Shell model analysis of ∑-hypernuclear spectra for mass A=12 and A=16

We present a systematic shell-model analysis of ∑-hypernuclear states as seen in K^-, π) reactions. A consistent description of data obtained both with stopped kaons and with in-flight kinematics can be achieved with a ∑-nucleus single particle potential depth between 15 and 20 MeV, a weak ∑N residual interaction and a ∑N-spin-orbit interaction about twice as strong as the one for the nucleon. At the same time we point out unresolved problems and uncertainties related to the continuum properties and the widths of ∑-hypernuclear states.