The solid angle subtended by a circular detector for a linear source

An exact solution is presented for the solid angle subtended by a circular detector for a linear source. It is based on Conway's equation for a non-coaxial point source, involving an integral of Bessel functions [Conway, J.T., 2006. Generalizations of Ruby's formula for the geometric efficiency of a parallel-disk source and detector system. Nucl. Instrum. Methods A 562, 146-153]. Some numerical examples are calculated and compared with the results obtained with a recently published closed formula (Galiano, E., Pagnutti, C., 2006. An analytical solution for the solid angle subtended by a circular detector for a symmetrically positioned linear source. Appl. Radiat. Isot. 64, 603-607), which is incorrect but can be improved by applying a correction factor