\section{Decay heat of an irradiated MYRRHA FA}\label{coreDH}
The time evolution of the decay heat in a MYRRHA FA for the critical and sub-critical reactor operation is displayed in Fig. \ref{fig:dh_ass}.\\
\begin{figure}[h!]
    \centering
    \begin{minipage}{0.94\textwidth}
        \includegraphics[width=\linewidth]{images/plots/FA/ref_dh/cr_ass.png} 
    \end{minipage}
    \hfill
    \begin{minipage}{0.94\textwidth}
        \includegraphics[width=\linewidth]{images/plots/FA/ref_dh/sc_ass.png}
    \end{minipage}
\caption{Fuel assembly decay heat rate as function of FA burnup and decay time. Critical configuration in the top figure, sub-critical in the bottom.}
\label{fig:dh_ass}
\end{figure}

\textit{Envelope decay heat}\\
The main focus both from the safety point of view and the dimensioning of components is to draw an envelope decay heat curve that provides the largest value of decay heat as function of decay time.
The envelope decay heat curve in the sub-critical case is shown in Fig.~~\ref{fig:env_dh_sc}, following the considerations in Sect.~\ref{Activity_FA}.  
\begin{figure}[h!]
\centering
\includegraphics[width=0.95\textwidth]{images/plots/FA/ref_dh/sc_env.png}
\caption{Evolution of envelope decay heat curve in sub-critical configuration.}\label{fig:env_dh_sc}
\end{figure}
For short decay times, FAs with low burnup --- irradiated at high power --- release the largest decay heat because of great amount of short-lived nuclides.
In the mid-term, from 14 days to 2 years, FAs with a intermediate burnup levels provide the largest decay heat.
At longer time scales the FAs with the largest burnup and minor actinide concentrations produce the largest decay heat.\\

\textit{Decay heat associated to particle emission}\\
The decay heat is produced by $\alpha$, $\beta$ and $\gamma$-particles emitted as a part of the decay process of the nuclides that form the radioactive inventory of a FA.
The envelope FA decay heat curve was sub-divided according to the responsible decay process and it is presented in Fig. \ref{fig:dh_rad}.
\begin{figure}[h!]
\centering
\includegraphics[width=0.89\textwidth]{images/plots/FA/ref_dh/sc_rad.png}
\caption{Decay heat envelope curve associated to particle emission. The sub-critical configuration is taken into account.}\label{fig:dh_rad}
\end{figure}
The majority of the fission products $\beta$-decays and generates unstable nuclei that stabilize by the emitting gamma radiation. This decay path is the most relevant in the first several days of decay, with an even apportioning of the decay heat between $\beta$ and $\gamma$ radiation. 
The decay chain $^{137}$Cs/$^{137m}$Ba is an example, where the $\beta^-$ decay of $^{137}$Cs is rapidly followed by the emission of a $\gamma$-ray from $^{137m}$Ba ( $t_{\frac{1}{2}} = $ 2.55 min).
$\alpha$-particles dominate the decay heat at longer decay time because of the major $\alpha$-emitters $^{238}$Pu and $^{241}$Am.\\

\textit{Decay heat contributors}\\
All the nuclides that contribute for at least 5\% to the FA decay heat at any decay time are reported in Fig. \ref{fig:frac_sc_dh}.
\begin{figure}[H]
\centering
\includegraphics[width=0.89\textwidth]{images/plots/FA/ref_dh/sc_frac.png}
\caption{Fractional evolution of major contributors to the envelope decay heat. Actinides are plotted with solid line while fission products with dashed.}\label{fig:frac_sc_dh}
\end{figure}

