On the Equivalent Sources and Geometric Factor Calculation for a Circular Detection Case


  • Tony Viloria A. Enviromental Engineering Career, Salesian Polytechnical University, Cuenca, Ecuador
  • Luis Montiel Physics Department, University of Zulia, Maracaibo, Venezuela.
  • Lasjlo Sajo-Bohus Nuclear Physics Laboratory, University Simón Bolívar, Baruta, Venezuela.
  • Daniel Palacios Nuclear Physics Laboratory, University Simón Bolívar, Baruta, Venezuela.




geometric factor, Monte Carlo method, equivalent source


In all absolute measurements of the intensity of the radioactive materials and calibration of the detectors, it is essential the knowledge of the geometric efficiency. This work describes how to obtain the sources with different geometries and equal geometric efficiency (equivalent sources for geometric factor), corresponding to a linear, circumferential and circular homogeneous sources parallel to a circular detector. It is estimated the geometric factor of them by the Monte Carlo method. The results are compared with the published in the literature, thus confirming the validity of this method.


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Abbas M.I., Analytical calculations of the solid anges subtended by a well-type detector at point and extended circular sources, Applied Radiation and Isotopes, 64, 1048-1056 (2006). http://dx.doi.org/10.1016/j.apradiso.2006.04.010

Conway J., Generalizations of Ruby’s formula for the geometric efficiency of a parallel-disk source and detector system, Nucl Instrum Methods A, 562, 146-153 (2006). http://dx.doi.org/10.1016/j.nima.2006.02.197

Conway J., Geometric efficiency for a circular detector and a ring source of arbitrary orientation and position, Nucl Instrum Methods A, 640, 99-109 (2011). http://dx.doi.org/10.1016/j.nima.2011.03.014

Galiano E. and Pagnutti C., An analytical solution for the solid angle subtended by a circular detector for a symetrically positioned linear source, Appl Radiat Isotopes, 64, 603-607 (2006). http://dx.doi.org/10.1016/j.apradiso.2005.12.006

Pommé S., Johansson L., Sibbens G. and Denecker B., An algorithm for the solid angle calculation applied in alpha-particle counting, Nucl Instrum Methods A, 505, 286-289 (2003). http://dx.doi.org/10.1016/S0168-9002(03)01070-2

Pommé S., A complete series expansion of Ruby’s solid-angle formula, NucI Instrum Methods A, 531, 616-620 (2004). http://dx.doi.org/10.1016/j.nima.2004.05.088

Pommé S., The solid angle subtended by a circular detector for a linear source, Appl Radiat Isotopes, 65, 724-727 (2007). http://dx.doi.org/10.1016/j.apradiso.2006.08.003

Pommé S., Jan Paepen. A series expansion of Conway’s generalized solid-angle formulas, Nucl Instrum Methods A, 579, 272-274 (2007). http://dx.doi.org/10.1016/j.nima.2007.04.054

. Prata M.J., Solid angle subtended by a cylindrical detector at a point source in terms of elliptic integrals, Radiat Phys Chem, 67, 599-603 (2003). http://dx.doi.org/10.1016/S0969-806X(03)00144-0

Rizk R.A., Hathout A.M., and Hussein A.Z., On solid angle calculation NucI Instrum Methods A, Vol 245, 162-166, (1986).

Ruby L., Rechen J., A simple approach to the geometrical efficiency of a paralleldisk source and detector system, Nuclear Instruments and Methods, 58, 345-346 (1968). http://dx.doi.org/10.1016/0029-554X(68)90491-6

Sosa S. Integración numérica por el método de Monte Carlo (Para obtener el título de Licenciada en Matemáticas). Facultad de ciencias exactas y naturales. Universidad de Sonora. Hermosillo (México). 83 pp. 1997. http://lic.mat.uson.mx/tesis/99TesisSonia.PDF

Vega-Carrillo H., “Geometrical efficiency for a parallel disk source and detector”. Nuclear Instruents and Methods in Physics Reaserch A 371 (1996).

Viloria T., Soldovieri T., Bong. and Palacios D., “Sobre el ángulo sólido y las fuentes equivalentes”, Ciencia, Vol. 17, No. 4, 288-298, (2009).

Wielopolski L., “The Monte Carlo calculation of the average solid angle subtended by a right circular cylinder from distributed sources”. NucI Instrum Methods A, Vol. 143, 577-581, (1977). http://dx.doi.org/10.1016/0029-554X(77)90249-X

Zhang J., et al. “Development of software package for solid-angle calculations using the Monte Carlo method”, Nuclear Instruments and Methods in Physics Research A, 736, 40-45, (2014). http://dx.doi.org/10.1016/j.nima.2013.10.048




How to Cite

Viloria A., T. .; Montiel, L. .; Sajo-Bohus, L. .; Palacios, D. . On the Equivalent Sources and Geometric Factor Calculation for a Circular Detection Case. J. Nucl. Phy. Mat. Sci. Rad. A. 2016, 4, 31-48.