Nuclear Science and Engineering ISSN: 0029-5639 (Print) 1943-748X (Online) Journal homepage: http://www.tandfonline.com/loi/unse20 How to Randomly Evaluate Nuclear Data: A New 239 Data Adjustment Method Applied to Pu D. Rochman & A. J. Koning To cite this article: D. Rochman & A. J. Koning (2011) How to Randomly Evaluate Nuclear Data: A New Data Adjustment Method Applied to DOI: 10.13182/NSE10-66 239 Pu, Nuclear Science and Engineering, 169:1, 68-80, To link to this article: http://dx.doi.org/10.13182/NSE10-66 Published online: 12 May 2017. Submit your article to this journal Article views: 2 View related articles Citing articles: 3 View citing articles Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/journalInformation?journalCode=unse20 Download by: [Tufts University] Date: 27 October 2017, At: 03:21 NUCLEAR SCIENCE AND ENGINEERING: 169, 68–80 ~2011! How to Randomly Evaluate Nuclear Data: A New Data Adjustment Method Applied to 239 Pu D. Rochman* and A. J. Koning Nuclear Research and Consultancy Group NRG P.O. Box 25, 1755 ZG Petten, The Netherlands Downloaded by [Tufts University] at 03:21 27 October 2017 Received September 14, 2010 Accepted January 25, 2011 Abstract – This paper presents a novel approach to combine Monte Carlo optimization and nuclear data to produce an optimal adjusted nuclear data file. We first introduce the methodology, which is based on the so-called “Total Monte Carlo” and the TALYS system. As an original procedure, not only a single nuclear data file is produced for a given isotope but virtually an infinite number, defining probability distributions for each nuclear quantity. Then, each of these random nuclear data libraries is used in a series of benchmark calculations. With a goodness-of-fit estimator, a best evaluation for that benchmark set can be selected. To apply the proposed method, the neutron-induced reactions on 239 Pu are chosen. More than 600 random files of 239 Pu are presented, and each of them is tested with 120 criticality benchmarks. From this, the best performing random file is chosen and proposed as the optimum choice among the studied random set. I. INTRODUCTION clear data files to better fit a selected set of integral measurements. This approach has produced evaluations that are used worldwide, approved by safety authorities and the nuclear industry, and finally used in simulation codes for reactor design and safety assessment. For instance, the JEFF-3.1.1 nuclear data library 2 was produced following the previous scheme, including an “incremental approach” ~meaning minimal changes, targeted to improve a number of reference calculations, from one library version to another!, and is now the reference library for the French nuclear authorities, operator, and designers. There are nevertheless a few inconveniences related to this method of work, especially in a world with higher constraints on safety, efficiency, and cost-effectiveness. The incremental approach, which is used to improve a series of benchmarks, advocates minimal changes to nuclear quantities such as cross sections. It allows one to find the closest best solution in the multidimensional nuclear data space, but there is no guarantee that this local best solution is the absolute best solution. It is in principle possible to choose a different set of nuclear data ~far from a solution given by an incremental approach! and to have better agreement with the same series of benchmarks. Because of the large turnaround time of data library The evaluation of neutron-induced reactions is not a new branch of nuclear science. This field of applied research is considered quite mature, and nuclear data specialists have delivered a large number of nuclear data evaluations since the 1950s. Many well-recognized and respected nuclear data libraries exist, as for instance ~and to cite only one!, the U.S. ENDF0B-VII.0 library.1 As nuclear data are relevant for different kinds of applications, all countries with a large nuclear industry possess their own team~s! of nuclear data evaluators to answer their special needs. From a common historical background, these research groups share the same experimental databases and nuclear reaction theories and have a restricted number of codes0programs to produce the so-called “evaluated files.” Also, as a heritage of historical segregation, nuclear data specialists are often not the same people as the application specialists. They are separated by buildings, language, education, and sometimes countries ~in short, they do not share the same culture!. A consequence is that application specialists often modify evaluated files to produce “adjusted” nu*E-mail: [email protected] 68 Downloaded by [Tufts University] at 03:21 27 October 2017 239 Pu ADJUSTMENT creation, adoption, validation, and industrial acceptation ~once every 10 to 15 years!, it can