  The stability of thermonuclear burning of hydrogen and helium accreted onto
neutron stars is strongly dependent on the mass accretion rate. The burning
behavior is observed to change from Type I X-ray bursts to stable burning, with
oscillatory burning occurring at the transition. Simulations predict the
transition at a ten times higher mass accretion rate than observed. Using
numerical models we investigate how the transition depends on the hydrogen,
helium, and CNO mass fractions of the accreted material, as well as on the
nuclear reaction rates of triple alpha and the hot-CNO breakout reactions
15O(a,g)19Ne and 18Ne(a,p)21Na. For a lower hydrogen content the transition is
at higher accretion rates. Furthermore, most experimentally allowed reaction
rate variations change the transition accretion rate by at most 10%. A factor
ten decrease of the 15O(a,g)19Ne rate, however, produces an increase of the
transition accretion rate of 35%. None of our models reproduce the transition
at the observed rate, and depending on the true 15O(a,g)19Ne reaction rate, the
actual discrepancy may be substantially larger. We find that the width of the
interval of accretion rates with marginally stable burning depends strongly on
both composition and reaction rates. Furthermore, close to the stability
transition, our models predict that X-ray bursts have extended tails where
freshly accreted fuel prolongs nuclear burning.
