  The lifetimes and decay channels of ultralong-range Rydberg molecules created
in a dense BEC are examined by monitoring the time evolution of the Rydberg
population using field ionization. Studies of molecules with values of
principal quantum number, $n$, in the range $n=49$ to $n=72$ that contain tens
to hundreds of ground state atoms within the Rydberg electron orbit show that
their presence leads to marked changes in the field ionization characteristics.
The Rydberg molecules have lifetimes of $\sim1-5\,\mu$s, their destruction
being attributed to two main processes: formation of Sr$^+_2$ ions through
associative ionization, and dissociation induced through $L$-changing
collisions. The observed loss rates are consistent with a reaction model that
emphasizes the interaction between the Rydberg core ion and its nearest
neighbor ground-state atom. The measured lifetimes place strict limits on the
time scales over which studies involving Rydberg species in cold, dense atomic
gases can be undertaken and limit the coherence times for such measurements.
