Looking for short story read in the '60s.
In the future, space exploration uses a sort of astral projection. The traveller is in the lab and hooked up to monitors, but they don't allow real-time analysis. Just as his trip to another barren world ends, he encounters an intelligence which says "with you I exchange my mind". In a flash the trip ends and he is "woken" in the lab. They ask if there was anything of note and he says not and goes home.
He soon becomes aware of what happened and realises it's monumental, as the mind he exchanged with had been collecting minds for eons and he has them all for sharing only his. He's reluctant to admit to the authorities and realises they will soon finish the analysis and come after him......