AI is Ackley Improved.
Basically, it takes the parent case and moves the shoulder closes to the case mouth and steepens the shoulder angle to 40 degrees. The case has very little taper from the base to the shoulder. Check out the various versions at
www.reloadbench.com under cartridges and reload then under wildcat cartridges. The 30-30 AI is discussed and dimensions are available.
The beauty of the AI is that you fire form the cases to the chamber, and do not need case forming dies. You do need AI dies for loading the formed case. And if you run out of ammo, you can fire the regular parent in the chamber.
With the Handi being a break open action, the AI version is easier done with the rimmed cartridges like the 22 Hornet and the 30-30. With the rimless cartridges like the 223 and 308, it is more difficult to due if the barrel is the cartridge you want to improve. For the 223 Remington, to AI a handi, I would start with a 22 Hornet barrel and replace the ejector. The rimless headspace on the shoulder, and therefor the AI chamber is typically 0.004" shorter to the shoulder/neck than the regular cartridge chamber in order to allow regular rounds to headspace.