to reproduce the nucleon spectra. This fact, does not allow us to draw a definite conclusion about the importance of the interference terms.