Impact of TSL for light water on the French plutonium temperature effect experimental program 

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TSL evaluations for light water in the JEFF-3.3 and ENDF/B-VIII.0 library

The previous section describes the different methodology adapted for generating TSL evaluations for light water. In this section, attention will be focused on the latest TSL evaluations for light water in JEFF-3.3 and ENDF/B-VIII.0 of ENDF/B. A comparative study of the frequency spectrum utilized by both these evaluations have been discussed in the previous section. Also, it is worth mentioning again that ENDF/B-VIII.0 uses Egelstaff and Schofield diffusion model and JEFF-3.3 relies on the free gas model to model the molecular diffusion at low energy transfers. However, both these evaluations utilizes harmonic oscillators to model the bending and the stretching mode of the frequency spectrum at somewhat similar energies. The impact of TSL data on nuclear systems at thermal energies do not have significant impact at higher energy transfers and both these TSL evaluations do not differ much in this energy region. But, at thermal and cold neutron energy region both these model differ significantly. It is worth observing the shape of the TSL data to observe the differences in these two evaluations. TSL data, i.e. S(, ) is generally a matrix that defines the scattering process as a function of momentum transfer and energy transfer . A comparison of the S(, ) at 293.6 K as a function of for both JEFF-3.3 and ENDF/B-VIII.0 TSL evaluation is presented in Fig. 3.11. Several values are chosen to demonstrate the difference, especially low beta values (<7.5 meV) corresponding to an energy transfer of around 190 meV below which the two models differ significantly. At high energy transfers (high ) both the evaluations rely on the same model, i.e. discrete oscillators at nearly same energies and hence the shape of the S(, ) do not differ much. Figure 3.11 clearly indicates that both the JEFF-3.3 and ENDF/B-VIII.0 differ significantly at low energy transfers ( < 0.1) since ENDF/B-VIII.0 uses Egelstaff and Schofield diffusion model and JEFF-3.3 relies on the free gas model to define molecular diffusion at low energies. However, this difference reduces at high energy transfers ( >2.5). For instance, around 2.5, corresponds to an energy transfer associated to the rotational motion of the water molecule. A small difference in this energy region is due to the peak position of the energy of the rotation band in the frequency spectrum utilized by JEFF-3.3 and ENDF/B-VIII.0 at 293.6 K as discussed in the previous section. To see the impact of the S(, ) at high temperature (close to reactor operating temperature), a comparison of the S(, ) at 573.6 K as a function of for both JEFF-3.3 and ENDF/B-VIII.0 TSL evaluation is presented in Fig. 3.12. As compared to Fig. 3.11 the differences in the S(, ) at low value ( <0.1) between JEFF-3.3 and ENDF/B-VIII.0 reduces as the impact of molecular diffusion on the TSL at high energies are low. However, for >0.1 the overall differences in the shape of the S(, ) increases due to the difference in the position of the
rotation band in the frequency spectrum between both the evaluations at 573.6 K. A thorough investigation is further necessary to observe the impact of these evaluations by comparing it with double differential and total scattering cross sections that will be discussed in the following sections.

Impact of TSL evaluations on the double differential cross section of light water

The double differential cross section is calculated based on Eq. 3.1 using S(, ) from JEFF-3.3 and ENDF/BVIII. 0 TSL evaluations at room temperature and compared with a series of experimental data. The double differential cross sections obtained using TSL evaluations are free from resolution effects. A direct comparison of the experimental data with the derived double differential cross section from the TSLs cannot be achieved unless the experimental resolution effects are convoluted on the calculations as the experimental data are limited by the experimental resolution. For instance, the quasi-elastic peak in the experimental double differential data is broadened due to the resolution of the experiment. The appropriate resolution function of the TOF spectrometer is approximated by a Gaussian function. The standard deviation of the Gaussian function was estimated from the knowledge of the experimental resolution available in the literature.
As a matter of explanation, it should be emphasized that the double differential cross section is a function of the secondary energy of the neutrons in the laboratory system after scattering with the target. It should not be confused with the energy exchange between the neutron and the scattering target as is the case with some authors to represent the double differential experimental data [33]. In the case where the double differential cross section is represented as a function of the energy transfer }!, the final energy E0 must be obtained as a subtraction of the incident energy E from }!. The comparison of double differential data with the experimental data presented in this work is expressed as a function of scattered neutron energy E0.
Double differential data were calculated for an incident neutron energy of 154 meV and 231 meV, using S(, ) from JEFF-3.3 and ENDF/B-VIII.0 TSL evaluations at room temperature. Two scattering angles were chosen in each case, i.e. = 14 and = 25 . The results are displayed in Fig. 3.13, 3.14, 3.15 and 3.16, compared with measurements carried out by Bischoff et al. in 1967 [43]. The resolution of this experimental data were approximated to be around 5%.

Impact of TSL evaluations on the total cross section of light water

Several TSL evaluations for light water are chosen to demonstrate the impact of TSL on total scattering cross sections. Special attention is given on the high temperature data so as to investigate the behavior of existing TSLs for light water at high temperatures. The impact of the shape of the frequency spectrum particularly at high temperatures is addressed.
The total scattering cross-section for light water has been computed using the TSL and the THERMR module of the NJOY code. The oxygen cross section is treated as a free gas. The total scattering cross-section is obtained in the following manner:
Here, (H2O),t is the total scattering cross section of light water. H,s and H, are the inelastic scattering cross section and capture cross section of hydrogen, respectively. O,t is the total cross section of oxygen.

