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Analytical Formulae to Calculate the Total Efficiency of an Arbitrarily Positioned Point Source by an Elliptical Cylindrical Detector

Year 2015, Volume: 2 Issue: 2, 11 - 22, 20.06.2015

M. Abbas S. Hammoud T. Ibrahim M. Sakr

https://doi.org/10.1501/nuclear_0000000008

Abstract

In this paper, a direct analytical method is presented for calculating the absolute efficiency of an elliptical cylindrical detector in the case of an arbitrarily positioned (above the major axis a) point source. The absolute efficiency is required to determine the activity of an unknown radioactive source, taking into account the
attenuation of the gamma-ray photons. The validity of the derived analytical expressions was successfully confirmed by the comparison with some published data.

Keywords

Analytical formula Solid angle Elliptical cylindrical detector Absolute efficiency

References

  • Abbas, M., “A direct mathematical method to calculate the efficiencies of a parallelepiped detector for an arbitrarily positioned point source”, J. Radiat. Phys. Chem.60, 3 (2001a).
  • Abbas, M., “HPGe detector photopeak efficiency calculation including self-absorption and coincidence corrections for Marinilli beaker sources using compact analytical expressions”, J. Radiat. Phys. Chem. 54, 761 (2001b).
  • Abbas, M., Selim, Y., “Calculation of relative full-energy peak efficiencies of well-type detectors”, Nucl. Instrum. Methods Phys. Res. A480, 651 (2002).
  • Abbas, M., Selim, Y., Nafee, S., “A simple mathematical method to determine the efficiencies of log-conical detectors”, J. Radiat. Phys. Chem. 75 (7), 729-736 (2006).
  • Jiang, S., Liang, J., Chou, J., Lin, U., Yeh, W., "A hybrid method for calculating absolute peak efficiency of germanium detectors", Nucl. Instrum. Methods Phys. Res. A413, 281-292 (1998).
  • Lippert, J., “Detector-efficiency calculation based on point-source measurement”, Int. J. Appl. Radiat. Isot. 34 (8), 1097-1103 (1983).
  • Moens, L., Hoste, J., “Calculation of the peak efficiency of high-purity germanium detectors”, Int. J. Appl. Radiat. Isot. 34(8), 1085–105 (1983).
  • Nakamura, T., Suzuki, T., “Monte Carlo calculation of peak efficiencies of Ge(Li) and pure Ge detectors to voluminal sources and comparison with environmental radioactivity measurement”, Nucl. Instrum. Methods Phys. Res. 205 (1), 211-218 (1983).
  • Rieppo, R., “Calculated absolute full-energy peak efficiencies for true coaxial Ge(Li) detector in the photon energy region 0.1-0.3 MeV with different source-to-detector geometries”, Int. J. Appl. Radiat. Isot. 36 (11): 861-865 (1985).
  • Selim, Y, Abbas, M., “Source-detector geometrical efficiency”, J. Radiat. Phys. Chem. 44 (1), 1-4 (1994).
  • Selim, Y., Abbas, M., “Analytical calculations of gamma scintillators efficiencies. II: total efficiency for wide co-axial disk sources”, J. Radiat. Phys. Chem. 53, 15–19 (2000).
  • Selim, Y., Abbas, M., Fawzy, M., “Analytical calculation of the efficiencies of gamma scintillators. Part I: Total efficiency for coaxial disk sources”, J. Radiat. Phys. Chem. 53 (6), 589- 592 (1998).
  • Wang, T., Mar, W., Ying, T., Liao, C., Tseng, C., “HPGe detector absolute-peak-efficiency calibration by using the ESOLAN program”, Int. J. Appl. Radiat. Isot. 46 (9), 933–944 (1995).
  • Wang, T., Mar, W., Ying, T., Tseng, C., Liao, C., Wang, M., “HPGe detector efficiency calibration for extended cylinder and marinellibeaker sources using the ESOLAN program”, Int. J. Appl. Radiat. Isot. 48(1), 83–95 (1997).
  • Yalcin, S, Gurler, O, Kaynak, G, Gundogdu, O., “Calculation of total counting efficiency of a NaI(Tl) detector by hybrid Monte-Carlo method for point and disk sources”, Int. J. Appl. Radiat. Isot. 65, 1179–1186 (2007).

