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Abstract
An analytic solution for the fluence rate of primary (non-scattered) gamma rays emerging from a spherical radioactive source is presented. The solution takes self-attenuation into account and is valid at any distance from the source. It is derived using elementary integral calculus and does not require special functions. The key to the relatively simple solution is a shift of the center of the sphere along the z-axis by a distance equal to the radius, so that the surface of the sphere passes through the origin of the coordinate system.
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