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Register a new userThe nonmesonic weak decay of the hypertriton
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J. Golak
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The nonmesonic decay of the hypertriton is calculated based on a hypertriton wavefunction and 3N scattering states, which are rigorous solutions of 3-body Faddeev equations using realistic NN and hyperon-nucleon interactions. The pion-exchange together with heavier meson exchanges for the $Lambda N to N N $ transition is considered. The total nonmesonic decay rate is found to be 0.5% of the free $Lambda$ decay rate. Integrated as well as differential decay rates are given. The p- and n- induced decays are discussed thoroughly and it is shown that the corresponding total rates cannot be measured individually.
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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.
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.
Nonmesonic weak decays of the A=4, and 5 hypernuclei are studied. The short range parts of the hyperon-nucleon weak interactions are described by the direct quark (DQ) weak transition potential, while the longer range interactions are given by the $pi$ and $K$ meson exchange processes. Virtual $Sigma$ mixings of the coherent type are found to give significant effects on the decay rates of $^4_{Lambda}{rm He}$. A large violation of the $Delta I = 1/2$ rule is predicted in the J=0 transition amplitudes.
The nonmesonic decay of $Lambda$-hypernuclei provides access to the nonleptonic weak decay process $Lambda N to NN$, which is achievable only through the observation of hypernuclear ground-state decays. We continue the discussion of some specific cases which make it possible to detect a few exclusive transitions, namely, the stripping of nucleon from the ground state results in a resonance state decaying via emission of two clusters. Delayed clusters accompanying weak decay of light hypernuclei give a unique information on spin dependence of the weak decay matrix elements.
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