\section{LBE inventory in the STA}
The elemental composition of the irradiated LBE is reported in Tab. \ref{tab_elem}. It is normalized on the mass of LBE present in the STA before irradiation. The results refers to the \acrshort{EoL} concentrations after 40 years of irradiation in the reactor. The elemental composition is globally influenced by the initial impurities present in the LBE and locally from the fluxes in each region.\\
The table clearly shows that most of the activation and spallation products are generated in the central region. The elemental content in the whole spallation target assembly calculated with the homogeneous approach differs from the the volume-weighted sum of the concentrations in each region,  as reported in Fig. \ref{inv_discr}. This confirms that discrepancies arise if the depletion is performed averaging the condition in the STA instead of considering separate regions. The same conclusion was drawn from Fig. \ref{discr_3z}, shown in the previous chapter. 
\begin{table}[H]
\begin{center}
\begin{minipage}{0.99\textwidth}
\caption{LBE spallation and activation products concentrations in the STA at the end of life (\acrshort{EoL}) after 40 of operation.}\label{tab_elem}
\begin{tabular}{lrrrrr}
\toprule
{} &   \makecell{Initial\\concentration\\ (mg/kg)} &  \makecell{Bottom\\region\\ (mg/kg)} &  \makecell{Central\\region\\ (mg/kg)} &  \makecell{Top\\region\\ (mg/kg)} &  \makecell{Whole LBE\\in STA\\ (mg/kg)} \\
\textbf{Element} &                               &                       &                        &                    &                          \\
\midrule
\textbf{H      } &                          0.00 &                 13.53 &                2859.43 &              23.58 &                   347.42 \\
\textbf{He     } &                          0.00 &                 21.80 &                1179.17 &              36.83 &                   172.82 \\
\textbf{Kr     } &                          0.00 &                  0.97 &                1072.97 &               1.68 &                   124.40 \\
\textbf{Sr     } &                          0.20 &                  1.17 &                1056.43 &               1.87 &                   125.70 \\
\textbf{Zr     } &                          0.23 &                  1.25 &                1357.23 &               1.97 &                   176.92 \\
\textbf{Mo     } &                          0.12 &                  1.15 &                1554.85 &               1.90 &                   201.03 \\
\textbf{Ru     } &                          0.03 &                  1.05 &                1468.16 &               1.80 &                   190.40 \\
\textbf{Pd     } &                          0.34 &                  1.42 &                1492.65 &               2.17 &                   188.14 \\
\textbf{Cd     } &                          0.23 &                 11.46 &                1133.41 &              15.39 &                   172.63 \\
\textbf{Sn     } &                          1.33 &                  2.18 &                 876.59 &               2.83 &                   117.72 \\
\textbf{Er     } &                          0.02 &                  0.14 &                 778.04 &               0.22 &                    37.45 \\
\textbf{Yb     } &                          0.00 &                  1.15 &                2444.79 &               2.01 &                   182.68 \\
\textbf{Lu     } &                          0.18 &                  0.78 &                 826.41 &               1.12 &                    72.68 \\
\textbf{Hf     } &                          0.00 &                  5.55 &                5995.54 &               9.48 &                   591.98 \\
\textbf{Ta     } &                          0.00 &                  2.79 &                1883.80 &               4.16 &                   182.05 \\
\textbf{W      } &                          0.00 &                 10.99 &                6919.96 &              19.48 &                   810.23 \\
\textbf{Re     } &                          0.00 &                  3.75 &                1206.73 &               4.74 &                   118.66 \\
\textbf{Os     } &                          0.05 &                 68.32 &               19658.87 &             118.84 &                  2499.83 \\
\textbf{Ir     } &                          0.00 &                 21.23 &                2979.66 &              25.40 &                   333.20 \\
\textbf{Pt     } &                          0.14 &                185.25 &               33060.42 &             331.37 &                  4381.94 \\
\textbf{Au     } &                          0.53 &                 61.61 &                5702.84 &              83.39 &                   615.91 \\
\textbf{Hg     } &                          1.73 &                983.64 &               58458.96 &            1700.19 &                  9411.62 \\
\textbf{Tl     } &                          0.00 &                616.04 &               17942.85 &            1056.28 &                  3078.49 \\
\textbf{Pb     } &                     444908.35 &             446378.18 &              384549.00 &          447401.66 &                439867.17 \\
\textbf{Bi     } &                     554910.38 &             551217.54 &              408631.32 &          548610.20 &                531518.27 \\
\textbf{Po     } &                          0.00 &                 14.12 &                 699.31 &              24.03 &                   121.34 \\
\bottomrule
\end{tabular}
\end{minipage}
\end{center}
\end{table}

\begin{figure}[h!]
\centering
\includegraphics[width=0.79\textwidth]{images/plots/LBE/inventory_sta/inv_sta.png}
\caption{Variation of elemental concentrations taking into account or not the separate regions in the STA. The deviations are evaluated at EoI, only the elements with content higher than 10 mg/kg are shown.}\label{inv_discr}
\end{figure}
The deviations range from 5\% for polonium up to over 100\% for Er and Yb. They come from the different spatial discretization of the fluxes and they witness how the actual spectra are relevant to determine the production of certain nuclide species.
