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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Radon emanation coefficients larger than 0.6 have been reported; such large values were unexpected. This led the authors to study how the maximum possible radon emanation coefficient (hereafter referred to as 'maximum radon emanation probability') could be determined. Theoretical calculations were repeated in which the grain configuration was changed in order to get the maximum radon emanation probability. Two types of grains were targeted. The first type consisted of two components mixed together; one component was a large amount of mother grains including no radium and the other component was a small amount of very fine grains including radium. For this type, the maximum radon emanation probability was obtained as 0.75. The second type consisted of only one grain component including radium. For this type, the maximum radon emanation probability was 0.625. In both types, the high coefficients were attributed to the extremely small size of the radium-bearing grains. This finding hinted at a possible countermeasure to suppress radon emanation, i.e., sintering at a rather low temperature, which may best be fitted to industries which process naturally occurring radioactive materials (NORM).