Validity of the Four-Parameter Empirical Formula in Approximating the Response Functions for Gamma-ray, Neutron, and Secondary Gamma-ray Skyshine Analyses

Abstract

A four-parameter approximating formula, R= A e a x b f (x), accurately represents the skyshine line beam response function (LBRF) as a function of the distance (x) of the source-to-detector separation. Here, A is a constant for a given source energy and f (x)=e cx x dx is a damping factor. The four parameters are obtained as follows. (1) The value of parameter a corresponds to that of the LBRF at x=1 meter, which is the result of integrating the basic dose spectrum due to a single scattering particle from an emitted beam for a specified angle and a specified source energy. (2) The value of parameter b corresponds to the slope of a straight line of the response function, log R vs. log x, in the range of small distance from a source, where a single scattering particle dominates. (3) The damping factor ( f (x)) represents the attenuation trend of the LBRF at distances far from the source; the values of parameters c and d control the quantity of attenuation. The necessary reference LBRF data for point mono-directional photon source energies ranging from 0.1 to 10 MeV were generated using the EGS4 Monte Carlo code at 20 emission angles from 0.0 to 180• for 24 source-detector distances up to 2,000 m. The validity of using the four-parameter formula to interpolate the LBRF in the source-todetector distance, in the emitted angle, and in the energy was also ascertained. Furthermore, this formula was applied to the skyshine conical beam response function (CBRF) for a neutron and an associated secondary gamma-ray with the source energy ranged from thermal to 3 GeV. It was ascertained that the CBRF could be accurately approximated by an interpolation of the fitting parameters at an arbitrary distance and emitted cosine angle.

Development of a new calculation system to estimate decontamination effects

“…As a result, the C/E value in Okuma town (1) was 0.8 on average. Figure 5 shows an aerial photo of Okuma town (1). Figure 6 shows an air dose rate map before decontamination in this area as calculated by SOPHIDA based on dose rate measurement results for the ground surface.…”

“…SOPHIDA was first applied to Okuma town (1) . By comparing the measured values with the results calculated by SOPHIDA in this area, we have confirmed the validity of the calculated results.…”

“…The radiation dose rate map of Okuma town (2) was created using the same evaluation method used for Okuma town (1). Moreover, the predicted dose rate map after decontamination of Okuma town (2) was calculated by entering the decontamination factors according to the decontamination plan.…”

“…In order to reduce the calculation time, we defined the empirical formula proposed by Harima [1], and it was adopted in the SOPHIDA calculation system. This formula is shown below.…”

Development of a new simulation software system to evaluate radiation doses and facilitate decontamination tasks in reactor buildings

“…(2). To have calculation time as short as possible, calculation points in figure 2 were set only vertical direction to the plane source and this means a(L) has no direction dependency.…”