Mahmoud I. Abbas

HPGe detector photopeak efficiency calculation including self-absorption and coincidence corrections for Marinelli beaker sources using compact analytical expressions

Direct mathematical methods to calculate total and full-energy peak (photopeak) efficiencies, coincidence correction factors and the source self-absorption of a closed end coaxial HPGe detector for Marinelli beaker sources have been derived. The source self-absorption is determined by calculating the photon path length in the source volume. The attenuation of photons by the Marinelli beaker and the detector cap materials is also calculated. In the experiments gamma aqueous sources containing several radionuclides covering the energy range from 60 to 1836 keV were used. By comparison, the theoretical and experimental full-energy peak efficiency values are in good agreement.

ANALYTICAL FORMULAE FOR WELL-TYPE NAI(TL) AND HPGE DETECTORS EFFICIENCY COMPUTATION

A straightforward analytical formulae for the computation of total and full-energy peak efficiencies of NaI (Tl) and HPGe well-type detectors are deduced. In addition, the attenuation of photons by the source container and the detector end cap materials is presented in a direct mathematical expression. Results are compared with previous treatments.

Analytical calculation of the efficiencies of gamma scintillators. Part I : Total efficiency for coaxial disk sources

Total efficiencies of clad right cylindrical NaI(Tl) scintillation detectors exposed to photons emitted by circular disk sources have been calculated by using rigid mathematical expressions. Results are tabulated for various gamma energies.

Analytical calculations of gamma scintillators efficiencies — II. Total efficiency for wide coaxial circular disk sources

Abstract A statistical integral formulation of the total efficiency for the general wide coaxial circular disk source–cylindrical NaI(Tl) detector arrangement (source radius S>detector radius R) is presented. Simple programming is possible and short computer time is needed.

A direct mathematical method to calculate the efficiencies of a parallelepiped detector for an arbitrarily positioned point source

Abstract A direct mathematical method is applied to calculate total and geometrical efficiencies of a parallelepiped ( a × b × c ) detector for an arbitrarily positioned isotropic radiating point source.

Calculation of relative full-energy peak efficiencies of well-type detectors

A mathematical expression to calculate the full-energy peak efficiency of HPGe well-type detectors has been derived in an integral form. The attenuation of photons by the source itself (self-absorption), the source container and the detector end cap materials is also included. The calculated values of the efficiency are found to be in good agreement with the published experimental data.

Source-detector geometrical efficiency

Abstract By the use of simple analytical spherical-trigonometry a mathematical expression of a solid angle subtended by a point to a plane triangle is deduced. Generalizing, solid angles subtended by a non-axial point source to a circular disk detector and a circular disk source to a circular disk detector are deduced into rigid mathematical expressions very easily computed, for the first time. Results were compared with previous tabulations. By this method, with some mathematical manipulations, solid angles could be deduced for detectors of different geometrical shapes, e.g. rectangular, elliptical, spherical and cylindrical.

HPGE DETECTOR ABSOLUTE FULL-ENERGY PEAK EFFICIENCY CALIBRATION INCLUDING COINCIDENCE CORRECTION FOR CIRCULAR DISC SOURCES

A direct mathematical approach is presented to calculate the absolute full-energy peak (photopeak) efficiency and coincidence correction of hyper pure germanium (HPGe) detectors for extended circular disc sources. The calculation of the full-energy peak efficiency is based on elliptic integration and its validity was checked by comparison with experimental measurements. Extensive experimental readings have been carried out; gamma sources containing several radionuclides covering the energy range from 60 to 1836 keV were used. By comparison, the theoretical and experimental full-energy peak efficiency values are in good agreement; the overall percentage error is less than 3%.

Direct calculation of the total efficiency of cylindrical scintillation detectors for extended circular sources

Abstract By the use of spherical coordinates, direct expressions for the total efficiency of a cylindrical NaI(Tl) detector arising from a non-axial point (ϱ > R) and coaxial-circular disk (S > R) of isotropic radiating sources, are deduced. Results are compared with previous treatments.

A theoretical approach to calibrate radiation portal monitor (RPM) systems

Radiation portal monitor (RPM) systems are widely used at international border crossings, where they are applied to the task of detecting nuclear devices, special nuclear material, and radiation dispersal device materials that could appear at borders. The requirements and constraints on RPM systems deployed at high-volume border crossings are significantly different from those at weapons facilities or steel recycling plants, the former being required to rapidly detect localized sources of radiation with a very high detection probability and low false-alarm rate, while screening all of the traffic without impeding the flow of commerce [Chambers, W.H., Atwater, H.F., Fehlau, P.E., Hastings, R.D., Henry, C.N., Kunz, W.E., Sampson, T.E., Whittlesey, T.H., Worth, G.M., 1974. Portal Monitor for Diversion Safeguards. LA-5681, Los Alamos Scientific Laboratory, Los Alamos, NM]. In the present work, compact analytical formulae are derived and used to calibrate two RPM systems with isotropic radiating sources: (i) polyvinyltoluene (PVT) or plastic and (ii) thallium-doped crystalline sodium iodide, NaI(Tl), gamma-ray detector materials. The calculated efficiencies are compared to measured values reported in the literatures, showing very good agreement.