Procedure for calculating the structure of hypernuclei

Abstract

A simple procedure is described for determining the structure of hypernuclei. This procedure allows for complete flexibility in the hyperon wave function, while eliminating spurious center of mass components. The method is applied to ${}_{\Lambda }{}^6{}_{}{}^{}\mathrm{Li}$, ${}_{\Lambda }{}^7{}_{}{}^{}\mathrm{L}$, and ${}_{\Lambda }{}^{16}{}_{}{}^{}\mathrm{O}$. Center of mass corrections are large for the ${}_{\Lambda }{}^6{}_{}{}^{}\mathrm{Li}$ and ${}_{\Lambda }{}^7{}_{}{}^{}\mathrm{Li}$ $p$ states and still substantial for ${}_{\Lambda }{}^{16}{}_{}{}^{}\mathrm{O}$. Spectra and selected transition and formation rates are calculated. Comparison is made with the recently measured ${\frac{5}{2}}^{+}\to {\frac{1}{2}}^{+}$ gamma-ray energy in ${}_{\Lambda }{}^7{}_{}{}^{}\mathrm{Li}$. Large changes are seen in the $l_{\Lambda }=1\mathrm{}$ wave functions between ${}_{\Lambda }{}^6{}_{}{}^{}\mathrm{Li}$ and ${}_{\Lambda }{}^{16}{}_{}{}^{}\mathrm{O}$. The $l_{\Lambda }=1\mathrm{}$ levels inferred from (${\mathrm{K}}^{-}$,${\pi }^{-}$) are well reproduced. The ground state ${}_{\Lambda }{}^{16}{}_{}{}^{}\mathrm{O}$ is overbound, suggesting that a two-body $\Lambda \mathrm{N}$ interaction must be modified in the nuclear interior.