be argued that in the European community, the recent adoption of JEFF-3.1.1 by various nuclear industries gives nuclear data evaluators time to look for a better solution and deviate from the incremental approach. Another drawback of this approach is that nuclear data are considered as input for a specific, well-validated, and fixed reactor code “A” designed a few decades ago. By incrementally adjusting the inputs, the combination “new inputs and code A” is improving its performance compared to “previous inputs and code A.” The changes in nuclear data can nevertheless be seen as correction factors for imperfections of this code, and this becomes particularly dangerous if the adjusted data fall outside high-quality differential measurement uncertainties. Equally important, it does not automatically imply that the combination “new inputs and code B” will perform better than “previous inputs and code B.” It is obvious that a lot of evaluation knowledge exists in the current libraries. But with responsible nuclear scientists retiring, the real understanding of the library content is sometimes difficult to keep, even though the basic data, like the EXFOR database, remain available ~in traditional evaluation methods, reproducibility is not seen as an asset!. Finally, as a consequence of the similarity of codes and integral experiments used worldwide, data libraries are becoming more alike. An important and positive effect of this is that there is gradual improvement of the quality of current evaluations for important data and applications ~regarding both their content and format!. In parallel to the global convergence of the nuclear data community and in an effort to offer an alternative and unconventional approach, a new method of nuclear data evaluation procedure has recently been proposed.3 It is based on principles that have been embraced by many other industries long ago: quality, automation, reproducibility, completeness, and consistency. It relies on the robust nuclear model code TALYS ~Ref. 4! and on the two simple ideas that any information used to create a nuclear data file is kept “forever” to be reused as necessary and that manual intervention during the library production is strictly forbidden. The spin-offs of such a new method are multiple ~see Fig. 1!: complete nuclear data libraries ~TENDL! on an unprecedented scale,5,6 including covariance production, exact ~Monte Carlo! uncertainty propagation 3 for fission systems,7 fusion applications,8 or new GEN-IV reactors.9 It is even possible to “clone” an existing library ~e.g., the entire ENDF0BVII.0 library! and start further development from that point, such as filling all missing sections using TALYS, addition of covariance data, etc. As a new spin-off of this working method, this paper presents a random search for the best possible adjusted nuclear data file of 239 Pu. Based on a Monte Carlo variation of the TALYS model and resonance parameters, not one but many ~virtually an infinite number! files for 239 Pu are calculated and used in criticality-safety benchmarks. On the basis of a goodness-of-fit estimator, such as x 2 , it can be judged whether the result is better, at least from the integral point of view, than any existing traditional library. We believe that as long as experimental cross sections ~and other nuclear data! are not perfectly known, it is perfectly acceptable to envisage a large number of evaluated curves to simulate our imperfect knowledge and to guide us toward the best possible choice for applications. This random variation should of course take place inside the uncertainty bands associated with each cross section. In other words, we simply use differential and integral measurements at the same time, realizing of course that one experimental data set may give more exclusive information than the other—as done in traditional data adjustment methods. Fig. 1. Presentation of the possible outcomes based on the TALYS system, as presented in this paper. NUCLEAR SCIENCE AND ENGINEERING VOL. 169 SEP. 2011 69 70 ROCHMAN and KONING Downloaded by [Tufts University] at 03:21 27 October 2017 II. METHODOLOGY The working method has already been presented in a few dedicated papers ~see, for instance, Refs. 3, 7, 8, and 9!. It is not specific to actinides, although it should be mentioned that the main difference between an evaluation of a major actinide and a regular isotope is the amount of time spent to obtain the best possible TALYS input parameters. As mentioned previously, once these input parameters are known ~together with their uncertainties!, they are stored to be reused as needed. The complete schematic approach is presented in Fig. 2. The full nuclear data file production relies on a small number of codes and programs, automatically linked together. The output of this system is either one ENDF-6 