On some behavioral anomalies in an analytical expression for the solid angle subtended by a circular detector from a symmetrically positioned linear source

We explore the causes of an interesting behavioral anomaly in an analytical result which has been previously derived for the solid angle subtended by a circular detector for a line source in a parallel plane—whose midpoint is coaxial with the detectorʹs center. The anomalous behavior is verified by comparing it to the results produced by a special purpose Monte Carlo code. In addition, the relevant cases of a very large detector, a very long source, a very short source, and a very small detector, are investigated using standard analytical techniques in the theory of limits. We demonstrate that in these limiting cases, the analytical expression correlates well with the Monte Carlo code. These results are presented in analytical, and graphical forms.