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Register a new userNonmesonic Weak Decay of $Lambda$ Hypernuclei: The Three--Nucleon Induced Mode
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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.
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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.
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.
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.
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.
Recent progress has been experienced in the field of hypernuclear weak decay, especially concerning the ratio of the neutron- to proton-induced Lambda non-mesonic decay rates, G_n/G_p. Theoretical analyses of nucleon coincidence data have been performed in a finite nucleus framework. They led to the extraction of G_n/G_p values in agreement with pure theoretical estimates, thus providing an evidence for the solution of a longstanding puzzle. Here we present an alternative approach to the problem, based on a nuclear matter formalism extended to finite nuclei via the local density approximation. The work is motivated by the exigence to make the determination of G_n/G_p from data less model dependent. One-meson-exchange potentials are used for describing both the one- and two-nucleon induced decays, Lambda N -> n N and Lambda N N -> n N N. For the latter, treated within a microscopic approach, the channels Lambda n n -> n n n and Lambda p p -> n p p are included in addition to the mode Lambda n p -> n n p already considered, in a phenomenological way, in previous studies. The propagation of the final nucleons in the residual nucleus is simulated by an intranuclear cascade code. We evaluate single and double coincidence nucleon spectra for the non-mesonic decay of C-12-Lambda. Through the comparison of our predictions with KEK coincidence data we determine G_n/G_p=0.43 pm 0.10 for this hypernucleus, confirming previous finite nucleus analyses.
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