From Der Spiegel I quote the following:
The scariest consequence is damage to the genome.
But for the body, even that kind of damage is not necessarily a dramatic event in the near term.
Every single cell experiences it thousands of times every day.
Often enough, the attack comes from inside: Cell metabolism creates aggressive molecules, so-called oxygen radicals, that continuously impair DNA.

Even Radiation Hormesis has been allowed out of the cupbord.