Analytical calculation of the solid angle defined by a cylindrical detector and a point cosine source with parallel axes

TL;DR

This paper derives analytical formulas for calculating the solid angle subtended by a cylindrical detector at a cosine-distributed point source aligned with the cylinder axis, including related disc source and detector configurations.

Contribution

It provides new analytical expressions for the solid angle in specific geometries involving cylindrical detectors and cosine sources, enhancing precision in radiation detection modeling.

Findings

Derived formulas for the solid angle of a cylinder at a cosine source

Provided expressions for disc source and detector configurations

Enhanced analytical tools for radiation detection geometry

Abstract

We derive analytical expressions for the solid angle subtended by a right finite circular cylinder at a point source with cosine angular distribution in the case where the source direction is parallel to the cylinder axis. As a subsidiary result, an expression for the solid angle subtended by a disc detector at a spread disc source is also provided, in the case where the two discs have a common symmetry axis which is also coincident with the source direction.