None. You do not delete any database tables, that would destroy your JIRA system.
The question is asking for completely the wrong thing, but only because you do not know what the index is.
The index is a *local* copy of most of the database. It is built for search rather than storage, and the whole thing is a set of files on the JIRA server's disk.
It is independent of the database. When you run a full "reindex", JIRA throws away the whole index, every file, and then rebuilds it from scratch, re-reading every issue in the database.
So, I think your question really is "I can't start JIRA after a crash, how do I get it to start". We can't tell you that without knowing what errors you are getting.
What Nic said is accurate. In the most ideal situation you would have a backup you could recover from. If you're seeing JIRA crashing during the indexing here's what I would do:
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