Microscopic approach to nucleon spectra in hypernuclear non-mesonic weak decay

Abstract

A consistent microscopic diagrammatic approach is applied for the first time to the calculation of the nucleon emission spectra in the non-mesonic weak decay of Λ-hypernuclei. We adopt a nuclear matter formalism extended to finite nuclei via the local density approximation, a one-meson exchange weak transition potential and a Bonn nucleon-nucleon strong potential. Ground state correlations and final state interactions, at second order in the nucleon-nucleon interaction, are introduced on the same footing for all the isospin channels of one-and two-nucleon induced decays. Single and double-coincidence nucleon spectra are predicted for 12 Λ C and compared with recent KEK and FINUDA data. The key role played by quantum interference terms allows us to improve the predictions obtained with intranuclear cascade codes. Discrepancies with data remain for proton emission.

Microscopic approach to the proton asymmetry in the nonmesonic weak decay ofΛhypernuclei

“…The only kind of FSI effects considered within the finite nucleus approach of [9,15] are those between the two nucleons emitted in the nonmesonic decay, which are represented by a wave function describing their relative motion under the influence of a suitable NN interaction [7]. Although a discrepancy with data still remains for proton emission spectra [20,21], one can safely assert that a formalism which takes care of FSI leads to a good agreement between theory and experiment concerning n / p and a M . In the present contribution we evaluate the asymmetry a M employing an alternative approach to the hybrid one of [9,15].…”

“…In our microscopic diagrammatic approach, which was developed in Refs. [20,22,23], both the weak decay and the nucleon FSI are part of the same quantum-mechanical problem and are thus described in a unified way. Therefore, the present formalism has a self-consistency that is not present in previous approaches.…”

Nonmesonic weak decay of Λ hypernuclei: The ΛN−ΣN coupling

“…The same microscopic approach showed that ground state correlation contributions are crucial for a detailed calculation of the rates, the asymmetry parameter and the nucleon emission spectra [19,20,22,24]. Less pronounced effects were reported by including the ∆-baryon resonance [23].…”

“…Different measurements of single and coincidence spectra of the nucleons emitted in hypernuclear nonmesonic decay, by the SKS Collaboration at KEK [5,6] and the FINUDA Collaboration at LNF [7][8][9], their theoretical analysis and the many calculations incorporating: 1) complete meson-exchange weak interaction potentials (with both oneand two-meson exchange) [10][11][12][13], 2) the description of the ΛN and NN short-range correlations in terms of quark degrees of freedom [14], 3) twonucleon induced modes, ΛNN → nNN [15][16][17][18][19][20], as well as 4) nucleon final state interactions [21][22][23], have proven crucial to solve the "Γ n /Γ p puzzle", in a continuous dialogue and exchange between theory and experiment. The two-nucleon induced decay mechanism is rather well understood at present too, although the data on Γ 2 are still affected by large error bars.…”

“…One should remember that involved nuclear many-body processes such as multinucleon induced nonmesonic weak decays and nucleon final state interactions due to the nucleon-nucleon strong interaction complicate the extraction of the relevant elementary information. Discrepancies between theory and experiment indeed remain and mainly concern proton emission, i.e., proton kinetic energy spectra and neutron-proton angular and momentum correlation spectra [4,23]. A detailed description of the hyperon weak interactions underlying hypernuclear decay is thus impossible at present.…”