  We measured the thermonuclear burning efficiency as a function of accretion
rate for the Type I X-ray bursts of five low-mass X-ray binary systems. We
chose sources with measured neutron star spins and a substantial population of
bursts from a large observational sample. The general trend for the burst rate
is qualitatively the same for all sources; the burst rate first increases with
the accretion rate up to a maximum, above which the burst rate declines,
despite the increasing accretion rate. At higher accretion rates, when the
burst rate decreases, the {\alpha}-value (the ratio of accretion energy and
burst energy) increases by up to a factor of 10 above that in the rising burst
rate regime. These observations are contrary to the predictions of 1D numerical
models, but can be explained as the consequence of a zone of stable burning on
the neutron star surface, which expands with increasing accretion rate. The
stable burning also "pollutes" the unstable burning layer with ashes,
contributing to the change in burst properties measured in the falling burst
rate regime. We find that the mass accretion rate at which the burst rate
begins to decrease is anti-correlated with the spin of the neutron star. We
conclude that the neutron star spin is a key factor, moderating the nuclear
burning stability, via the local accretion rate and fuel composition over the
star.
