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Descrizione
Hypernuclear structure studies have been progressing steadily through the $K$- and $\pi$-induced production reaction experiments, especially by the recent $\gamma$-ray coincidence measurements with the large volume Ge detector. Moreover a series of recent $(e,e' K^+)$ reaction experiments from the Jefferson Laboratory provide high-resolution data of the low-lying energy levels for $p$-shell hypernuclei. These data are quite helpful in better understanding of hyperon-nucleon interactions, though the data are still limited to about ten hypernuclear species.
As the next stage of hypernuclear studies, new projects of high-intensity and high-resolution $(K^-, \pi^- \gamma)$ and $(\pi^+, K^+ \gamma)$ reaction experiments are being scheduled at the J-PARC facility. New experiments are also planned at the Jefferson Laboratory.
In order to meet these experimental projects, updated theoretical studies are needed for prediction and/or comparison with the coming quality data. So far we have made detailed theoretical analyses of hypernuclear level stuctures, $\gamma$-transition rates, and the production cross sections by employing the extended shell models for $_{\;\;\;\;\;\Lambda}^{9,10,11}$Be, $_{\;\;\;\,\Lambda}^{11,12}$B, $_{\,\Lambda}^{19}$F, etc.
In this talk we focus our attention on the interplay between the hyperon motion and the nuclear core states. First, we discuss that the extended shell-model calculation is successful in explaining the new peak observed in the $^{10}$B $(e,e' K^+)$ $^{10}_{\,\Lambda}$Be experiment. It is attributed to the lowering of $p_{\Lambda}$ (perpendicular) state due to the strong coupling with $\alpha$-$\alpha$ like nuclear core deformation as already known in the case of $_{\Lambda}^{9}$Be. Second, we will show the results of new calculations for an $sd$-shell hypernuclear structure of $_{\,\Lambda}^{27}$Mg, in which the even-even core nucleus $^{26}$Mg is shown to have rotational bands. Thus we see coupling of the $p_{\Lambda}$ orbital and the core deformation. For the $^{27}$Al $(\gamma, K^+)$ $_{\,\Lambda}^{27}$Mg reaction, we also discuss the DWIA cross-section spectra that are calculated with the microscopic shell-model wave functions.
