IV. RADIATION IN AIR DUE TO EXPONENTIALLY DISTRIBUTED (FALLOUT) SOURCES IN THE SOIL Radioisotopes in the soil as a result of fallout from weapons tests (or accidental escape from reactors) usually remain on or just below the surface of the ground. For very short times after deposition, the sources can even be assumed to be distributed as an infinitesimally thin plane source directly on the interface. For longer lived fallout which has been in the biosphere for some time, we have found that a reasonable approximation is to assume the sources to be distributed exponentially with depth in the soil according to the relation S = So e~%4 where S is the activity at depth Z, So is the surface activity, and a is the reciprocal of the relaxation length (a ~- © is equivalent to a plane source on the interface). For fallout deposited in the U. S. during 1962 - 1965 an assumed relaxation length of 3 cm gave a reasonable fit to actual depth distribution measurements‘®? . Many investigators calculate the exposure rate from fallout isotopes as if the source were a plane source buried at some depth z beneath the surface in order to account for the effect of ground "roughness". For a widely distributed source, for detector heights at least a meter above the interface and for a moderately flat surface, the assumption of an average exponential depth distribution should be more realistic and should also account for ground roughness since an exponential source is equivalent to burying plane sources successively deeper in the ground with decreasing intensities. The choice of the best relaxation length to use for a given source depends on such factors as the type of surface, the source energy, the time since deposition, and the type of soil. Variations in the source energy, relaxation length, and detector height affect the exposure rate, energy spectra, and angular distributions in air. It is important to