formatted file, including covariances if needed, or a large number of random ENDF-6 files. The central evaluation tool is the TALYS code. A few other satellite programs are used to complete missing information and randomize input files. At the end of the calculation scheme, the formatting code TEFAL produces the ENDF files. II.A. The TALYS Code The nuclear reaction code TALYS has been extensively described in many publications ~see Refs. 4 through 10!. It simulates reactions that involve neutrons, gamma rays, etc., from thermal to 200-MeV energy range. With a single run, cross sections, energy spectra, angular distributions, etc., for all open channels over the whole incident energy range are predicted. The nuclear reaction models are driven by a restricted set of parameters, such as optical model, level density, photon strength, and fission parameters, which can all be varied in a TALYS input file. All information that is required in a nuclear data file, above the resonance range, is provided by TALYS. II.B. The TASMAN Code TASMAN is a computer code for the production of covariance data using results of the nuclear model code TALYS and for automatic optimization of the TALYS results with respect to experimental data. The essential idea is to assume that each nuclear model ~i.e., TALYS input! parameter has its own uncertainty, where often the uncertainty distribution is assumed to have either a Gaussian or uniform shape. Running TALYS many times, whereby each time all elements of the input parameter vector are randomly sampled from a distribution with a specific width for each parameter, provides all needed statistical information to produce a full covariance matrix. The basic objective behind the construction of TASMAN is to facilitate all this. Fig. 2. Flowchart of the nuclear data file evaluation and production with the TALYS system. NUCLEAR SCIENCE AND ENGINEERING VOL. 169 SEP. 2011 Downloaded by [Tufts University] at 03:21 27 October 2017 239 Pu ADJUSTMENT TASMAN is using central value parameters and a probability distribution function. The central values were chosen to globally obtain the best fit to experimental cross sections and angular distributions ~see, for instance, Ref. 11!. The uncertainties on parameters ~or widths of the distributions! are also obtained by comparison with experimental data, which are directly taken from the EXFOR database.12 The distribution probability can then be chosen between equiprobable, Normal, or other. In principle, with the least information available ~no measurement, no theoretical information!, the equiprobable probability distribution should be chosen. Otherwise, the Normal distribution is considered. An important quantity to obtain rapid statistical convergence in the Monte Carlo process is the selection of random numbers. Several tests were performed using pseudorandom numbers, quasi-random numbers ~Sobol sequence!, Latin Hypercube random numbers, or Centroidal Voronoi Tessellations random numbers. As the considered dimension ~number of parameters for a TALYS calculation! is rather high ~from 50 to 80!, not all random number generators perform as required ~covering as fast as possible the full parameter space, without repeating very similar configurations and avoiding correlations!. For the time being, the random data files are produced using the Sobol quasi-random number generator. II.C. The TEFAL Code TEFAL is a computer code for the translation of the nuclear reaction results of TALYS, and data from other sources if TALYS is not adequate, into ENDF-6 formatted nuclear data libraries. The basic objective behind the construction of TEFAL is to create nuclear data files without error-prone human interference. Hence, the idea is to first run TALYS for a projectile-target combination and a range of incident energies, and to obtain a readyto-use nuclear data library from the TEFAL code through processing of the TALYS results, possibly in combination with experimental data or data from existing data libraries. This procedure is completely automated, so the chance of ad hoc human errors is minimized ~of course, we may still have systematic errors in the TEFAL code!. II.D. The TARES Program The TARES program is a code to generate resonance information in the ENDF-6 format, including covariance information. It makes use of resonance parameter databases such as the EXFOR database,12 resonance parameters from other libraries ~ENDF0B-VII.0! ~Ref. 1!, or compilations.13 ENDF-6 procedures can be selected, for different R-matrix approximations, such as the multilevel Breit-Wigner or Reich-Moore formalism. The covariance information is stored either in the “regular” covariance format or in the compact format. For short-range correlation between resonance parameters, simple formulas as preNUCLEAR SCIENCE AND ENGINEERING VOL. 169 SEP. 2011 71 