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Approximate relationship for calculating the dose rate from radioactive fallout

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Abstract

as a result of the Chernobyl nuclear power plant accident. Evaluations and measurements made at the site showed that vertical migration of the radionuclides into the soil in the first months after the accident lowered the dose rate by a factor of 1.5-2.5 [1]. Experimental methods and mathematical models that were developed make it possible to determine the shape of the radionuclide distribution function in the soil [2, 3]. It would be convenient to use analytical relationships, which give a satisfactory approximation to the dose rate, for engineering processing of data on the radionuclide composition of the soil. Calculations of the dose rate from buried sources, which were done using buildup factors for an infinite air space and concrete [4], depend strongly on the initial data and can be off by a factor of 2-3 from Monte Carlo results [5]. An approximate relationship has been suggested [6] which can calculate the effective equivalent dose from sources distributed uniformly in the soil with an error of 10-15%. Here the results of numerical Monte Carlo calculations of the dose rate from a plane source in the soil for photon energies of 0.015-5 MeV are approximated by an analytical relationship obtained by using an expression for the buildup factor in the Berger form. Direct approximation of the numerical modeling results increases the accuracy of the calculation, as compared to a method which uses a buildup factor for an infinite medium. The simple form of the analytical relationship makes it possible to do engineering calculations for various radiation source distributions in the soil. In the problem at hand, a plane monoenergetic isotopic source of photons of energy E.ro extends to infinity along the earth's surface at a depth z s in the soil. The energy was varied from 0.015 to 5 MeV. For energies >_0.1 MeV, the depth was varied from 0 to 30 cm for a characteristic soil density Ps = 1.6 g/cm 3, i.e., z s _< 24-48 cm for 2 _< Os -< 1 g/cm 3. For Evo < 0.1 MeV, z s does not exceed five mean-free paths of photons in the soil, which corresponds to a decrease of the dose rate by roughly 1000 times compared to the dose from a surface source. The chosen ranges of E.ro and z s are sufficient for calculating the dose rate from global fallout and fallout from nuclear power plant ejecta [2, 3, 5, 6]. It was assumed that the detection point was located at a height of z a = 100 cm above the earth's surface. In choosing a Berger-type buildup factor, the absorbed dose rate in air and the effective equivalent dose rate per unit surface activity are determined by the relationship Fp= A {El(r) +

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