Providing solid angle formalism for skyshine calculations

Area of Science:

• Radiation physics
• Dosimetry
• Computational methods

Background:

• Skyshine calculations are crucial for radiation safety assessments.
• Accurate determination of dose-equivalent rates relies on precise geometric modeling.
• Existing guidance on solid angle variables in skyshine calculations requires technical correction.

Purpose of the Study:

• To detail, derive, and correct the technical application of the solid angle variable in skyshine calculations.
• To recommend the corrected solid angle variable for use in established radiation protection reports.
• To compare the accuracy of analytical pyramidal and conical solutions for dose-equivalent rate calculations.

Main Methods:

• Derivation and technical correction of the solid angle variable for skyshine.
• Analytical modeling using pyramidal and conical solutions.
• Comparison of calculated dose-equivalent rates for various beam sizes and shapes.

Main Results:

• The analytical pyramidal solution is recommended for square beams, while the analytical conical solution is recommended for circular beams.
• The analytical pyramidal solution yields results 1.27 times greater than the misapplied analytical conical solution for identical width beams.
• The deviation between solutions is within ±1.0% for field sizes up to 40 × 40 cm².

Conclusions:

• The corrected solid angle variable enhances the accuracy of skyshine calculations.
• The analytical pyramidal solution is superior for square beams, and the analytical conical solution for circular beams.
• Adoption of these methods will improve dose-equivalent rate assessments in radiation protection.