sented in Ref. 14 are used, based on the capture kernel. No long-range correlations are considered for now. In the case of major actinides, resonance parameters are taken from evaluated libraries, such as ENDF0BVII.0 or JEFF-3.1. These values are almost never given with uncertainties. In this case, uncertainties from compilations or measurements are assigned to the evaluated resonance parameters. Although not the best alternative, it nevertheless allows the combination of central values with uncertainties. For the unresolved resonance range, an alternative solution to the average parameters from TALYS is to adopt parameters from existing evaluations. In the following, this solution is followed. The output of this program is a resonance file with central values ~MF2!, a resonance file with random resonance parameters ~MF2!, and two covariance files ~MF32 standard and compact!. II.E. The TANES Program TANES is a simple program to calculate the fission neutron spectrum based on the Los Alamos model.15 The original Madland-Nix 16 or Los Alamos model for the calculation of prompt fission neutron characteristics ~spectra and multiplicity! has been implemented in a stand-alone module. The TANES code is using this standalone module, combined with parameter uncertainties ~on the total kinetic energy, released energy, and multichance fission probabilities! to reproduce and randomize the fission neutron spectrum. The output of this program is the central and random values for the fission neutron spectra at different incident energies ~MF5! and their covariances ~MF35!. II.F. The TAFIS Program TAFIS is used to calculate fission yields, prompt neutron emission from fission, and other necessary fission quantities ~kinetic energy of the fission products, kinetic energy of the prompt and delayed fission neutrons, total energy released by prompt and delayed gamma rays!. For fission yields, it uses the systematics of fission product yields from Wahl,17 combined with ad hoc uncertainties. It calculates the independent and cumulative fission yields at any incident energy up to 200 MeV and for different incident particles ~spontaneous, neutrons, protons, deuterons, etc.!. Empirical equations representing systematics of fission product yields are derived from experimental data. The systematics give some insight into nuclear-structure effects on yields, and the equations allow estimation of yields from fission of any nuclide ~Z ⫽ 90 to 98 and A ⫽ 230 to 252!. For neutron emission, different models are used depending on the energy range and are presented in Ref. 17. The output of this program is a fission yield file with uncertainties, prompt neutron emission files for central and random values ~MF1 MT452!, a list of central and random fission 72 ROCHMAN and KONING quantities ~MF1 MT458!, and prompt neutron covariances ~MF31!. II.G. Autotalys Autotalys is a script that takes care of the communication between all software and packages described above and runs the complete sequence of codes, if necessary, for the whole nuclide chart. Many options regarding TALYS and all other codes can be set, and it makes the library production straightforward. once this set of parameters and uncertainties is found, it is kept at the start of the whole file production and can be used in future work. Examples of typical random cross sections used by MCNP are presented in Fig. 3 for fission, inelastic, elastic, and ~n, 2n! reactions. It can be seen that the central cross sections are very close to the ones from the ENDF0B-VII.0 library. Similar results are obtained from other important nuclear quantities such as n-bar, resonance parameters, and fission neutron spectrum. IV. BENCHMARKING AND RANDOM SELECTION Downloaded by [Tufts University] at 03:21 27 October 2017 III. TOTAL MONTE CARLO AND APPLICATIONS TO 239 Pu With such a system, it is quite easy to understand that if a calculation can be done once, it can also be done a large number of times. Hence, each new calculation can be performed with a new set of model parameters, thus simulating uncertainties on cross sections, nu-bar, fission neutron spectrum, and others. The general description of the method can be found in Ref. 3, with different applications in Refs. 7, 8, and 9. The present Total Monte Carlo methodology relies on a large number of nuclear data files for a single isotope. In each file, resonance parameters ~MF2!, cross sections ~MF3 in ENDF terminology!, angular and energy distributions ~MF4 and MF5! and doubledifferential distributions, gamma-ray production cross sections ~MF6!, n-bar ~MF1!, and fission neutron spectrum ~MF5! are randomly changed. This is achieved by modifying theoretical parameters for the TALYS calculations, such as the optical model, Reich-Moore, compound nucleus, direct, and preequilibrium parameters, constrained by their uncertainties. The basic approach can be summarized as follows: 1. A restricted number of isotopes for the criticalitysafety benchmarks are considered. 