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What Is Factually Wrong with This Belief:   "Harm from
Low-Dose Radiation Is Just Hypothetical — Not Proven"

By John W. Gofman, M.D., Ph.D.
Fall 1995

  • Part 1 — An "Open Letter" to Editors of Major Journals and Newspapers, to Science Reporters and Physicians
  • Part 2 — Some Introductory Information
  • Part 3 — Where's the Controversy, in View of Such Evidence?
  • Part 4 — How Ionizing Radiation "Works"
  • Part 5 — Human Studies Showing Radiation-Induced Cancer from Minimal Doses
  • Part 6 — A Five-Point Summary
  • References

*  The Author: John W. Gofman, M.D., Ph.D, is Professor Emeritus of Molecular and Cell Biology at the University of California (Berkeley), former Associate Director of the Livermore National Laboratory, and author of four scholarly books on radiation health effects.

Part 1.   *    An "Open Letter" to Editors of Major Journals and Newspapers, to Science Reporters and Physicians

                *   Advances in identifying the causes of cancer and inherited afflictions receive much attention in your publications and broadcasts --- because you and your customers care very much about preventing these miseries.

                *   You do not want mistakes slipping through your various filters against misinformation. The mistake we address here is the claim that harm from ionizing radiation, a proven carcinogen and mutagen, is "only hypothetical" at low dose-levels. This misinformation is routinely treated as credible and is disseminated widely; recent conduits include the Journal of the Amer. Medical Association (Skolnick 1995, p.367, p.368), the Lancet (Hulka 1995, p.885), the Wall Street Journal (Chase 1995, p.B-1), Nuclear News (Sept.1995, p.26) --- and even a current syllabus for residents in radiology (Goldberg 1995, p.5, p.7).

                *   The purpose of this communication is to show you, in abbreviated fashion, the factual basis for rejecting the claim that no harm has yet been proven from low-dose radiation --- and for rejecting suggestions that your duty is to fight "radio-phobia" over a carcinogen which "requires" high doses.

                *   The stakes are worth some of your time. How so? Because ionizing radiation is not an exotic carcinogen and mutagen which exposes a small segment of the population. Low-dose ionizing radiation is received from natural background sources, numerous medical procedures, nuclear pollution, flying, and sometimes from occupational exposures. How many other proven human carcinogens can you name to which everyone is exposed on a daily and lifelong basis?

                *   The evidence that there is no safe dose-level of ionizing radiation (no threshold dose) means that journals and other media contribute to cancer (and inherited afflictions) whenever they include disproven claims which encourage a casual attitude toward extra exposures to low-dose ionizing radiation. We believe that you want to help prevent such miseries.

Part 2.   *    Some Introductory Information

                *   Assertions in this communication are supported in detail, and with very specific sourcing, in Gofman 1990 (Chapters 18, 19, 20, 21, 32, 33).

          a.   *   Cancers require the presence of damaged genetic molecules in the single cells which turn malignant. Likewise, inherited afflictions require the presence of damaged genetic molecules in the single cell from which a baby develops. The genetic molecules in a human cell-nucleus are the 46 human chromosomes, each consisting of one double-strand DNA helix plus associated proteins.

          b.   *   After damage occurs to a genetic molecule, the cell attempts to repair it. If the cell achieves perfect repair, the genetic molecule regains its "mint quality" --- as if no damage had ever occurred.

          c.   *   The menace to health involves the genetic damage which is unrepaired, unrepairable, or misrepaired. The "troublesome trio."

          d.   *   When the damage is complex --- for example, when the opposite strands of the double helix have been broken --- pieces of the DNA double-helix sometimes end up in the wrong place, or become permanently lost. These failures of repair are not in dispute.

          e.   *   By contrast, the cell is exquisitely efficient at repairing injury to single strands of the double helix. It has been estimated that, every day, each cell copes with at least 10,000 DNA injuries induced by routine chemical sources (including free radicals produced by the cell itself). Such standard repairs might be compared to replacing a lamp's broken light bulb with a new bulb. After "repair," the lamp works perfectly again.

          f.   *   Ionizing radiation has demonstrated beyond any doubt its ability to break both strands of the DNA double helix at the same time. This ability has made it "famous" among toxic agents as a chromosome-breaker. (If only one DNA strand breaks, the other strand holds the chromosome together.)

