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Register a new userExclusive Measurement of the Nonmesonic Weak Decay of ^{5}_{Lambda}He Hypernucleus
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We performed a coincidence measurement of two nucleons emitted from the nonmesonic weak decay (NMWD) of ^{5}_{Lambda}He formed via the ^{6}Li(pi^+,K^+) reaction. The energies of two nucleons and the pair number distributions in the opening angle between them were measured. In both np and nn pairs, we observed a clean back-to-back correlation coming from the two-body decay of Lambda p --> n p and Lambda n --> n n, respectively. The ratio of the nucleon pair numbers was N_{nn}/N_{np}=0.45 pm 0.11(stat)pm 0.03(syst) in the kinematic region of cos(theta_{NN}) < -0.8. Since each decay mode was exclusively detected, the measured ratio should be close to the ratio of Gamma(Lambda p --> np)/Gamma(Lambda n --> nn). The ratio is consistent with recent theoretical calculations based on the heavy meson/direct quark exchange picture.
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To comprehend the recent Brookhaven National Laboratory experiment E788 on $^4_Lambda$He, we have outlined a simple theoretical framework, based on the independent-particle shell model, for the one-nucleon-induced nonmesonic weak decay spectra. Basically, the shapes of all the spectra are tailored by the kinematics of the corresponding phase space, depending very weakly on the dynamics, which is gauged here by the one-meson-exchange-potential. In spite of the straightforwardness of the approach a good agreement with data is acheived. This might be an indication that the final-state-interactions and the two-nucleon induced processes are not very important in the decay of this hypernucleus. We have also found that the $pi+K$ exchange potential with soft vertex-form-factor cutoffs $(Lambda_pi approx 0.7$ GeV, $Lambda_K approx 0.9$ GeV), is able to account simultaneously for the available experimental data related to $Gamma_p$ and $Gamma_n$ for $^4_Lambda$H, $^4_Lambda$He, and $^5_Lambda$He.
We have measured the energy spectra of pions and protons emitted in the weak decay of 12_Lambda_C, 28_Lambda_Si, and Lambda_Fe hypernuclei produced via the (pi+, K+) reaction. The decay widths of the pi- mesonic decay (Lambda -> p + pi-) and the nonmesonic decay (Lambda + N -> N + N) were extracted. The present results demonstrate an increase of the mesonic decay width due to a distortion of the pion wave function in nuclear medium for the first time. The ratios of the neutron- to proton-induced nonmesonic decay widths, Gamma_n(Lambda + n -> n + n)/Gamma_p(Lambda + p -> n + p), were evaluated by a direct comparison of the measured proton energy spectra with the calculated ones. No theoretical calculation which has been proposed so far can simultaneously account for both the nonmesonic decay widths and the Gamma_n/Gamma_p ratios in the present data.
Having in mind its future extension for theoretical investigations related to charmed nuclei, we develop a relativistic formalism for the nonmesonic weak decay of single-$Lambda$ hypernuclei in the framework of the independent-particle shell model and with the dynamics represented by the $(pi,K)$ one-meson-exchange model. Numerical results for the one-nucleon-induced transition rates of ${}^{12}_{Lambda}textrm{C}$ are presented and compared with those obtained in the analogous nonrelativistic calculation. There is satisfactory agreement between the two approaches, and the most noteworthy difference is that the ratio $Gamma_{n}/Gamma_{p}$ is appreciably higher and closer to the experimental value in the relativistic calculation. Large discrepancies between ours and previous relativistic calculations are found, for which we do not encounter any fully satisfactory explanation. The most recent experimental data is well reproduced by our results. In summary, we have achieved our purpose to develop a reliable model for the relativistic calculation of the nonmesonic weak decay of $Lambda$-hypernuclei, which can now be extended to evaluate similar processes in charmed nuclei.
The nonmesonic weak decay of $Lambda$ hypernuclei is studied within a microscopic diagrammatic approach which is extended to include the three--nucleon induced mechanism. We adopt a nuclear matter formalism which, through the local density approximation, allows us to model finite hypernuclei, a one--meson--exchange weak transition potential and a Bonn nucleon--nucleon strong potential. One--, two-- and three--nucleon induced weak decay rates are predicted for $^{12}_Lambda$C by including ground state correlations up to second order in the nucleon--nucleon potential and the recoil of the residual nucleus. Three--nucleon stimulated decays, $Lambda NNNto nNNN$ ($N=n$ or $p$), are considered here for the first time. The obtained decay rates compare well with the latest KEK and FINUDA data. The three--nucleon induced rate turns out to be dominated by $nnp$-- and $npp$--induced decays, it amounts to $sim$ 7% of the total nonmesonic rate and it is $sim 1/2$ of the neutron--induced decay rate. The reduction effect of the nuclear recoil is particularly relevant for the three--nucleon induced rates ($sim$ 15%), less important for the two--nucleon induced rates ($sim$ 4%) and negligible for the one--nucleon induced rates. Given the non--negligible size of the three--nucleon induced contribution and consequently its importance in the precise determination of the complete set of decay rates, new measurements and/or experimental analysis are encouraged.
The results of a measurement of the proton spectra following the Non--Mesonic Weak Decay of $mathrm{^5_{Lambda}He}$, $mathrm{^7_{Lambda}Li}$ and $mathrm{^{12}_{Lambda}C}$ are presented and discussed. The experiment was performed at the ($e^+$ $e^-$) collider DA$Phi$NE at Laboratori Nazionale di Frascati of INFN. It is the first measurement for $mathrm{^7_{Lambda}Li}$, and for all the spectra the lower limit on the energy of the protons is 15 MeV, never reached before. All the spectra show a similar shape, namely a peak at around 80 MeV as expected for the free $Lambda p to np$ weak reaction, with a low energy rise that should be due to Final State Interactions and/or two--nucleon induced weak processes. The decay spectrum of $mathrm{^5_{Lambda}He}$ is somehow similar to the ones reported by previous measurements and theoretical calculations, but the same doesnt happen for the $mathrm{^{12}_{Lambda}C}$ one.
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