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Total cross section based on free gas TSL model

The effect of the atoms bound in the molecules on the cross section is governed by S(, ). Light water in the liquid state, can also be approximated by a scattering law assuming it to be free gas. The free gas TSL, SFG(, ) can be given by Eq. 2.41. The total cross section of light water in the thermal energy range can be approximated using SFG(, ) for hydrogen bound in water molecule. The free gas total cross section for light water at room temperature is given in Fig. 3.21. Figure 3.21 shows the total cross section of light water based on free gas model at high temperatures, i.e. between 323.6 K and 623.6 K in steps of 50 K. The bottom part in this figure, is the ratio of the cross section w.r.t. 323.3 K data. One can see that the ratio of the cross sections increases with increasing temperature in the thermal region and converges to the free gas scattering cross section of light water. This observation is in agreement with the fact that cross sections in the thermal energy range increase with increasing temperatures due to an increase in the probability of up scattering.

Table of contents :

Abstract
Résumé
Acknowledgments
List of Figures
List of Tables
List of Abbreviations
List of Symbols
1 Introduction 
1.1 Nuclear data and its importance
1.2 Motivations and objectives
1.3 Thesis organization
2 Thermal scattering law formalism 
2.1 General description
2.2 Thermal Scattering Law (TSL)
2.3 Neutron scattering
2.3.1 Coherent and Incoherent scattering
2.4 Approximations while generating TSL
2.5 Evaluation of thermal scattering law using the LEAPR module of NJOY code
2.5.1 Molecular translation
2.5.2 Continuous solid type spectrum
2.5.3 Discrete vibrational oscillators
2.5.4 Short Collision Time Approximation (SCTA)
2.6 Generation of TSL for light water using the LEAPR module of NJOY
3 Presently available TSL evaluations for light water 
3.1 TSL generation methodology
3.1.1 TSL for light water based on experimentally measured frequency spectrum
3.1.2 TSL for light water based on molecular dynamics simulations
3.1.3 Comparative study of the frequency spectrum obtained from TOF experiments and MD simulations
3.2 TSL evaluations for light water in the JEFF-3.3 and ENDF/B-VIII.0 library
3.3 Impact of TSL evaluations on the double differential cross section of light water
3.4 Impact of TSL evaluations on the total cross section of light water
3.4.1 Total cross section based on free gas TSL model
3.4.2 Total cross section based on JEFF-3.1.1 and ENDF/B-VII.1 TSL evaluation
3.4.3 Comparative study of the total cross section based on JEFF-3.3 and ENDF/B-VIII.0 TSL
evaluation at room temperature
3.4.4 Total cross section based on JEFF-3.3 TSL evaluation at high temperatures
3.4.5 Total cross section based on ENDF/B-VIII.0 TSL evaluation at high temperatures .
3.4.6 Comparative study of the total cross section based on JEFF-3.3 and ENDF/B-VIII.0 TSL
evaluation at high temperatures
3.4.7 Development of a new evaluation based on ENDF/B-VIII.0 and JEFF-3.3 TSL library .
4 TOF inelastic neutron scattering experiment for light water 
4.1 TOF neutron scattering
4.1.1 Types of TOF spectrometer
4.1.2 Accessible regions of (~q, !) in a TOF experiment
4.2 TOF experiment at ILL
4.2.1 Sample preparation
4.2.2 IN4c TOF spectrometer
4.2.3 IN6 TOF spectrometer
4.3 TOF data reduction
4.3.1 Data reduction procedure
4.4 Analysis of the TOF experimental data
4.4.1 Resolution of the IN4c and IN6 spectrometers
4.4.2 S(~q, !) derived from TOF measurements
4.5 Double differential scattering cross section
4.5.1 Pressure dependence on the double differential scattering cross section
4.5.2 Temperature dependence on the double differential scattering cross section
4.6 Frequency spectrum
4.6.1 Pressure Dependence on the Frequency Spectrum
4.6.2 Temperature Dependence on the Frequency Spectrum
4.7 Total scattering cross section
4.7.1 Pressure dependence on the total scattering cross section of light water
4.7.2 Temperature dependence on the total scattering cross section of light water
5 Molecular Dynamics simulations for light water 
5.1 General overview
5.2 Water models and force fields
5.2.1 TIP4P/2005f water potential
5.2.2 TCPE water potential
5.2.3 Preferred choice between TIP4P/2005f and TCPE water potential for reactor physics
applications
5.3 Light water simulations using TCPE model
5.3.1 Analysis of the MD simulation data
6 Evaluation and processing of TSL for light water 
6.1 Nuclear data evaluation and processing at IRSN
6.1.1 GAIA project
6.2 SAB Module
6.3 Impact of TSL for light water on the French plutonium temperature effect experimental program
6.3.1 Experimental setup
6.3.2 Benchmark Specifications
6.3.3 MORET Monte Carlo simulations
7 Verification and validation of new TSL evaluations for light water 
7.1 Double differential scattering cross section
7.2 Differential scattering cross section
7.3 Total scattering cross section
7.4 Testing new TSL evaluations on ICSBEP critical benchmarks
7.4.1 Testing of new TSL evaluations
7.4.2 Additional tests with new TSL evaluations
New TSL evaluations along with the new IRSN 16O evaluation
New TSL evaluations along with the new IRSN 16O and 235U evaluations
New TSL evaluations along with the new IRSN 16O, 235U evaluation and 235U prompt
fission neutron spectra (PFNS) from ENDF/B-VIII.0
Conclusions

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