          g.   *   Countless experiments have been done on cells to measure the speed with which they repair radiation-induced DNA damage, both single-strand and double-strand injuries. Even after extremely high radiation doses, that repair which does occur is complete within about 8 hours, and most of it is complete within about 2 hours.

          h.   *   An "extremely high radiation dose" can be understood by comparison with the annual dose which everyone receives from natural sources. Excluding radon, the natural dose per year is about 0.1 rad. Therefore a common experimental dose to cells of 100 rads, delivered in an instant ("acute" dose-delivery), is about 1,000 times higher than the total annual natural dose. And yet experiments show that human cells mobilize enough repair capacity (repair enzymes) to cope with 100 rads all at once. Indeed, repair capacity seems not overwhelmed even at doses of 500 rads and more.

          i.   *   The explanation for residual, post-repair damage is not a lack of repair-capacity or time, but rather an inherent inability of the repair-system to fix certain complex injuries to genetic molecules.

          j.   *   A radiation-induced chromosome abnormality does not always kill the cell in which it persists, nor does it always prevent the cell from dividing. When the injured cell divides, the same injury is replicated in the new cells. In the A-bomb survivors, extra chromosome abnormalities have been observed even 40 years after the bombings. Their radiation-causation is indicated by the positive dose-response: The higher the bomb-dose, the higher the frequency of abnormalities (Kodama 1993).

          k.   *   Residual unrepaired and misrepaired chromosome damage in human blood samples, irradiated in lab dishes (in vitro), is visually detectable at acute radiation doses as low as 2 rads, despite crude methods of observation (Lloyd 1988). Moreover, the residual genetic damage which can not be detected with such methods may swamp the amount detected.

          L.   *   Does residual damage also exist, after repair-time, if low doses are received slowly by living humans (in vivo)? Yes. For example, extra chromosome damage has been observed among Alaskan natives from nuclear fallout, in spite of very gradual accumulation of about 0.08 rad of extra exposure per year for 10 years (AEC 1970); extra chromosome damage has been observed among nuclear dockyard workers exposed very slowly to less than 5 rads per year (Evans 1979); extra chromosome damage has been observed among various populations living where the chronic natural dose from radiation is above average (for example, see Barcinski 1975;   Maruyama 1976). [One rad is also called 0.01 Gray.]

Part 3.   *    Where's the Controversy, in View of Such Evidence?

          m.   *   If residual genetic damage has been observed even from low radiation doses at slow dose-rates (para. L, above), how can anyone still claim that evidence of harm at low doses is "just hypothetical," or that harm requires high doses?

          n.   *   Here's how. If challenged, they say: (1) Since a connection is just hypothetical between real-world health effects and misrepaired or unrepaired genetic injury from radiation, the evidence of harm to health from low-dose radiation is just hypothetical; and (2) Since there are radiation doses lower than occupational doses, and lower than fallout doses, and lower than any doses we can ever afford to study, the harm at these lower doses will always remain unproven. They suggest that maybe, at some extremely low dose or dose-rate, "repair" becomes perfect.

          o.   *   We recognized a method which could cope with both difficulties. Beginning with Gofman 1971 (pp.275-277), it evolved in Gofman 1981 (pp.405-411), and Gofman 1986 (pp.6-14). In Gofman 1990, we developed the method and the evidence in detail. Full presentation takes 70 pages --- not suitable for a journal. We wanted to know if the threshold issue, for ionizing radiation, could be settled. Our analysis proves, by any reasonable standard of scientific proof, that there is no safe dose or dose-rate of ionizing radiation.

          p.   *   We have found no refutation of our proof. On the contrary, our method is extensively confirmed in the 1993 report of the United Nations (UNSCEAR 1993, esp. pp.627-636, p.681, p.696 Table 17).

          q.   *   For readers to understand how our method overcomes the obstacles described above (para. n), you need to know how ionizing radiation "works." It works very differently from toxic chemicals (para. cc, below).

