Geometrical efficiency for a parallel disk source and detector

In a recent paper in this journal, Ruby presented a formal derivation of the solid angle between a parallel disk source and detector [L. Ruby, Nucl. Instr. and Meth. A 337 (1994) 531]. The resulting expression does not have a closed solution and an algebraic approximation is presented. Here an expression that gives better results is presented. Several cases of geometrical efficiency for a parallel disk source and detector system are calculated using the expressions given by Ruby, using Monte Carlo methods and the expression here presented. This geometrical factor is widely used during absolute methods to calibrate detectors or to determine, using absolute methods, the activity of a radioactive source.