2. For each isotope, a large number of different ENDF-6 nuclear data libraries are created ~1000 to 2000! using random model and resonance parameters included in the TALYS system. 3. All ENDF-6 files are processed with the NJOY code 18 to produce ACE libraries for the MCNP Monte Carlo code.19 4. For each selected benchmark,20 calculations are performed using a different set of ACE files ~for each isotope of a given element! each time. For the Monte Carlo evaluation procedure, the most difficult part of the work is now accomplished. We have at our disposal a virtually infinite number of 239 Pu files, all different and all reflecting our current imperfect knowledge. For existing libraries, the evaluation procedure is rather close to this work: Evaluators search for a set of cross sections ~and other nuclear data!, which gives the best comparison to differential and integral experimental data. The difference is that they are using a given ~educated! unique set of cross sections, whereas we are using a large set of cross sections. A key in the success of the approach is an absolute automation, and reproducibility for the whole evaluation-benchmarking flow. The next step is to select a set of integral data. This selection will vary from one application group to another, simply because of different expertise, purpose of the evaluation, and accessibility to benchmarks. But independently of this choice, the present procedure can be applied to any number of benchmarks and any kind ~criticality, dosimetry, fusion, activation, and others!. For the present study, we have selected a few benchmarks from the ICSBEP database.20 The benchmarks that are highly sensitive to plutonium ~denominated by “pst,” “pmf,” “pmm,” “pci,” or “pmi”! are selected for the random search ~see Table I!. We thus calculate all these benchmarks, with MCNP, for one random 239 Pu library at the time. IV.A. x 2 Test As a large number of benchmarks are considered, it is easier to compare the performances of different libraries with a unique number such as the x 2 statistic, defined as n x ⫽( 2 ~Ci ⫺ Ei ! 2 i It is important to start from good central values for model parameters. As usual in the nuclear data evaluation process, a large amount of time is first dedicated to find suitable model parameters to reproduce experimental data and other evaluations. But in the present case, Ci , ~1! where Ci ⫽ calculated value for the i benchmark Ei ⫽ benchmark value. NUCLEAR SCIENCE AND ENGINEERING VOL. 169 SEP. 2011 Downloaded by [Tufts University] at 03:21 27 October 2017 239 Pu ADJUSTMENT 73 Fig. 3. Examples of random cross sections for 239 Pu, generated with the TALYS system and compared to ENDF0B-VII.0. Random cross sections are presented in plain lines ~red in the online version!. TABLE I List of Plutonium Benchmarks Selected for the Random Search Name Cases Name Cases Name Cases Name Cases pmf1 pmf8 pmi2 pst4 pst8 1 1 1 13 29 pmf2 pmf12 pst1 pst5 pst12 1 1 6 9 22 pmf5 pmf13 pst2 pst6 pmm1 1 1 6 3 6 pmf6 pci1 pst3 pst7 1 1 8 9 Depending on the considered nuclear data library, a specific value of x 2 is obtained. If the benchmarks presented in Table I are used, the following x 2 values are obtained: 1. for JEFF-3.1, x 2 ⫽ 8.08 ⫻ 10⫺3 6 7.2 ⫻ 10⫺4 2. for ENDF0B-VII.0, x 2 ⫽ 9.55 ⫻ 10⫺3 6 7.9 ⫻ 10⫺4 3. for ENDF0B-VI.8, x 2 ⫽ 8.45 ⫻ 10⫺3 6 7.2 ⫻ 10⫺4 4. for JENDL-3.3, x 2 ⫽ 1.31 ⫻ 10⫺2 6 1.0 ⫻ 10⫺3. NUCLEAR SCIENCE AND ENGINEERING VOL. 169 SEP. 2011 Even if in principle our current approach for 239 Pu adjustments can be used for all nuclides at once ~requiring a huge number of TALYS and MCNP!, only 239 Pu is varied, and the other nuclides are kept constant and equal to the JEFF-3.1 evaluations. A total of 120 benchmarks are used as shown in Table I, and 630 random 239 Pu files are produced. The total scope of this work thus involves 75 600 MCNP criticality calculations. Figures 4 and 5 present examples of k eff distributions for 12 fast, intermediate, and thermal benchmarks. Similar types of distributions are obtained for other benchmarks. These distributions are similar to those reported in Ref. 7. Downloaded by [Tufts University] at 03:21 27 October 2017 74 ROCHMAN and KONING Fig. 4. Calculated k eff values for six fast benchmarks: pmf1, pmf2, pmf5, pmf6, pmf8, and pmf12. IV.B. Results Following this present evaluation method, a large number of evaluated files are produced, the number being limited by the production time ~on average, the production of a single file takes about 1 to 2 h on a typical 3-GHz personal computer while its validation with all selected benchmarks takes 12 h!. Figure 6 presents the results of the benchmarks of the random files in terms of x 2 as defined in