Part 4.   *    How Ionizing Radiation "Works"

          r.   *   Ionizing radiation includes beta particles, alpha particles, gamma rays, and x-rays; the term excludes radio, microwave, infra-red, and visible radiations.

          s.   *   Beta particles are electrons --- but they differ from the ordinary non-beta electrons in the human body in one important way. Beta particles are endowed with biologically unnatural energy. This energy causes them to travel through the cell (and beyond) at high speed, like tiny bullets.

          t.   *   Many radioactive atoms (called radio-nuclides, radio-isotopes) decay into stable atoms by spitting out beta particles --- or alpha particles, which are much larger. Radio-nuclides often emit gamma rays too, in the process of decaying into stable nuclides.

          u.   *   Gamma rays are photons --- a sort of light having too much energy for humans to see. X-rays are like gamma rays, except x-rays have less energy per photon. Both are generated by "nature" and by man-made generators.

          v.   *   The photons of x-rays and gamma rays do their damage to cells by knocking electrons out of ordinary molecules and causing them to become beta particles --- which travel through the cell (and beyond) with biologically unnatural energy. There are about 600 million typical cells in 1 cubic centimeter.

          w.   *   The biological damage caused by ionizing radiation, including gamma rays and x-rays, is due to high-speed particles traveling through cells and unloading concentrated amounts of energy in unnatural places at random. Each particle creates a very narrow path of disturbance (called a primary "ionization track") as it unloads energy at irregular intervals. Alpha particles don't travel far; they unload their energy within just a few cells. Since virtually no one claims any threshold dose (safe dose) for alpha irradiation, our work involves high-speed electrons (para. s + v, above).

          x.   *   The amount of energy transferred in an instant, from the high-speed electron to nearby molecules, is often many times larger than the single energy-transfers which occur "anyway" in normal cell chemistry and metabolism. This unique feature of ionizing radiation probably explains why ionizing radiation is so "good" at breaking chromosomes and inflicting other complex injuries on the genetic molecules. Every track --- acting without help from any other track --- has a chance of causing an unrepairable carcinogenic injury in a cell.

          y.   *   At high radiation doses, many tracks from high-speed electrons pass through every cell-nucleus. We focus on the nucleus because that is where the human's genetic molecules are located. How many tracks? At 100 rads from medical x-rays, about 130 primary tracks cross every cell-nucleus (Gofman 1990; based on 30 KeV x-rays on the average, from 90 kV peak). At 100 rads from gamma rays, about 300 tracks cross every cell-nucleus (Gofman 1990; based on ~630 KeV gamma rays from radium-226 or decay of cesium-137 into stable barium-137).

          z.   *   What happens at low doses? When the total dose is about 0.75 rad (750 milli-rads) from medical x-rays, the average number of tracks per cell-nucleus is one track (Gofman 1990, Table 20-M). At total doses of about 0.33 rad (330 milli-rads) from radium-226 or cesium-137, the average number of tracks per cell-nucleus is one track. At a total annual dose of 0.1 rad from natural background sources, the average number of tracks per cell-nucleus is a fraction of one track during a year.

          aa.   *   But electrons can not be subdivided into fractions. So, either a cell-nucleus experiences an electron-track, or it does not. Yes or no. At very low total doses, some nuclei experience one track or a few tracks, and other nuclei experience no irradiation at all.

          bb.   *   When the average number of tracks per nucleus is one track, 37% of the nuclei experience no track at all, 37% experience one track, 18% experience two tracks, 6% experience 3 tracks (Gofman 1990, Table 20-N).

          cc.   *   Tracks are a special property making ionizing radiation very different from toxic chemicals. Chemicals can be present in a cell-nucleus at lower and lower concentrations. For chemicals, there is no minimum concentration. But for ionizing radiation, one track is the least possible invasion it can inflict upon a cell-nucleus. At the cellular level, one track is the lowest possible "dose," and one track presents the least possible challenge for the repair-system. The split-second occurrence of one track is also the slowest possible dose-rate.

          dd.   *   If human evidence shows health harm caused by doses which deliver just one or a few tracks per cell-nucleus, then such evidence wipes out the hope that "repair" can ever deliver a threshold or safe dose (para. n, above).

