title: Minimizing the 1/r(2) perturbation for ideal fluence detectors in small source γ-irradiation fields.
abstract: A technique for analyzing the effect of the geometrical shape of a source or a detector, using a quadrupole expansion, is described herein. It is shown that this method may be exploited to predict, optimize the geometry of a source, or a measurement device, and nearly eliminate, the departure from the 1/r(2) fall-off characteristic due to irradiation from small sources. We have investigated several simple shapes that have a vanishing Q2 quadrupole moment: a right circular cylinder with a diameter to depth ratio of √[2], a cone with a radius to height ratio of unity, and an oblate ellipsoid with a diameter to depth ratio of √[3/2]. These ideal shapes produce optimally small departures in a 1/r(2) field, nearly mimicking a point-like detector. We have also found a rotationally symmetric shape, intermediate to the other three, that has additionally, a vanishing Q4, the hexadecapole moment. This geometry further improves the 1/r(2)-perturbation characteristics and has an additional free parameter that may be adjusted to model the ideal cylinder, cone or oblate spheroid.
authors: Department of Nuclear Engineering, Radiological Sciences The University of Michigan, 2355 Bonisteel Boulevard Ann Arbor, MI 48109, USA.
authors: Alex F
authors: AF
authors: Bielajew
mesh_terms: D005720:Gamma Rays; D009010:Monte Carlo Method; D011874:Radiometry / Q000295:instrumentation*; D012542:Scattering, Radiation