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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, evenodd 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, Γ n and Γ p , which does not involve the spectroscopic factors. For the strangeness-changing weak ΛN → N N 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 Λ Si hypernuclei, with commonly used parametrization for the OMEM, and compare the results with the available experimental information. The calculated rates Γ N M = Γ n + Γ p are consistent with the data, but the measurements of Γ n/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. I IntroductionHypernuclear physics adds another flavor (strangeness) to the traditional nuclear physics, and its goal is to study the behavior of hyperons (Λ, Σ, Ξ, Ω) in the nuclear environments, which are now bound system of neutrons, protons and one or more hyperons. Interesting strange nuclei with strangeness S = −1 are the Λ hypernuclei, in which a Λ hyperon, having a mass of 1116 MeV and zero charge and isospin, replaces one of the nucleons. Same as the free Λ hyperon, they are mostly produced via the strong interactions, i.e., in the reaction processes π, by making use of the pion (π) and kaon (K) beams. They also basically decay through the weak interactions, as the free Λ does. Yet, as it is well known and explained below, there are some very important differences in the corresponding decaying modes. First, it should be remembered that the free Λ hyperon decays nearly 100 % of the time by the Λ → N π weakmesonic mode (Fig. 1): sec). For the decay at rest the energy-momentum conservation impliesTherefore the energy released isand the kinetic energies and momenta in the final state are:
The recently developed formalism for the evaluation of nuclear form factors in neutrinoless double beta decay is applied to 48 Ca, 76 Ge, 82 Se, 100 Mo, 128 T e and 130 T e nuclei. Explicit analytical expressions that follows from this theoretical development, in the single mode model for the decay of 48 Ca, have been worked out. They are useful both for testing the full numerical calculations, and for analytically checking the consistency with other formalisms. Large configuration space calculations are compared with previous studies, where alternative formulations were used. Yet, besides using the G-matrix as residual interaction, we here use a simple δ-force.Attention is paid to the connected effects of the short range nuclear correlations and the finite nucleon size. Constraints on lepton number violating terms in the weak Hamiltonian (effective neutrino Majorana mass and effective right-handed current coupling strengths) are deduced.PACS: 13.15+q;14.80;21.60Jz;23.40 † Fellow of the CONICET from Argentina.
Nonleptonic hyperon and f2 -decays are analyzed in the framework of the Weinberg-Salam model of weak interactions. Various effective weak nonlepton~c Hamiltonians are tested with and without quantumchromodynamic corrections, including extensive variations of all the parameters in question. The influence of quark models is also investigated using both the MIT bag model and the harmonic-oscillator model. Various dynamical assumptions connected with particular selections of current-commutator and pole terms are also considered. Irrespective of all variations and uncertainties, it seems that orders of magnitude and relative signs for various amplitudes are always correctly reproduced.
We examine in detail the predictions of the charged majoron model, introduced recently by Burgess and Cline, for 0
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