Part 5.   *    Human Studies Showing Radiation-Induced Cancer from Minimal Doses

          ee.   *   In the mainstream medical literature are quite a number of epidemiological studies showing that even minimal doses of ionizing radiation induce extra cases of cancer. The references are flagged (#) in the list.

          ff.   *   For the flagged studies, we figured out the average number of tracks per nucleus caused by each exposure (Gofman 1990).

          gg.   *   The average number of tracks through each cell-nucleus, per exposure, ranged from 0.3 track to 12 tracks, with this distribution: 0.3; 0.7; 1.2; 1.3; 2.1; 6.2; 10; 12 tracks. In other words, some studies meet a very strict definition of lowest possible radiation dose (para. cc, above), and others are nearly minimal.

          hh.   *   If only the 6-track, 10-track, and 12-track studies existed, someone would be sure to speculate that "maybe 6 tracks overwhelm a cell's repair-capacity. Maybe there is a safe dose at 4 tracks." Six tracks (average) correspond with radiation doses of 2 to 5 rads, so such speculation would be hard to reconcile with evidence of abundant repair-capacity at 100 to 500 rads (see para. h, above). In any case, such speculation is ruled out by the studies showing excess cancer from even lower track-averages per nucleus.

          ii.   *   By any reasonable standard of proof, the combination of human epidemiology and track-analysis demonstrates that there is no threshold dose or dose-rate below which "repair" invariably prevents health harm.

          jj.   *   It is an error to assert that no human evidence exists of harm to health at minimal dose-levels. It does exist (see Reference List, flagged (#) entries). Cancer is a very serious harm. The flagged studies rule out speculation that low-dose radiation may be either risk-free or "good for you." Moreover, if radiation carcinogenesis is the result of residual injury to the genetic molecules, then the flagged studies strongly warn us that there is no safe dose of gonadal irradiation with respect to human inherited afflictions.

          kk.   *   It is especially powerful evidence when a common result arises from a variety of radiation experiences. The flagged studies include infants in-utero, children, adolescents, young women, high-energy gamma rays, medical x-rays, acute single doses, acute serial doses, and chronic occupational doses.

          LL.   *   It is worth noting that acute serial doses, in women who received repeated low-dose chest fluoroscopies, occurred with plenty of time for the repair-system to complete its work on damaged molecules before the next x-ray exam (para. g, above). If repair could always work flawlessly when the x-ray dose is low, then such women would show no radiation-induced cancer from the very high radiation doses which they gradually accumulated. After flawless repair-work, the women would never have any cancer-risk left from the previous exposure when they received the next exposure in the series. Each exposure would occur on a "clean slate."

          mm.   *   The evidence of excess breast cancer in the fluoroscoped women is very solid, and shows a positive dose-response. This evidence of radiation-induced human cancer is widely acknowledged and cited --- but not many people recognize that it is evidence of cancer-induction resulting from nearly minimal doses of radiation per exposure (about 6 to 10 tracks per average cell-nucleus, per x-ray examination).

          nn.   *   Our final point concerns the immune response. We've heard people speculate like this: "Even if a fraction of low-dose genetic damage is unrepaired, or unrepairable, or misrepaired at the lowest dose-levels, the resulting cancers would be so few that the immune system and the body's other defenses against cancer would eliminate them." The evidence in the flagged studies refutes that speculation, and so does logic. If a body's natural defenses automatically eliminate single cancers, humans would never develop cancer from any cause (including high-dose radiation). But lots of people do develop cancer. Fatal cancer. In the USA, 22% of all deaths are due to cancer.

Part 6.   *    A Five-Point Summary

          *   Point One: The radiation dose from x-rays, gamma rays, and beta particles is delivered by high-speed electrons, traveling through human cells and creating primary ionization tracks. Whenever there is any radiation dose, it means some cells and cell-nuclei are being traversed by electron-tracks. There are about 600 million typical cells in 1 cubic centimeter.

          *   Point Two: Every track --- without any help from another track --- has a chance of inflicting a genetic injury if the track traverses a cell-nucleus.

          *   Point Three: There are no fractional electrons. This means that the lowest "dose" of radiation which a cell-nucleus can experience is one electron-track.

          *   Point Four: There is solid evidence that extra human cancer does occur from radiation doses which deliver just one or a few tracks per cell-nucleus, on the average. See paragraphs ee-mm, above.

          *   Point Five: Thus we know that there is no dose or dose-rate low enough to guarantee perfect repair of every carcinogenic injury induced by radiation. Some carcinogenic injuries are just unrepaired, unrepairable, or misrepaired. The "troublesome trio."

