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Register a new userNonmesonic weak decay spectra of $^4_Lambda$He
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Alfredo Pio Noronha Rodrigues Galeao
Publication date
2008
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English
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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.
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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.
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.
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.
We study the effects of final state interactions in the non-mesonic weak decay $Lambda N rightarrow nN$ (n is a neutron and N is either a neutron or a proton) of the hypernucleus $_Lambda^4$He. Using a three-body model the effects of distortion of the interaction of the emitted nucleon pair with the residual nucleus is considered. We also study the influence of the final state interaction between the emitted nucleons using the Migdal-Watson model. The effect of spin symmetries in the final state of the pair is also considered. Based on our calculations, we conclude that final state interactions play a minor role in the kinetic energy spectrum of the emitted nucleon pair.
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.
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