FSKY4C: Gamma Ray Skyshine Analysis Code

Institute of Nuclear Safety System, Sata 64, Mihama-cho, Mikata-gun, Fukui, Japan and Radiation Dose Analysis Network, Kita-machi 4-13-14, Kokubunji-city, Tokyo, Japan through the OECD NEA Data Bank, Issy-les-Moulineaux, France.

Fortran 95 (C000771PCX8600).

FSKY4C computes skyshine dose of gamma ray for a system consisting of point sources, multilayer shields simulating a reactor containment vessel and an infinite homogeneous medium of air. The output includes both the exposure and effective gamma ray dose at detection points arranged on the horizontal plane in the medium of air. FSKY4C can be applied to shields with 3 types of geometry including upper spherical shell (spherical dome), upper slab, and side cylinder or a combination of up to 3 layers. It is assumed that all shields are symmetric against rotation with respect to the Z axis and perpendicular to the plane, including points of detection for skyshine dose, and that all sources are located along the Z axis.

FSKY4C version 1.0 corrects problems in:

- calculation of radiation penetration through multilayer shields for the energy spectrum of a source specified by users,

- calculation of radiation penetration through multilayer shields for an angular limit specified by users,

- calculation of edge correction factor.

*Calculation of energy spectrum of gamma ray flux
penetrated with respect to shields:*

The energy spectrum of gamma ray flux penetrated through a single-layer shield with a path length X is an approximation computed by multiplying the flux of uncollided gamma ray penetration through the shield with data for gamma Buildup Flux Energy Spectrum (BFE), defined as the gamma flux energy spectrum at distance X from a point isotropic source in the infinite homogeneous medium with the same composition as the shield divided by the flux of uncollided gamma ray distance X in the same medium. The energy spectrum of gamma ray flux penetrated through a multilayer shield is computed with an approximation that angular distribution of flux penetrated through the first layer and incident on the second layer is concentrated into the direction of uncollided gamma ray. The data base, which includes BFE with 18 energy groups as the function of the distance and the source energy for 7 materials, is generated by the invariant embedding method and is used in FSKY4C.

The energy spectrum of gamma ray flux penetrated through the outer-most shield layer is corrected with the edge correction factor, defined as the flux on the outer surface of a semi-infinite medium located at distance X from the source divided by the flux at the same distance in the infinite medium. The data base for the edge correction factor is generated by the invariant embedding method and is used in FSKY4C.

*Transport calculation of gamma ray in the infinite
homogeneous medium of air: *

The gamma ray skyshine dose is computed in FSKY4C by solving the transport equation for gamma ray in the infinite homogeneous medium of air with the point source emitting radiation with the same energy-angle distribution as the flux penetrated through the shields, according to the Buildup Factor & Line Beam Response Function method (BF-LBRF). The method combines 1) calculation of skyshine dose due to a point isotropic source by using the buildup factor of gamma ray for air, and 2) calculation of skyshine dose due to a conical beam from the source by using the Line Beam Response Function. The data base for the buildup factor for air as the function of the distance from the source and the source energy is generated by the invariant embedding method. The data base for the anisotropy coefficient, defined as the skyshine dose due to a conical beam in a direction with energy E divided by the skyshine dose due to an isotropic source with the same energy E, is generated as the function of direction and energy of the source radiation, height of the source from the horizontal plane, and the distance from the source based on the Line Beam Response Function calculated by using the Monte Carlo code EGS4.

The geometry of shields simulating a reactor containment vessel is restricted to three types including upper spherical shell (spherical dome), upper slab, and side cylinder or a combination of up to three layers. The shield material is restricted at present to seven materials, including water, iron, four types of concrete, and lead. The composition of air is restricted at present to that given by the report NBS29.

About one second for a typical case (1 point source with 18 energy groups spectrum, 2 layers of shield, 28 points of detectors covering from 100 m to 10 km) on a PC.

An X86 processor.

Windows OS machines.

**a.) Included documentation:**

FSKY４C ver.1.0: Gamma Ray Skyshine Analysis Code User’s Guide, December 2009.

Revisions to FSKY4C version 1.0

**b.) Background information:**

Yasuhiro Sasaki, Yoshitaka Yoshida, Akinao Shimizu, et al.,
“Development of Quick Calculation Method for Gamma-Ray Skyshine Dose,” *INSS
Journal*, 14, pp 384-396.

A. Shimizu, T. Onda, and Y. Sakamoto, “Calculation of
gamma-ray buildup factors up to depths of 100 mfp by the method of invariant
embedding, (III) - Generation of an improved data set,” *J. Nucl. Sci.
Technol.* 41 (4), 413-424 (2004).

H. Hirayama, *et al.,* “Data Library of the Line-and Conical-Beam
Response Functions and Four-Parameter Empirical Formula in Approximating the
Response Functions for Gamma-ray Skyshine Analyses,” KEK Report. 2008-2 (2008).

Included in the package is a CD in a Windows self-extracting file which includes an installation procedure, executables, scripts, data files and documentation.

November 2011.

**KEYWORDS**: SKYSHINE, GAMMA-RAY