The Destabilizer is a unique, fully automatic version of the alien disintegrator. Per shot, the Destabilizer is much weaker than it appears to be, deals less damage and has a slower reload speed than an alien atomizer. Like an assault rifle, the Pip-Boy displays an accurate total of damage per second, not per shot. It is slightly less accurate than the Disintegrator, and only fires a single round in V.A.T.S., despite being automatic. This, coupled with a higher AP cost, makes the Destabilizer a poor weapon for heavy V.A.T.S. usage.
This weapon is found in the weapons lab's shooting range, after beaming up from the space walk and proceeding through the observation deck. It is in the same room as where the Xenotech Expertperk is obtained. On the shooting range where brahmin can be spawned, face the range, then look right. The Destabilizer should be on a low shelf. It is the only item on that shelf. Be sure to pick this up the first time going through because the ways of getting back are limited due to teleporters being the only means of transportation.