DEPARTMENT OF NUCLEAR PHYSICS - NUCLEAR ENGINEERING - MEDICAL PHYSICS

A dual-energy gamma-ray transmission method using ¹³⁷Cs and ²⁴¹Am sources for determining effective atomic number and mass attenuation coefficient of lightweight materials

Le Thi Ngoc Trang, Huynh Dinh Chuong, Vo Hoang Nguyen, Tran Thien Thanh

Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 1086 (2026) 171390

Abstract

This paper presents a dual-energy gamma-ray transmission method for determining the effective atomic number (Z_eff) and mass attenuation coefficient (MAC) of lightweight materials. The experimental setup consists of sealed ¹³⁷Cs and ²⁴¹Am sources and a NaI(Tl) detector arranged in a narrow-beam transmission geometry to measure gamma rays transmitted through the sample. A corresponding MCNP6 model was developed to closely reproduce the experimental configuration. Using this model, pulse-height spectra were simulated for a set of materials with atomic numbers from 1 to 20, thicknesses between 1 and 4 cm, and densities from 0.6 to 3.0 g cm⁻³. The Z_eff of a material was determined by exploiting the ratio of logarithmic attenuations measured at 59.5 keV and 661.7 keV, using a calibration curve established from the simulation data, without requiring any prior knowledge of the sample thickness, density, and elemental composition. In addition, an analytical model was constructed to describe the dependence of the MAC on both atomic number and photon energy, for atomic numbers from 1 to 20 and photon energies in the range 50 keV to 20 MeV. This model enables the MAC of a material to be estimated at various photon energies directly from its previously determined Z_eff. The proposed method was validated for several lightweight materials, including graphite, aluminum, polymers, pine wood, brick, glass, concrete, and stone, using both simulated and experimental data. The results show that the Z_eff values obtained by this method are well correlated with the elemental composition of the materials. For materials that either do not contain hydrogen or contain it only in low concentrations, the MAC values estimated by the proposed method exhibit generally good agreement with reference XCOM data, whereas for materials with a high hydrogen content the discrepancies of up to approximately 16.8% are observed.

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