Exchange terms in the two-nucleon induced non-mesonic weak decay of Λ-hypernuclei

Abstract

The contribution of Pauli exchange terms to the two-nucleon induced non-mesonic weak decay of 12 Λ C hypernuclei, ΛN N → nN N (N = n or p), is studied within a nuclear matter formalism implemented in a local density approximation. We have adopted a weak transition potential including the exchange of the complete octets of pseudoscalar and vector mesons as well as a residual strong interaction modeled on the Bonn potential. The introduction of exchange terms turns out to reduce the two-nucleon induced non-mesonic rate by 18% and, jointly with an increase in the one-nucleon induced rate by the same magnitude, reveals to be significant for an accurate determination of the full set of hypernuclear non-mesonic decay widths in theoretical and experimental analyses. Hypernuclei, bound systems of neutrons, protons and hyperons, embody an important source of information able to match nuclear and particle physics. On the one hand, studies on the production mechanisms and the structure of hypernuclei [1] are of interest since they provide indications on the hyperonnucleon and hyperon-hyperon strong interactions which cannot be determined with precision from scattering experiments (such experiments are very challenging due to the very short hyperon lifetimes). Hypernuclear weak decay is on the other hand the only available tool to acquire knowledge on the baryon-baryon strangeness-changing interactions [2-5]. The above subjects, which presuppose the solution of complex many-body problems, are in turn crucially related to the renormalization of hyperons and mesons properties in

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].…”

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

“…The effect of the nuclear recoil is also taken into account as a new feature of our approach, which is applied to 12 Λ C. Formally, this corresponds to implement translational invariance and exact momentum conservation in the nonmesonic decays. 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.…”

“…(6). In what follows, we focus on Γ 3 (for a detailed discussion on Γ 1 and Γ 2 we refer to [19,20]), for which one obtains:…”

“…In [19] we evaluated the full set of diagrams for Γ 2 by using the same microscopic approach and weak and strong potentials of the present calculation. The reduction due to the exchange terms turns out to be stronger than the increase due to the neglected hole diagrams, resulting in a net decrease of Γ 2 by ∼ 20%.…”