  Theory and observations favor stable helium burning as the most important
means to produce fuel for superbursts on neutron star surfaces. However, all
known superbursters exhibit unstable burning as well. This ambiguity prompted
us to search for superbursts in data from the BeppoSAX Wide Field Cameras of
ten luminous LMXBs, most of which do not exhibit normal type-I X-ray bursts. We
found no superbursts and determine a lower limit on the recurrence time which
varies between 30 and 76 days (90% confidence). All recurrence time limits
except one are longer than the observed recurrence time for GX 17+2. This
difference can be understood if the mass accretion rate in GX 17+2 is several
tens of percent higher than in the other sources; alternatively, the accreted
material in GX 17+2 might be hydrogen deficient, leading to larger carbon
yields than in the other sources. We compare our results to the latest models
of superbursts. As our search method is indiscriminate of the burst ignition
scenario, the recurrence time limits may also be applied to other bursts of
similar duration and brightness.
