The protonic inversal axe is a variant of the proton axe, having a dark blue-violet blade, whitish capacitors, and a black handle. Compared to the standard proton axe, it deals increased damage and much more critical damage, in addition to being much more durable. It is a very effective melee weapon against just about any enemy, especially robots or power armor users.
The proton inversal axe has a special V.A.T.S. attack unlocked at 50 Melee Weapons skill called "Inversal Scarifier", which costs 35 AP, and deals double damage.
Proton axe, a less powerful, but more common variant.