Theoretical study of medium-heavy Λ hypernuclei*

In the recent experimental studies of hypernuclei with a strangeness S=-1, the γ-ray measurements with Ge detector arrays have been performed to clarify the fine structures of low-lying energy levels for p-shell hypernuclei. In the J-PARC E13 experiment, the γ-ray measurements have been analyzed for low-lying states of ¹⁹_ΛF as a gateway to sd-shell and heavier systems. 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^-, π^- γ) and (π⁺, K⁺ γ) reaction experiments are being scheduled at the J-PARC facility. New experiments are also planned at the Jefferson Laboratory. In order to predict and/or compare with the coming quality data from these experimental projects, updated theoretical studies are needed. So far we have made detailed theoretical analyses of hypernuclear level stuctures, γ-transition rates, and the DWIA production cross sections by employing the extended shell models for ^9,10,11_ΛBe, ^11,12_ΛB, ¹⁹_ΛF, etc.

In this talk we focus our attention on the interplay between the hyperon motion and the nuclear core states. We will show the results of new calculations for an sd-shell hypernuclear structure of ²⁷_ΛMg, in which the even-even core nucleus ²⁶Mg is shown to have rotational bands. The band structure is studied with estimates of E2 transition rates. Thus we see coupling of the p_Λ orbital and the core deformation. For the ²⁷Al (γ, K⁺) ²⁷_ΛMg reaction, we also discuss the DWIA cross-section spectra that are calculated with the microscopic shell-model wave functions.