Structures of $p$-shell double-$\Lambda$ hypernuclei studied with microscopic cluster models

Abstract

$0s$-orbit $\Lambda$ states in $p$-shell double-$\Lambda$ hypernuclei (${}_{\Lambda \Lambda }^{A}Z$), ${}_{\Lambda \Lambda }^8\text{Li}$, ${}_{\Lambda \Lambda }^9\text{Li}$, ${}_{\Lambda \Lambda }^{10,11,12}\text{Be}$, ${}_{\Lambda \Lambda }^{12,13}\text{B}$, and ${}_{\Lambda \Lambda }^{14}\text{C}$ are investigated. Microscopic cluster models are applied to core nuclear part and a potential model is adopted for $\Lambda$ particles. The $\Lambda$-core potential is a folding potential obtained with effective $G$-matrix $\Lambda$-$N$ interactions, which reasonably reproduce energy spectra of ${}_{\Lambda }^{A-1}Z$. System dependence of the $\Lambda$-$\Lambda$ binding energies is understood by the core polarization energy from nuclear size reduction. Reductions of nuclear sizes and $E2$ transition strengths by $\Lambda$ particles are also discussed.

Comments: 15 pages, 7 figures