Year 2015, Volume: 2 Issue: 2, 11 - 22, 20.06.2015

M. Abbas S. Hammoud T. Ibrahim M. Sakr

https://doi.org/10.1501/nuclear_0000000008

Abstract

References

  • Abbas, M., “A direct mathematical method to calculate the efficiencies of a parallelepiped detector for an arbitrarily positioned point source”, J. Radiat. Phys. Chem.60, 3 (2001a).
  • Abbas, M., “HPGe detector photopeak efficiency calculation including self-absorption and coincidence corrections for Marinilli beaker sources using compact analytical expressions”, J. Radiat. Phys. Chem. 54, 761 (2001b).
  • Abbas, M., Selim, Y., “Calculation of relative full-energy peak efficiencies of well-type detectors”, Nucl. Instrum. Methods Phys. Res. A480, 651 (2002).
  • Abbas, M., Selim, Y., Nafee, S., “A simple mathematical method to determine the efficiencies of log-conical detectors”, J. Radiat. Phys. Chem. 75 (7), 729-736 (2006).
  • Jiang, S., Liang, J., Chou, J., Lin, U., Yeh, W., "A hybrid method for calculating absolute peak efficiency of germanium detectors", Nucl. Instrum. Methods Phys. Res. A413, 281-292 (1998).
  • Lippert, J., “Detector-efficiency calculation based on point-source measurement”, Int. J. Appl. Radiat. Isot. 34 (8), 1097-1103 (1983).
  • Moens, L., Hoste, J., “Calculation of the peak efficiency of high-purity germanium detectors”, Int. J. Appl. Radiat. Isot. 34(8), 1085–105 (1983).
  • Nakamura, T., Suzuki, T., “Monte Carlo calculation of peak efficiencies of Ge(Li) and pure Ge detectors to voluminal sources and comparison with environmental radioactivity measurement”, Nucl. Instrum. Methods Phys. Res. 205 (1), 211-218 (1983).
  • Rieppo, R., “Calculated absolute full-energy peak efficiencies for true coaxial Ge(Li) detector in the photon energy region 0.1-0.3 MeV with different source-to-detector geometries”, Int. J. Appl. Radiat. Isot. 36 (11): 861-865 (1985).
  • Selim, Y, Abbas, M., “Source-detector geometrical efficiency”, J. Radiat. Phys. Chem. 44 (1), 1-4 (1994).
  • Selim, Y., Abbas, M., “Analytical calculations of gamma scintillators efficiencies. II: total efficiency for wide co-axial disk sources”, J. Radiat. Phys. Chem. 53, 15–19 (2000).
  • Selim, Y., Abbas, M., Fawzy, M., “Analytical calculation of the efficiencies of gamma scintillators. Part I: Total efficiency for coaxial disk sources”, J. Radiat. Phys. Chem. 53 (6), 589- 592 (1998).
  • Wang, T., Mar, W., Ying, T., Liao, C., Tseng, C., “HPGe detector absolute-peak-efficiency calibration by using the ESOLAN program”, Int. J. Appl. Radiat. Isot. 46 (9), 933–944 (1995).
  • Wang, T., Mar, W., Ying, T., Tseng, C., Liao, C., Wang, M., “HPGe detector efficiency calibration for extended cylinder and marinellibeaker sources using the ESOLAN program”, Int. J. Appl. Radiat. Isot. 48(1), 83–95 (1997).
  • Yalcin, S, Gurler, O, Kaynak, G, Gundogdu, O., “Calculation of total counting efficiency of a NaI(Tl) detector by hybrid Monte-Carlo method for point and disk sources”, Int. J. Appl. Radiat. Isot. 65, 1179–1186 (2007).
There are 15 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

M. Abbas

S. Hammoud

T. Ibrahim

M. Sakr

Publication Date June 20, 2015
Submission Date September 12, 2014
Published in Issue Year 2015Volume: 2 Issue: 2

Cite

APA Abbas, M., Hammoud, S., Ibrahim, T., Sakr, M. (2015). Analytical Formulae to Calculate the Total Efficiency of an Arbitrarily Positioned Point Source by an Elliptical Cylindrical Detector. Journal of Nuclear Sciences, 2(2), 11-22. https://doi.org/10.1501/nuclear_0000000008
AMA Abbas M, Hammoud S, Ibrahim T, Sakr M. Analytical Formulae to Calculate the Total Efficiency of an Arbitrarily Positioned Point Source by an Elliptical Cylindrical Detector. Journal of Nuclear Sciences. June 2015;2(2):11-22. doi:10.1501/nuclear_0000000008
Chicago Abbas, M., S. Hammoud, T. Ibrahim, and M. Sakr. “Analytical Formulae to Calculate the Total Efficiency of an Arbitrarily Positioned Point Source by an Elliptical Cylindrical Detector”. Journal of Nuclear Sciences 2, no. 2 (June 2015): 11-22. https://doi.org/10.1501/nuclear_0000000008.
EndNote Abbas M, Hammoud S, Ibrahim T, Sakr M (June 1, 2015) Analytical Formulae to Calculate the Total Efficiency of an Arbitrarily Positioned Point Source by an Elliptical Cylindrical Detector. Journal of Nuclear Sciences 2 2 11–22.
IEEE M. Abbas, S. Hammoud, T. Ibrahim, and M. Sakr, “Analytical Formulae to Calculate the Total Efficiency of an Arbitrarily Positioned Point Source by an Elliptical Cylindrical Detector”, Journal of Nuclear Sciences, vol. 2, no. 2, pp. 11–22, 2015, doi: 10.1501/nuclear_0000000008.
ISNAD Abbas, M. et al. “Analytical Formulae to Calculate the Total Efficiency of an Arbitrarily Positioned Point Source by an Elliptical Cylindrical Detector”. Journal of Nuclear Sciences 2/2 (June 2015), 11-22. https://doi.org/10.1501/nuclear_0000000008.
JAMA Abbas M, Hammoud S, Ibrahim T, Sakr M. Analytical Formulae to Calculate the Total Efficiency of an Arbitrarily Positioned Point Source by an Elliptical Cylindrical Detector. Journal of Nuclear Sciences. 2015;2:11–22.
MLA Abbas, M. et al. “Analytical Formulae to Calculate the Total Efficiency of an Arbitrarily Positioned Point Source by an Elliptical Cylindrical Detector”. Journal of Nuclear Sciences, vol. 2, no. 2, 2015, pp. 11-22, doi:10.1501/nuclear_0000000008.
Vancouver Abbas M, Hammoud S, Ibrahim T, Sakr M. Analytical Formulae to Calculate the Total Efficiency of an Arbitrarily Positioned Point Source by an Elliptical Cylindrical Detector. Journal of Nuclear Sciences. 2015;2(2):11-22.