A transient-diffusion measurement method for radon diffusion coefficients in porous materials was first developed in the U.S.A. To get a correct interpretation of measured data by the transient-diffusion method, more attention needs to be put on mathematical treatment which has been somewhat neglected perhaps because of the inherent mathematical difficulty. Strictly speaking, the measured radon concentrations have to be interpreted mathematically as a two-region problem. But, solving diffusion equations is quite difficult analytically because of time-dependent boundary conditions for the two-region problem. On the other hand, the advent of high performance computers has made it possible to easily solve diffusion equations numerically. However, without good knowledge of the diffusion phenomena in the actual measuring system, there is a possibility that the wrong boundary conditions are set. To prevent this, prior consideration by mathematical interpretation leading to visual understanding of the diffusion phenomena is necessary. The present paper examined how to set up boundary conditions in diffusion equations to obtain radon diffusion coefficients in porous materials, especially Japanese soils, using transient-diffusion data. To reduce the two-region problem to a one-region problem, effective length to the radon measuring device was proposed using the relationship, D air =ðB 1 Þ 2 ¼D soil =ðB 2 Þ 2 , where the subscripts refer to each region, D denotes the radon diffusion coefficient and B denotes the length to the measuring device. This formula was derived in a general form and has universal application; it is not limited to soils. Additionally, as part of a mathematical discussion, a checking method for detector calibration was proposed.

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Distribution coefficients of 226Ra and 227Ac on soils and tuff have been obtained by a batch method. The distribution coefficients of Ra on loam, two kinds of sand and tuff were 28m3/kg, 0.45m3/kg, 0.19m3/kg and 1.9m3/kg, respectively. A linear relationship between the distribution coefficients of Ra on each soil and Cation Exchange Capacity(CEC) of each soil was obtained to suggest cation exchange sorption reaction of Ra2+ on soil surface. Sorption-migration behavior of Ra in sand column has been studied. Most of Ra remained in the column after passing of 5,000 pore volume of the column, showing several times the distribution coefficients of Ra than that by the batch method. The distribution coefficients of 227Ac on the soil samples were in the range from 1m3/kg to 10m3/kg.