There are many fields of the private industry that are looking for physicist. I will drop the ones outside the physics field.
With a doctorship in nuclear physics, you can definitely work in a nuclear power plant. You can also work for nuclear power plant designer (Westinghouse, GE, Mitsubishi, Areva, ...). You could also find a job in the field of nuclear fuel, either in the mining for uranium, or into recycling of used fuel. To get on the other side, you could find a job at the government, for the licensing authorities.
These are the jobs that come to my mind just like that. I am sure by searchin a bit, I could find some more for you. As you can see, the nuclear field is very active. And I only talked about the nuclear fission, where there are other jobs in nuclear fusion.
Cheers