Nuclear structure in nonmesonic weak decay of hypernuclei

Abstract

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:

Nonmesonic Weak Decay Spectra of Light Hypernuclei

“…In the evaluation of Γ N M , and the corresponding spectra, are used the Shell Model (SM) and the Fermi Gas Model (FGM) for Γ 1 (within the two-particle phase space) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][20][21][22][23], while for Γ 2 (within the three-particle phase space) only the later model has been employed so far [20][21][22][23].…”

Kinetic energy sum spectra in nonmesonic weak decay of hypernuclei

“…The novelties here, in comparison with our previous works Refs. [6][7][8], are the recoil effect and the spreading of the single-particle configurations. As will be shown in Sec.…”

“…[6][7][8]. It is also worth noting that the overall outcome of the recoil on N is very small, mostly because the effect of the factor [(A − 2)/A] 3/2 in Eq.…”

“…As previously [6][7][8], it will be assumed that the hyperon in the state j , with single-particle energy j , is weakly coupled to the A − 1 core, with spin J C and energy E C = E J I − j . Then the initial state is |J I ≡ |(J C j )J I , and the spectroscopic amplitude…”

“…(See, for instance, Table 3 in Ref. [7].) In spite of large uncertainties involved in the indirect evaluation of neutrons, this discrepancy between data and theory was considered to be a serious puzzle in the NMWD.…”