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تسجيل مستخدم جديدSingle and double coincidence nucleon spectra in the weak decay of Lambda hypernuclei
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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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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 approximat
ion, 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.
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 an
d 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 non--mesonic weak decay of double--$Lambda$ hypernuclei is studied within a microscopic diagrammatic approach. Besides the nucleon--induced mechanism, $Lambda Nto nN$, widely studied in single--$Lambda$ hypernuclei, additional hyperon--induced me
chanisms, $Lambda Lambdato Lambda n$, $Lambda Lambdato Sigma^0 n$ and $Lambda Lambdato Sigma^-p$, are accessible in double--$Lambda$ hypernuclei and are investigated here. As in previous works on single--$Lambda$ hypernuclei, we adopt a nuclear matter formalism extended to finite nuclei via the local density approximation and a one--meson exchange weak transition potential (including the ground state pseudoscalar and vector octets mesons) supplemented by correlated and uncorrelated two--pion--exchange contributions. The weak decay rates are evaluated for hypernuclei in the region of the experimentally accessible light hypernuclei $^{10}_{LambdaLambda}$Be and $^{13}_{LambdaLambda}$B. Our predictions are compared with a few previous evaluations. The rate for the $Lambda Lambdato Lambda n$ decay is dominated by $K$--, $K^*$-- and $eta$--exchange and turns out to be about 2.5% of the free $Lambda$ decay rate, $Gamma_{Lambda}^{rm free}$, while the total rate for the $Lambda Lambdato Sigma^0 n$ and $Lambda Lambdato Sigma^- p$ decays, dominated by $pi$--exchange, amounts to about 0.25% of $Gamma_{Lambda}^{rm free}$. The experimental measurement of these decays would be essential for the beginning of a systematic study of the non--mesonic decay of strangeness $-2$ hypernuclei. This field of research could also shed light on the possible existence and nature of the $H$--dibaryon.
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