## 6 MCNP6
### Uncertainty Propagation and Quantification  
Following the BEPU concept, the fuel depletion and canister criticality calculations with BUCSS-R are furthermore complemented by UQs. CSEs in preparation of long-term geological disposal are in general affected by the following uncertainty sources:  
* Nuclear data;
* Operating conditions of the FA in the reactor core;
* Design and technological parameters of the FAs and the disposal canister;
* Radiation-induced changes in the FA geometry. A comprehensive, although still preliminary, quantification of the uncertainties from all of these sources was summarised in [11]. ND-UQ results therein have been adopted from another study, also conducted at PSI [4]. Since ND are, in one format or another,essential input required for steps 3, 4 and 6 of the BUCSS-R scheme, several tools were developed and eventually used to quantify ND-related uncertainties stemming from each of those steps, see red frame in Figure 2. Using these tools, ND uncertainties can be propagated through the calculation chain by repeating the calculations for a large number of times, each time with a different set of ND, randomly sampled following information on the ND uncertainties provided in the selected ND library. The methods of the tools are based on stochastic sampling (SS), which has been explored extensively in the context of ND-uncertainty assessments for reactor physics applications and validation studies [24]. The UQ finally consists in the statistical analysis of the outcome of all the simulations. The following tools can be employed independently from each other:  
1. SHARK-X  
ND (i.e., cross sections, fission neutron yields \(\overline{v}\) and fission spectra) can be perturbed with the SHARK-X [16; 25; 26; 27] tool, which also takes care of the correct formatting for usage in CASMO5. First, ENDF covariance files are processed with NJOY into a number of energy groups from thermal energy up to 20 MeV. These matrices are then used to produce random realizations of ND by means of SS from joint probability distributions defined with normal distributions. SHARK-X has been used for a previous study [28] assessing uncertainties for Swiss LWR spent nuclear fuels due to ND, however, with a focus on other quantities of interest: assembly burnup, decay heat, neutron and gamma sources, as well as isotope inventory for realistic fuel histories. 2. Fission yields sampling  
The UQ due to fission yields is similar to the case of the above ND. A stochastic sampling of evaluated fission yields is performed, based on fission yield uncertainties (as provided in the evaluated libraries), and on an in-house correlation matrix (as no fission yield correlations are provided in such evaluated libraries). Details on the correlation matrix can be found in [29]. 3. ENDF2C  
The impact of decay data uncertainties on keff results can be investigated with a modified version of the ENDF2C tool [30]. This routine uses stochastic sampling for a perturbation of the decay constants and branching ratios, whose uncertainties are contained and read from original ENDF decay data files. Furthermore, the physical relationship between the branching ratios is respected. The perturbed decay data are formatted for use in SERPENT2. A previous study with ENDF2C [4] showed that the effect of decay data uncertainties on system criticality in the present context is negligible when compared with the effects of uncertainties in cross section or fission yield (FY) data. This finding is in line with other publications addressing decay data uncertainties in this respect [31; 32; 33]. An assessment of the effects of decay data uncertainties is, hence, not part of this work. 4. NUSS  
The Nuclear data Uncertainty Stochastic Sampling method (NUSS) [5; 25; 34; 35] applies perturbations in groups to pointwise nuclear data given in the specific ACE format which is used for criticality calculations with MCNP6. NUSS hereby follows the descriptions of ND sampling in [25].