Washington’s Blog 
April 30, 2011
As everyone knows, exposure to high levels of radiation can quickly sicken or kill us. Here’s an illustration  from Columbia University:
Radiation can sicken or kill us by directly  damaging cells:
Or indirectly … by producing free radicals :
Indeed, some radiation experts argue  that the creation of a lot of free radical creation is the most dangerous mechanism of low level ionizing radiation:
During exposure to low-level doses (LLD) of ionizing radiation (IR), the most of harmful effects are produced indirectly, through radiolysis of water and formation of reactive oxygen species (ROS). The antioxidant enzymes – superoxide dismutase (SOD): manganese SOD (MnSOD) and copper-zinc SOD (CuZnSOD), as well as glutathione (GSH), are the most important intracellular antioxidants in the metabolism of ROS. Overproduction of ROS challenges antioxidant enzymes.
Scientists from the Institute of Nuclear Science claim  in the Archive of oncology:
Chronic exposure to low-dose radiation doses could be much more harmful than high, short-term doses because of lipid peroxidation initiated by free radicals.
Peroxidation of cell membranes increases with decreasing dose rate (Petkau effect).
(See this  for more on the Petkau effect.)
Countering free radicals is therefore one of the most important ways we can help protect ourselves from the effects of low-level radiation from Japan, from Chernobyl and elsewhere.
Now that you know, I invite you to read the following articles to learn how to help counter free radicals:
- What Foods Are Highest in Antioxidants? Some Inexpensive Foods Are Higher In Antioxidants than the Newest Pricey “Superfoods” 
- The Compounds Plants Use to Protect Themselves from Damage Also Help to Protect People From Damage 
Note: The Bulletin of Atomic Scientists reported  that one of the best-known scientists of the 20th century – Dr. John Gofman – also believed that chronic low level radiation is more dangerous than acute exposure to high doses. Gofman was a doctor of nuclear and physical chemistry and a medical doctor who worked on the Manhattan Project, co-discovered uranium-232 and -233 and other radioactive isotopes and proved their fissionability, helped discover how to extract plutonium, led the team that discovered and characterized lipoproteins in the causation of heart disease, served as a Professor Emeritus of Molecular and Cell Biology at the University of California Berkeley, served as Associate Director of the Livermore National Laboratory, was asked by the Atomic Energy Commission to undertake a series of long range studies on potential dangers that might arise from the “peaceful uses of the atom”, and wrote four scholarly books on radiation health effects.
But whether or not chronic, low doses of radiation cause more or less damage than acute, higher doses is beyond the scope of this article. The point is that they both can cause damage.
Disclaimer: I am not a health care professional.