Nonmesonic Weak Decay Dynamics from proton spectra of $\Lambda$-Hypernuclei

A novel comparison between the data and the theory is proposed for the nonmesonic (NM) weak decay of hypernuclei. Instead of confronting the primary decay rates, as is usually done, we focus attention on the effective decay rates that are straightforwardly related with the number of emitted particles. Proton kinetic energy spectra of $^5_\Lambda$He, $^7_\Lambda$Li, $^9_\Lambda$Be, $^{11}_\Lambda$B, $^{12}_{\Lambda}$C, $^{13}_\Lambda$C, $^{15}_{\Lambda}$N and $^{16}_{\Lambda}$O, measured by FINUDA, are evaluated theoretically. The Independent Particle Shell Model (IPSM) is used as the nuclear structure framework, while the dynamics is described by the One-Meson-Exchange (OME) potential. Only for the $^{5}_{\Lambda}$He, $^{7}_{\Lambda}$Li, and $^{12}_{\Lambda}$C hypernuclei is it possible to make a comparison with the data, since for the rest there is no published experimental information on number of produced hypernuclei. Considering solely the one-nucleon-induced ($1N$-NM) decay channel, the theory reproduces correctly the shapes of all three spectra at medium and high energies ($E_p \geq 40 $ MeV). Yet, it greatly overestimates their magnitudes, as well as the corresponding transition rates when the full OME ($\pi+K+ \eta+\rho+\omega+K^*$) model is used. The agreement is much improved when only the $\pi+K$ mesons with soft dipole cutoff parameters participate in the decay process. We find that the IPSM is a fair first order approximation to disentangle the dynamics of the $1N$-NM decay, the knowledge of which is indispensable to inquire about the baryon-baryon strangeness-flipping interaction. It is shown that the IPSM provides very useful insights regarding the determination the $2N$-NM decay rate. In a new analysis of the FINUDA data, we derive two results for this quantity with one of them close to that obtained previously.