Fourier Fitting Interpolation Method and Asym2Sig Method for spectral data

This method is urgently needed due to the cumbersome processes required for the detection of β-nuclides in nuclear power radioactive effluents, such as radioactivity equilibrium and pretreatment separation of the samples. The analysis of mixed β-energy spectrum is proposed in this paper as a new algorithm, taking advantage of the spectral analysis of β-logarithmic energy spectrum and the fitting ability of Fourier series. The logarithmic energy spectrum is obtained by converting the hybrid linear energy spectrum logarithmically. The Fourier series interpolation method is then used to numerically fit the logarithmic energy spectrum. Next, the interpolation points for the ‘effective high-energy window’ and ‘effective low-energy window’ corresponding to the highest Em nuclide in the hybrid logarithmic fitted energy spectrum are set, and three times spline interpolation is performed to obtain the logarithmic fitted energy spectrum of the highest Em nuclide. Finally, the logarithmic fitted spectrum of the highest Em nuclide is subtracted from the mixed logarithmic fitted spectrum to obtain the logarithmic fitted spectrum composed of the remaining lower Em nuclides. the above process is iterated in a loop to finally resolve the logarithmic spectra of the nuclides in the original mixed logarithmic spectra, and then calculate the radioactivity of the Em nuclides to be measured. energy spectrum of each nuclide in the original mixed logarithmic energy spectrum, and then calculate the activity of the measured Em nuclide. In the experimental tests, the 14C, 90Sr, and 90Y spectra obtained through Fourier series fitting interpolation are compared with the original simulated 14C, 90Sr, and 90Y spectra of GEANT4. The measured liquid scintillation data of the 90Sr/90Y sample source and the simulated data of GEANT4 are then analyzed. The analysis of the experimental results indicates that the Fourier series fitting interpolation method accurately solved the 14C, 90Sr and 90Y energy spectra, which were in good agreement with the original GEANT4 simulation. The error in the 90Y activity calculated using the actual detection efficiency was less than 10%, and less than 5% when using the simulation full-spectrum detection efficiency, meeting the experimental expectations.