No. Soul is a word that describes our sense of self which is a product of our biology.
But, once you're dead or braindead even, it's over. Whatever it is that was you is 100% gone forever. That's the only conclusion I can draw.
Believing in a soul that outlives your brain is just wishful thinking and flattering yourself.
That has to be the most depressing outlook on death that I have ever read.
I dunno, better than eternal punishment.
I've heard about a theory that the quantum physics could prove our consciousness can survive in some other dimension after we die. Since my knowledge about the quantum physic is next to nothing, I reserve my judgement. Still, even if it's true, I wouldn't call it a "soul".