Nope. He died, but his head never was chopped off. Luke let him die "peacefully" while Vader, in his final moments, asked Luke to take off his helmet so he can see him with his own eyes. Vader died on the floor, without the helmet. Then, Luke burned his helmet as a bury ceremony... maybe you remember the helmet on the fire and that's why you think his head was chopped off...
I bet for a V shaped 7 string.
PS: Star Wars fanboy here... hahahaha!
Well, if you want to get picky, Luke does decapitate Vader during his hallucination on Dagobah before seeing his own face in the helmet...