Ban people with a history of being mentally unstable from owning guns

It seems as though people who have been diagnosed with mental instability are the people who end up committing murder and/or mass murder. In light of the Sandy Hook school shootings, it seems as though the shooter, Adam Lanza was deeply troubled. I believe that to own a gun, a person should have to divulge their medical records and have a complete psychiatric evaluation. If we do not limit guns to those who will only use it for self-defense, then our country will continue to suffer horrible tragedies like the shootings in Sandy Hook. Thank you, and I hope that we can become more responsible in who receives a firearms license.