\section{LBE activity in the STA}
The LBE activity evolution throughout the reactor lifetime and beyond is presented in Fig. \ref{vol_act}. The focus is given to the volatile radionuclides , since the activity associated to them is directly proportional to the dose in case of release.
For this reason it is particularly important to draw the evolution of the target nuclides both during operation and after the reactor shutdown.\\
The extensive list of the analyzed nuclides is available in Sect. \ref{obervables}.
\begin{figure}[h]
\centering
\includegraphics[width=0.95\textwidth]{images/plots/LBE/activity_sta/volatiles.png}
\caption{Time evolution of the activity of volatile products present in the spallation target assembly during reactor operation and after shutdown.}\label{vol_act}
\end{figure}
The plot shows the outputs of the homogeneous approach.
The activity in the LBE is dominated by $^{3}$H, a volatile nuclide largely generated by spallation reactions. $^{3}$H builds up during operation because of its relatively long  half life of about 12 years.
During operation the main contributors to the activity are $^{195}$Hg, $^{197}$Hg and $^{210}$Po, each of them providing an activity of around $1e15$ Bq. Their concentration (and activity) is approximately constant during operation. The mercurium isotopes are short lived so they completely decay during the maintenance periods and the same amount is produced in each irradiation cycle.\\
As regard $^{210}$Po, it has a half life of about $140 $ days that is comparable to a reactor irradiation cycle, therefore the build-up during the cycle is the net balance between production and depletion, being its decay not negligible. The oscillations in its activity are due to the reactor long maintenance periods (90 days), where the concentration decreases more. The other relevant nuclides have an associated activity that is at least one order of magnitude lower than what the previously mentioned nuclides.