The nonmesonic decay rates and the lifetimes of hypernuclei of mass Aϭ4Ϫ209 are extensively calculated based on the 1, correlated-2, and 1 exchange potentials. Two types of new hyperon-nucleon potentials have been constructed in which the two pions are correlated and coupled to and/or in the exchange process. The roles of these potentials and 1 exchange potential are discussed. The theoretical decay rates are consistent with the existing data for s-shell and p-shell hypernuclei within the present model. The calculated decay rate increases gradually up to AӍ60 and then tends to be almost constant for Aտ60. The A-dependent behavior of the hypernuclear lifetimes tends to be constant over the mass region AϾ30 of hypernuclei in our model. It is most remarkable that the cooperative effect of the correlated-2 and 1 exchanges enhances the neutron-stimulated decay rate ⌫ n ͑proton-stimulated one ⌫ p ) by 400-450 % ͑20-30 %͒ with respect to the standard 1-exchange estimate for AϾ5. As a result the ⌫ n /⌫ p ratios for light-to-heavy hypernuclei are calculated to be 0.4 -0.5, which values are several times larger than the 1-exchange estimate. Although the experimental ratios seem still about two times larger than these theoretical values, it has revealed that the representative 2-exchange and 1 exchange mechanisms give rise to a clear improvement on the ⌫ n /⌫ p ratios.

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Contributions of the direct quark mechanism are studied in the nonmesonic weak decays of light hypernuclei. The ΛN → N N transition is described by the one pion exchange mechanism and the direct quark mechanism, induced by the four-quark vertices in the effective weak Hamiltonian. By employing a realistic wave function of the Λ inside the hypernuclei, nonmesonic decay rates of 4 Λ H, 4 Λ He, and 5 Λ He are calculated. The results show that the direct quark mechanism is significantly large and gives a large ∆I = 3/2 contribution in the J = 0 channel. The relative phase between the one-pion exchange and the direct-quark contributions is determined so that the effective weak Hamiltonian for quarks give both of them consistently. We find that the sum of these two contributions reproduce the current available experimental data fairly well. *

For the last few decades the (π + , K + ) reaction has played an important role in heavy hypernuclear spectroscopy where the Λ spin-orbit splitting should be one of the most interesting subjects. In this article, first, various stages of calculational frameworks for hypernuclear production cross sections are discussed. Then, focusing on the 89 Y(π + , K + ) 89 Λ Y experimental data, new DWIA analysis has been carried out by taking full account of the core nuclear excitation effects. As a result we found that one of the doublet peaks comes from the nuclear core excitation and that the Λ spin-orbit splitting is small in consistent with the finding in the p-shell hypernuclei. §1. IntroductionFor the last few decades the (π + , K + ) reaction has played a special role in hypernuclear reaction spectroscopy. It excites Λ-particle, neutron-hole states of stretched angular momentum quite selectively, so that it has revealed a series of almost all the bound Λ single-particle states inside some nuclei. The reaction mechanism and the theoretical demonstrations were discussed first by Dover et al. 1) and by Bandō and one of the present authors (T.M.). 2) In fact, the first (π + , K + ) experiment on a 12 C target, carried out at Brookhaven National Laboratory, showed promising results. 3) Sophisticated calculations using the Kapur-Peierls framework were performed in order to include quasi-free continuum strengths in addition to the wellseparated bound-state peaks. 4) On the experimental side, the BNL group extended the (π + , K + ) studies up to medium-mass systems with A 28 − 89, 6), 7) while at KEK better energy resolution was ¡achieved using the SKS spectrometer up to a heaviest target of 208 Pb. 8)-11) See Ref. 13) for review of the (π + , K + ) experiments.One of the purposes of the (π + , K + ) experiments on heavy nuclear targets was to extract the Λ spin-orbit splittings over a wide range of hypernuclear species. 4), 5) The 89 Y(π + , K + ) 89 Λ Y experiment 11) among others provides us with the most typical spectrum with good energy resolution (1.65 MeV) in which four (five) well-separated major peaks are understood to correspond basically to the s Λ , p Λ , d Λ , and f Λ (g Λ ) orbits. In addition, according to the experimental analysis, each peak (labeled p Λ , d Λ , f Λ in Fig. 5 of Ref. 11)) consists of two subpeaks, which are denoted as (1L,1R), (2L,2R), and (3L,3R), respectively. 11) If this double-peak structure is attributed to the spin-orbit partners, the splittings are ΔE exp 1 = 1.37 MeV (p Λ ), ΔE exp 2 = 1.63 MeV (d Λ ), and ΔE exp 3 = 1.70 MeV (f Λ ), respectively, 11) but, as shown later, these values are two or three times larger than the spin-orbit splittings estimated using the

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