          *   Conclusion: It is factually wrong to believe or to claim that no harm has ever been proven from very low-dose radiation. On the contrary. Existing human evidence shows cancer-induction by radiation at and near the lowest possible dose and dose-rate with respect to cell-nuclei. By any reasonable standard of scientific proof, such evidence demonstrates that there is no safe dose or dose-rate below which dangers disappear. No threshold-dose. Serious, lethal effects from minimal radiation doses are not "hypothetical," "just theoretical," or "imaginary." They are real.

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# # # # #

*   "The extent to which radiation-induced DNA damage may be correctly repaired at very low doses and very low dose rates is beyond the resolution of current experimental techniques. If DNA double-strand breaks are critical lesions determining a range of cellular responses, including perhaps neoplastic transformation, then it may be that wholly accurate cellular repair is unlikely even at the very low lesion abundance expected after low dose and low-dose-rate irradiation."
UNSCEAR 1993 Report, p.634, para.74.

*   "It is highly unlikely that a dose threshold exists for the initial molecular damage to DNA, because a single track from any ionizing radiation has a finite probability of producing a sizable cluster of atomic damage directly in, or near, the DNA. Only if the resulting molecular damage, plus any additional associated damage from the same track, were always repaired with total efficiency could there be any possibility of a dose threshold for consequent cellular effects."
UNSCEAR 1993 Report, p.636, para.84.

*   "Biological effects are believed to arise predominantly from residual DNA changes that originate from radiation damage to chromosomal DNA. It is the repair response of the cell that determines its fate. The majority of damage is repaired, but it is the remaining unrepaired or misrepaired damage that is then considered responsible for cell killing, chromosomal aberrations, mutations, transformations and cancerous changes."
UNSCEAR 1993 Report, p.680-681, para.323.

