Lithium Inventory of 2 $M_\odot$ Red Clump Stars in Open Clusters: A
  Test of the Helium Flash Mechanism
  The temperature distribution of field Li-rich red giants suggests the
presence of a population of Li-rich red clump (RC) stars. One proposed
explanation for this population is that all stars with masses near 2 $M_\odot$
experience a short-lived phase of Li-richness at the onset of core He-burning.
Many of these stars have low 12C/13C, a signature of deep mixing that is
presumably associated with the Li regeneration. To test this purported
mechanism of Li enrichment, we measured abundances in 38 RC stars and 6 red
giant branch (RGB) stars in four open clusters selected to have RC masses near
2 $M_\odot$. We find six Li-rich stars (A(Li) > 1.50 dex) of which only two may
be RC stars. None of the RC stars have Li exceeding the levels observed in the
RGB stars, but given the brevity of the suggested Li-rich phase and the modest
sample size, it is probable that stars with larger Li-enrichments were missed
simply by chance. However, we find very few stars in our sample with low
12C/13C. Such low 12C/13C, seen in many field Li-rich stars, should persist
even after lithium has returned to normal low levels. Thus, if Li synthesis
during the He flash occurs, it is a rare, but potentially long-lived occurrence
rather than a short-lived phase for all stars. We estimate a conservative upper
limit of the fraction of stars going through a Li-rich phase to be <47\%, based
on stars that have low 12C/13C for their observed A(Li).