% short term / 90 days / 420 d / long term
% (remake the discussion)
The dashed and solid lines are used to distinguish fission products and actinides.
In the short term the FA decay heat is dominated by short-lived fission products and by $^{239}$Np ( $t_{\frac{1}{2}} = $ 2.356 d).
The major contributor between 1 and 10 days of decay is $^{140}$La ( $t_{\frac{1}{2}} = $ 1.678 d). $^{132}$I ( $t_{\frac{1}{2}} = $ 2.295 hr), $^{242}$Cm, $^{95}$Zr and its daughter $^{95}$Nb also contribute more that 10\% in this interval of time.\\
$^{242}$Cm and the decay chain $^{95}$Zr/$^{95}$Nb gain importance at intermediate decay times and they are the major contributors to decay heat at 90 days of decay. Also, a non negligible contribution comes from the decay chain $^{106}$Rh/$^{106}$Ru ( $t_{\frac{1}{2}} = $ 2.2 hr, $t_{\frac{1}{2}} = $ 1.017 years) and by $^{135}$I ( $t_{\frac{1}{2}} = $ 6.58 hr). At 90 days decay heat coming from actinides has the same magnitude of that generated by FPs and its relevance increases going further.\\
After 420 days of decay the relative decay heat contribution of $^{242}$Cm reduces from 40 to 25\% even if it still conveys the largest decay heat. At this point the $\alpha$-decay of $^{238}$Pu starts to be relevant.
Together with $^{241}$Am, $^{238}$Pu is the largest contributor up to at least 70 years of decay.
The fission products decay heat is less relevant in the longer decay period. A contribution between 5 and 10\% comes from the decay chains $^{90}$Sr ( $t_{\frac{1}{2}} = $ 28.80 y) /$^{90}$Y ( $t_{\frac{1}{2}} = $ 2.67 d) and in particular $^{137}$Cs/$^{137m}$Ba.
%The latter is the only relevant contributor among FPs at 5 y of cooling. It is produced by $\beta_{-}$ decay of long lived $^{137}$Cs and it decays to his ground state after almost 2 minutes emitting a $\gamma$.
The four main contributors to the MYRRHA FA decay heat at 70 years of decay are $\alpha$-emitters: $^{238,239,240}$Pu and $^{241}$Am.\\
\begin{center}
\fbox{\begin{minipage}{0.98\textwidth}
The time evolution of the decay heat of a MYRRHA FA was parametrically quantified as a function of the FA burnup to produce an envelope decay heat curve. In the short term the FAs with low burnup provide the largest decay heat because of the abundance of the $\beta$,$\gamma$-decay of short-lived fission products. For longer time scales the FAs with high burnup produce the largest decay heat mostly because $\alpha$-emitters $^{238}$Pu and $^{241}$Am. FAs with intermediate burnup values make up the envelope activity curve in the decay range 30-1000 days.
\end{minipage}}
\end{center}
The investigation of nuclear data uncertainty to the total decay heat is one of the objectives of this work.
Fig.~\ref{fig:frac_sc_dh} shows the nuclides that play a role and of which concentrations it is important to quantify the uncertainty.
This exercise is described in detail in \ref{sec_NDuncertainties}.

\begin{comment}
\subsubsection{Decay heat draft}
The study of decay heat produced in the fuel assembly after unloading from the core is of primary importance to determine the technical requirements for the handling and transferring in the Reactor Hall of one spent MOX fuel assembly (FA) between the Fuel Transfer Channel and the Spent Fuel Hot Cell.
The analysis is carried out on the subcritical core design and comparison with the critical one can be added for the sake completeness and to show the conservativity of the results.
The decay heat is determined by the isotopic composition of the FA and the decay constants; ones the assembly is irradiated for a certain amount of time the actinides and fission products decays according to their decay constants and particles emitted ($\alpha$,$\beta$,$\gamma$) generate a certain amount of heat to be evaluated in this section.\\
The spent fuel can be irradiated for a variable number of cycles up to 18 in critical and 13 in sub-critical conditions, reaching a burnup respectively of 55.1 and 47 MWd/t.
The most conservative approach consists of taking into account all the possibilities and studying the assembly that undergoes from one to the maximum number of reshuffling in the core. This allows to obtain a number of decay profiles and the approach followed to be conservative is to merge all the contributes taking the maximum decay heat produced at each decay step providing the envelope decay heat, that of course is made of different contributions at different time step.\\

The profile of each FA considered is presented in Fig. 
The least irradiated FA is the largest contributor in the first period of cooling because of the highest power generation. For intermediate cooling times the assembly with a cumulative burnup of (...) provide the maximum decay heat while at longer time scales the most irradiated assemblies decay heat gains importance, since they reach higher burnup and this implies greater long-lived fission products and actinides buildup.
On the contrary the decay heat conveyed in the short period is mainly due to decay of short lived fission products whose production is enhanced during the first irradiation cycles since the power is greater.\\
The envelope curve is taken as a reference to study the contribution of each nuclide to the total decay heat produced. The fraction by each contributor is reported in relative units in in Fig. Only nuclides participating to more than $5\%$ are shown in the plot.\\
Dashed lines report the profile of fission products: the major contributors to trace for the interval of interest are $^106$Rh, produced in large amount by the decay of $^106$Ru. $144$Pr is the second main contributor, produced by the $\beta_{-}$ decay of $^{144}$Ce, it's relevance for decay heat is 1 order of magnitude lower at 90 d cooling time.   
$^95$Zr and its daughter $^95$Nb contribute is non negligible until 200 days of cooling but can be discarded for longer term evaluations.
$^{89}$Sr, $^{91}$Y, $^{140}$La, $^{141}$Ce are also contributing to the total activity coming from fission products at 90 d of cooling. On the contrary $^{90}$Y, $^{137}$Cs and ${^137m}$Ba gains importance at longer time scale. The latter is the only relevant contributor among FP at 5 y of cooling. It is produced by $\beta_{-}$ decay of long lived $^{137}$Cs and it decays to his ground form after almost 2 minutes emitting a $\gamma$.\\
Actinides contribution to decay heat is negligible for the first period of cooling, when it is dominated by short lived nuclides. At 90 days of cooling decay heat coming from actinides has the same magnitude of that generated by FP's and it's relevance increase going further. 
The main contributors among ACT are marked with solid line in Fig.[]. $^242$Cm has the greatest weight for the time interval analyzed for unloading procedure and equipment designing. At longer time scales the most contributing are $^{283}$Pu and $^{241}$Am. The latter is produced after unloading of the fuel assembly by the decay of $^{241}$Pu, that is highly produced during irradiation and has $t_{1/2} = 14\;y$.
\end{comment}