We analyzed 123 thermonuclear (type-I) X-ray bursts observed by the Rossi X-ray Timing Explorer from the low-mass X-ray binary 4U 1636-536. All but two of the 40 radius-exansion bursts in this sample reached peak fluxes which were normally distributed about a mean of 6.4e-8 ergs/cm^2/s, with a standard deviation of 7.6%. The remaining two radius-expansion bursts reached peak fluxes a factor of 1.69+/-0.13 lower than this mean value; as a consequence, the overall variation in the peak flux of the radius-expansion bursts was a factor of ~2. This variation is comparable to the range of the Eddington limit between material with solar H-fraction (X=0.7) and pure He. Such a variation may arise if, for the bright radius-expansion bursts, most of the accreted H is eliminated either by steady hot CNO burning or expelled in a radiatively-driven wind. However, steady burning cannot exhaust the accreted H for solar composition material within the typical ~2 hr burst recurrence time, nor can it result in sufficient elemental stratification to allow selective ejection of the H only. An additional stratification mechanism appears to be required to separate the accreted elements and thus allow preferential ejection of the hydrogen. We found no evidence for a gap in the peak flux distribution between the radius-expansion and non-radius expansion bursts, previously observed in smaller samples. Assuming that the faint radius-expansion bursts reached the Eddington limit for H-rich material (X~0.7), and the brighter bursts the limit for pure He (X=0), we estimate the distance to 4U 1636-536 (for a canonical neutron star with M_NS=1.4M_sun, R_NS=10 km) to be 6.0+/-0.5 kpc, or for M_NS=2M_sun at most 7.1 kpc. (Abstract abridged)
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