Research on hybrid β-energy spectral analysis algorithm based on fourier series function

摘要: With the rapid development of the nuclear power industry on a global scale, the discharge of radioactive effluents from nuclear power plants and their impact on the environment have become important issues in radioactive waste management, radiation protection, and environmental impact assessments. β-detection of nuclides requires tedious processes, such as waiting for the radioactive balance of the sample and pretreatment separation, and there is an urgent need for a method specifically designed for mixing β rapid energy spectrum measurement method for nuclide samples. The analysis of hybrid β-energy spectrum is proposed in this study as a new algorithm, which takes advantage of the spectral analysis of β-logarithmic energy spectrum and fitting ability of Fourier series. The logarithmic energy spectrum is obtained by logarithmic conversion of the hybrid linear energy spectrum. The Fourier fitting interpolation method is used to fit the logarithmic energy spectrum numerically. Next, the interpolation points for the ‘effective high-energy window’ and ‘effective low-energy window’ corresponding to the highest E_m nuclide in the hybrid logarithmic fitted energy spectrum are set, and spline interpolation is performed three times to obtain the logarithmic fitted energy spectrum of the highest E_m nuclide. Finally, the logarithmic-fitted spectrum of the highest E_m nuclide is subtracted from the hybrid logarithmic-fitted spectrum to obtain a logarithmic-fitted spectrum comprised of the remaining lower E_m nuclides. The aforementioned process is iterated in a loop to resolve the logarithmic spectra of each nuclide in the original hybrid logarithmic spectra. Then, the radioactivity of E_m nuclides to be measured is calculated. In the experimental tests, ¹⁴C, ⁹⁰Sr, and ⁹⁰Y spectra, which are obtained using the Fourier fitting interpolation method are compared with the original simulated ¹⁴C, ⁹⁰Sr, and ⁹⁰Y spectra of GEANT4. The measured liquid scintillator data of ⁹⁰Sr/⁹⁰Y sample source and simulated data from GEANT4 are then analyzed. Analysis of the experimental results indicates that the Fourier fitting interpolation method accurately solves ¹⁴C, ⁹⁰Sr, and ⁹⁰Y energy spectra, which is in good agreement with the original GEANT4 simulation. The error in ⁹⁰Y activity, calculated using the actual detection efficiency, is less than 10% and less than 5% when using the simulated full-spectrum detection efficiency, satisfying the experimental expectations.