Nonmesonic Weak Decay Dynamics from proton spectra of Λ\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

RPA puzzle in C(12) weak decay processes

We explain the origin of the difficulties that appear in a straightforward application of the QRPA in C(12), and we demonstrate that it is imperative to use the projected QRPA (PQRPA). Satisfactory results, not only for the weak processes among the ground states of the triad B(12),C(12),N(12), but also for the inclusive ones are obtained. We sketch as well a new formalism for the neutrino-nucleus interaction that furnishes very simple final formulae for the muon capture rate and neutrino induced cross sections.Comment: 14 pages in LaTex, changes are included in the text, to appear in PL

Knowledge Economy Factors and the Development of Knowledge-based Economy

The aim of this paper is to identify the various knowledge economy factors that have an impact on the achieved economic growth of national economies. This paper argues that there is no single scenario for building a knowledge-based economy. It utilizes variables of the knowledge economy, collected according to the Knowledge Assessment Methodology (KAM - benchmarking tool of the World Bank), on a sample of 118 countries. The countries are divided in three income groups according to GDP per capita PPP in 2006. Multivariate analysis is used. The analysis was conducted twice on data from KAM 2007 and KAM 2008 to avoid drawing wrong conclusions through using data limited to a single year. The results suggest that there are many significant factors and variables of knowledge economy that have an impact on the achieved development of the three income groups. Based on these results, proposals and measures for enhancing sustainable development and building knowledge-based economies for the three income groups of countries are made.knowledge-based economy, knowledge assessment methodology, knowledge economy framework

Nonmesonic weak decay spectra of light hypernuclei

The nonmesonic weak decay spectra of light hypernuclei have been evaluated in a systematic way. As theoretical framework we adopt the independent particle shell model with three different one-meson-exchange transition potentials. Good agreement with data is obtained for proton and neutron kinetic energy spectra of 4ΛHe, and 5ΛHe, when the recoil effect is considered. The coincidence spectra of proton-neutron pairs are also accounted for quite reasonably, but it was not possible to reproduce the data for the neutron–neutron pair spectra. It is suggested that the π + K meson-exchange model with soft monopole form factors could be a good starting point for describing the dynamics responsible for the decays of these two hypernuclei. The 4ΛH spectra are also presented.Instituto de Física La Plat

Nuclear structure in nonmesonic weak decay of hypernuclei

A general shell model formalism for the nonmesonic weak decay of the hypernuclei has been developed. It involves a partial wave expansion of the emitted nucleon waves, preserves naturally the antisymmetrization between the escaping particles and the residual core, and contains as a particular case the weak Λ-core coupling formalism. The hypernuclei are grouped having in view their A-1 cores, that is in those with even-even, even-odd and odd-odd cores. It is shown that in all three cases the nuclear structure manifests itself basically through Pauli Principle, and very simple expressions are derived for the neutron and proton induced decays rates Γn and Γp, which does not involve the spectroscopic factors. For the strangeness-Changing weak ΛN → NN transition potential we use the One-Meson-Exchange Model (OMEM), which comprises the exchange of the complete pseudoscalar and vector meson octets (π,η, K, ρ, ω, K*). We evaluate 3H, 4H 4ΛHe, 5ΛHe,11B, 12ΛC, 16ΛO, 17ΛO, and 28ΛSi hypernuclei, with commonly used parametrization for the OMEM, and compare the results with the available experimental information, The calculated rates ΓNM = Γn + Γp are consistent with the data, but the measurements of Γn/p = Γn/Γp are not well accounted for by the theory. It is suggested that, unless additional degrees of freedom are incorporated, the OMEM parameters should be radically modified.Facultad de Ciencias Exacta

Nuclear Structure in Nonmesonic Weak Decay of Hypernuclei

A general shell model formalism for the nonmesonic weak decay of the hypernuclei has been developed.It involves a partial wave expansion of the emitted nucleon waves,preserves naturally the antisymmetrization between the escaping particles and the residual core, and contains as a particular case the weak Lambda-core coupling formalism. The hypernuclei are grouped having in view their A-1 cores, that is in those with even-even, even-odd and odd-odd cores.It is shown that in all three cases the nuclear structure manifests itself basically through Pauli Principle, and very simple expressions are derived for the neutron and proton induced decays rates, which does not involve the spectroscopic factors

Simple analytical expression for vector hypernuclear asymmetry in nonmesonic decay of 5Λ He and 12Λ C

We present general explicit expressions for a shell-model calculation of the vector hypernuclear parameter in nonmesonic weak decay. We use a widely accepted effective coupling Hamiltonian involving the exchange of the complete pseudoscalar and vector meson octets (π, η, K, ρ, ω, K*). In contrast to the approximated formula widely used in the literature, we correctly treat the contribution of transitions originated from single-proton states beyond the s-shell. Exact and simple analytical expressions are obtained for the particular cases of 5ΛHe and 12ΛC, within the one-pion-exchange model. Numerical computations of the asymmetry parameter, aΛ, are presented. Our results show a qualitative agreement with other theoretical estimates but also a contradiction with recent experimental determinations. Our simple analytical formulas provide a guide in searching the origin of such discrepancies, and they will be useful for helping to solve the hypernuclear weak decay puzzle.Facultad de Ciencias Exacta