Estimation of global level density parameters using an unscented transform Kalman filter technique

This study focuses on estimating the level density parameters for niobium (Nb) using the unscented transform Kalman filter technique. Niobium is widely utilized in accelerator components, particularly in superconducting radiofrequency cavities. To better understand the design of accelerator components and experimental setups, accurate information on both theoretical predictions and experimental results, including the uncertainties of nuclear reactions involving niobium, is essential. In this study, we have used the unscented transform Kalman filter technique to estimate level density parameters and their correlation matrix for ${}^{93}\mathrm{Nb}(\alpha ,2n){}^{95}\mathrm{Tc}$ and ${}^{93}\mathrm{Nb}(\alpha ,n){}^{96}\mathrm{Tc}$ reactions through the talys nuclear code. We have used the measured experimental nuclear reaction cross sections from this study to estimate the level density parameters for the above nuclear reactions. A comprehensive analysis of uncertainty propagation has been also conducted, encompassing both theoretical predictions and experimentally measured nuclear reaction cross sections. We have calculated uncertainties in both the theoretical calculations using the Monte Carlo method and experimentally measured reaction cross sections through covariance analysis for these nuclear reactions. We have also calculated the correlation matrix of the experimentally measured cross sections for the ${}^{93}\mathrm{Nb}(\alpha ,n){}^{95}\mathrm{Tc}$ and ${}^{93}\mathrm{Nb}(\alpha ,n){}^{96}\mathrm{Tc}$ nuclear reactions.

Figure 1

The $\gamma$-ray spectrum of the irradiated target and monitor foil.

Figure 2

The parameter correlation matrix, where parameters are organized based on their serial numbers as defined in Table 2.

Figure 3

Comparison of the experimentally measured cross section for ${}^{93}\mathrm{Nb}(\alpha ,2n){}^{95}\mathrm{Tc}$ with the existing experimental data from EXFOR as well as confidence interval of theoretical prediction.

Figure 4

Comparison of the experimentally measured cross section for ${}^{93}\mathrm{Nb}(\alpha ,n){}^{96}\mathrm{Tc}$ with the existing experimental data from EXFOR as well as confidence interval of theoretical prediction.