I'm not sure about the laws in Alaska, but in Georgia, and most other states, you can only use deadly force, without the threat of prosecution, to save your life, or the life of a third party.
IF you shoot someone for stealing, trespassing, or for the damage of property, you can, and most likely will, be arrested.
The thing we've all heard about shooting someone on your lawn, and drag him in the house is a myth. Even if you kill someone in your house, you have to be able to prove that your life, or that of a third party was in immediate danger. Also, the intruder will have to be armed.
Or, hope your lawyer does a good job of jury selection, and you get 12 people with some common sense.