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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.

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A simple calculation method for estimating gamma-ray skyshine dose rates has been developed on the basis of the line beam response function (LBRF). The new data of LBRFs were generated by the single scattering with point kernel technique (single-scattering method). These resulting LBRFs were compared with the EGS4 and MCNP Monte Carlo calculations. The values of the new LBRFs for the large emitted angle become smaller than the LBRFs obtained with the Monte Carlo calculations with an increase of the distance from the source. This discrepancy increases with an increase of the photon energy.

A simple calculation method for estimating gamma-ray skyshine dose rates has been developed on the basis of the line beam response function (LBRF). The new data of LBRFs were generated by the single scattering with point kernel technique (single-scattering method). These resulting LBRFs were compared with the EGS4 and MCNP Monte Carlo calculations. The values of the new LBRFs for the large emitted angle become smaller than the LBRFs obtained with the Monte Carlo calculations with an increase of the distance from the source. This discrepancy increases with an increase of the photon energy.