A search for Sigma hypernuclear states in p-shell hypernuclei her; been per
formed with the Moby Dick spectrometer and the low energy separated beam (L
ESB-2) at the Brookhaven Alternating Gradient Synchrotron (BNL AGS). Unlike
some previously published reports, no narrow states have been observed for
targets of Li-6 and Be-9 in (K-, pi(+/-)) reactions, either for bound stat
e or continuum regions, Together with the previously reported J = 0, T = 1/
2 bound state in He-4(Sigma), these results demonstrate the crucial role of
isospin in Sigma hypernuclei.