Mathematical method for large samples efficiency

Use of large samples for gamma-ray spectrometry of the natural radioactivity requires the measurement of the detector's voluminous efficiency for such samples. An assessment of the full energy-photopeak efficiency of point sources at different positions to a 3ⁿ × 3ⁿ NaI (Tl) detector is performed using a ¹⁵²Eu source. The choice of the positions of the source varies according to the dimensions of the sample containers used. The latter allows for determining the virtual detector center Zc which is a function of solid angle and incident photon energy. A Gauss-Legendre polynomials for integral calculation allow for the determination of large efficiency. A simulation based on the mathematical model of NaI (Tl) 3ⁿ × 3ⁿ detector and samples geometric parameters is defined to efficiency calculation of the large analyzed sample. The Gauss- Legendre integration method for efficiency calculation show good agreement with Monte Carlo simulation. (author)