   *   Reference Listing

    AEC 1970.
      Atomic Energy Commission. Reports dated March 27 and May 4, 1970, from John R. Totter, Director of AEC's Biology and Medicine Division, to U.S. Senator Mike Gravel of Alaska. Totter was reporting on a pilot study of Alaskan natives by J.G. Brewen.
    Barcinski 1975.
      M.A. Barcinski et al, "Cytogenetic Investigation in a Brazilian Population Living in an Area of High Natural Radioactivity," Amer. J. of Human Genetics 27: 02-806. 1975.
    Baverstock 1981. #
      Keith F. Baverstock et al, "Risk of Radiation at Low Dose Rates," Lancet 1: 30-433. Feb. 21, 1981.
    Baverstock 1983. #
      Keith F. Baverstock + J. Vennart, "A Note on Radium Body Content and Breast Cancers in U.K. Radium Luminisers," Health Physics 44, Suppl.No.1: 75-577. 1983.
    Baverstock 1987. #
      Keith F. Baverstock + D.G. Papworth, "The U.K. Radium Luminizer Survey," British J. of Radiology, Supplemental BIR Report 21: 1-76. (BIR = Brit. Inst. of Radiology.) 1987.
    Boice 1977. #
      John D. Boice, Jr. + R.R. Monson, "Breast Cancer in Women after Repeated Fluoroscopic Examinations of the Chest," J. of the Natl. Cancer Inst. 59: 23-832. 1977.
    Boice 1978. #
      John D. Boice, Jr. et al, "Estimation of Breast Doses and Breast Cancer Risk Associated with Repeated Fluoroscopic Chest Examinations..." Radiation Research 73: 73-390. 1978.
    Chase 1995.
      Marilyn Chase, quoting radiologist Stephen Feig, in "Health Journal," Wall Street Journal, p.B-1, July 17, 1995.
    Evans 1979.
      H.J. Evans et al, "Radiation-Induced Chromosome Aberrations in Nuclear Dockyard Workers," Nature 277: 31-534. Feb. 15, 1979.
    Gofman 1971.
      John W. Gofman + Arthur R. Tamplin, "Epidemiologic Studies of Carcinogenesis by Ionizing Radiation," pp.235-277 in Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, July 20, 1971. University of California Press, Berkeley.
    Gofman 1981.
      John W. Gofman. Radiation and Human Health. 908 pages. ISBN 0-87156-275-8. LCCN 80-26484. Sierra Club Books, San Francisco. 1981.
    Gofman 1986.
      John W. Gofman, "Assessing Chernobyl's Cancer Consequences: Application of Four `Laws' of Radiation Carcinogenesis." Paper presented at the 192nd national meeting of the American Chemical Society, Symposium on Low-Level Radiation. Sept. 9, 1986.
    Gofman 1990. Goldberg 1995.
      Henry Goldberg. Introduction to Clinical Imaging: A Syllabus. From the Steven E. Ross Learning Center, Department of Radiology, Univ. of California S.F. Medical School. 1995.
    Harvey 1985. #
      Elizabeth B. Harvey et al, "Prenatal X-Ray Exposure and Childhood Cancer in Twins," New England J. of Medicine 312, No.9: 541-545. Feb. 28, 1985.
    Hoffman 1989. #
      Daniel A. Hoffman et al, "Breast Cancer in Women with Scoliosis Exposed to Multiple Diagnostic X-Rays," J. of the Natl. Cancer Inst. 81, No.17: 1307-1312. Sept. 6, 1989. Publication of an expanded follow-up study is expected soon.
    Howe 1984. #
      Geoffrey R. Howe, "Epidemiology of Radiogenic Breast Cancer," pp.119-129 in (book) Radiation Carcinogenesis: Epidemiology and Biological Significance, edited by John D. Boice, Jr., and Joseph F. Fraumeni. Raven Press, New York City. 1984.
    Hulka 1995.
      Barbara S. Hulka + Azadeh T. Stark, "Breast Cancer: Cause and Prevention," Lancet 346: 883-887. Sept. 30, 1995.
    Kodama 1993.
      Yoshiaki Kodama et al, "Biotechnology Contributes to Biological Dosimetry...Decades after Exposure," in Radiation Effects Research Foundation's RERF Update 4, No.4: 6-7. Winter 1992-1993.
    Lloyd 1988.
      D.C. Lloyd et al, "Frequencies of Chromosomal Aberrations Induced in Human Blood Lymphocytes by Low Doses of X-Rays," Internatl. J. of Radiation Biology 53, No.1: 49-55. 1988.
    MacMahon 1962. #
      Brian MacMahon, "Prenatal X-Ray Exposure and Childhood Cancer," J. of the Natl. Cancer Inst. 28: 1173-1191. 1962.
    Maruyama 1976.
      K. Maruyama et al, "Down's Syndrome and Related Abnormalities in an Area of High Background Radiation in Coastal Kerala [India]," Nature 262: 60-61. 1976.
    Miller 1989. #
      Anthony B. Miller et al, "Mortality from Breast Cancer after Irradiation during Fluoroscopic Examinations..." New England J. of Medicine 321, No.19: 1285-1289. 1989.
    Modan 1977. #
      Baruch Modan et al, "Thyroid Cancer Following Scalp Irradiation," Radiology 123: 741-744. 1977.
    Modan 1989. #
      Baruch Modan et al, "Increased Risk of Breast Cancer after Low-Dose Irradiation," Lancet 1: 629-631. March 25, 1989.
    Myrden 1969. #
      J.A Myrden + J.E. Hiltz, "Breast Cancer Following Multiple Fluoroscopies during Artificial Pneumothorax Treatment of Pulmonary Tuberculosis," Canadian Medical Assn. Journal 100: 1032-1034. 1969.
    Skolnick 1995.
      Andrew A. Skolnick, quoting radiologist Stephen Feig and citing `many radiation physicists,' in "Medical News and Perspectives," J. Amer. Medical Assn. 274, No.5: 367-368. Aug. 2, 1995.
    Stewart 1956. #
      Alice M. Stewart et al, "Preliminary Communication: Malignant Disease in Childhood and Diagnostic Irradiation In-Utero," Lancet 2: 447. 1956.
    Stewart 1958. #
      Alice M. Stewart et al, "A Survey of Childhood Malignancies," British Medical Journal 2: 1495-1508. 1958.
    Stewart 1970. #
      Alice M. Stewart + George W. Kneale, "Radiation Dose Effects in Relation to Obstetric X-Rays and Childhood Cancers," Lancet 1: 1185-1188. 1970.
    UNSCEAR 1993.
      United Nations Scientific Committee on the Effects of Atomic Radiation. Sources and Effects of Ionizing Radiation: UNSCEAR 1993 Report to the General Assembly, with Scientific Annexes. 922 pages. No index. ISBN 92-1-142200-0. 1993.

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