Eq. ~1!. All single random files are represented by a x 2 value, and to compare with existing evaluations, results from other libraries are plotted as bands. The uncertainties on the dots ~and the widths of the bands! are the statistical uncertainties coming from the MCNP calculations together with the benchmark uncertainties. In Fig. 6, the results for 630 random 239 Pu libraries are presented. It is rather unconventional to visualize a library for which an isotope is represented by a set of files ~corresponding to probability distributions for different types of nuclear data!, and Fig. 6 is a collapsed way of looking at n random files applied to m benchmarks. As expected from a simple random approach, a large number of the files perform quite poorly compared to other libraries, but a small set ~;6% of the total number! outperforms all other traditional libraries. A different way of representing the same results is shown in Fig. 7, where x 2 values of Fig. 6 are projected onto the y-axis and counted as histograms. In Fig. 7, each random x 2 ~for each random 239 Pu file! is represented by a step of height 1 in the histograms. The four traditional libraries have a single step for their x 2 value. This distribution is not symmetric and has a large tail toward high x 2 values. The four traditional libraries are in the low-x 2 part of the graph, reflecting the amount of knowledge and time that have been invested in them. Again, we note that several of the random x 2 are smaller than the ones from JEFF-3.1, ENDF0B-VII.0, ENDF0BVI.8, or JENDL-3.3. According to this probability distribution, it would be interesting to know if the probability to obtain x 2 ⯝ 0 is theoretically possible ~meaning that even if its probability is small, it could be reached by having enough random files!. In the hypothesis that the variable Ci of Eq. ~1! is independent and normally distributed, the Pearson’s chi-square test used above follows a chi-square NUCLEAR SCIENCE AND ENGINEERING VOL. 169 SEP. 2011 Downloaded by [Tufts University] at 03:21 27 October 2017 239 Pu ADJUSTMENT 75 Fig. 5. Calculated k eff values for six fast, intermediate, and thermal benchmarks: pmf13, pci1, pst1-6, pmi2-1, pst6-1, and pst2-2. distribution with k degrees of freedom.21 It is defined in the interval @0,⫹`! and governs a nonzero probability for x 2 ⫽ 0. It is then theoretically possible to “continuously” improve the agreement with a set of benchmarks by using more random files. However, we do realize that in practice it will not be possible to obtain a perfect fit for all included benchmarks simultaneously. Additionally, the variable Ci is not fully independent, and a lognormal distribution seems to better represent the probability distribution of Fig. 7 ~which is also defined at x 2 ⫽ 0!. Nevertheless, figures like Fig. 7 are important to get an idea of how much room for improvement is left, even for conventional methods. V. APPLICATIONS This type of approach has at least two important applications: ~a! the propagation of nuclear data uncertainties to large-scale system quantities ~as was demonstrated in previous papers by the same authors! and ~b! the NUCLEAR SCIENCE AND ENGINEERING VOL. 169 SEP. 2011 random search for the adjusted nuclear data file producing a continuously improved agreement with a selected set of benchmarks. V.A. Optimum Pearson’s x 2 Value As the first point was extensively presented in other references, we will focus on the second one. To present the method, we have arbitrarily selected a number of criticality benchmarks ~120!, with an equal weight to all of them. It can be foreseen that this selection will not suit all nuclear data needs and that another evaluator will make a different choice. However, the present method is independent of the selection of tests, and the results presented in the following may or will vary if another choice is made. From Figs. 6 and 7, it can be seen that 40 to 50 random 239 Pu files give a smaller x 2 than any other conventional library. The smallest x 2 is obtained with the random run 307, giving a x 2 of 4.80 ⫻ 10⫺3 6 5.2 ⫻ 10⫺4. To illustrate the performance of run 307, results of the benchmarks for this random file are presented in Fig. 8. Downloaded by [Tufts University] at 03:21 27 October 2017 76 ROCHMAN and KONING Fig. 6. x 2 values for random 239 Pu files ~dots!, compared to x 2 for existing libraries ~bands!. One can see that for the selected benchmarks, the 239 Pu evaluation from JEFF-3.1 library performs better than other conventional library, whereas ;6% of our random 239 Pu files perform better than any other library. Fig. 7. x 2 values for each of the random 239 Pu files per bin, compared to x 2 values for JEFF-3.1, ENDF0B-VII.0, and JENDL-3.3. This figure is the projection on the y-axis of Fig. 6. Note that the x-axis for the large plot is in log scale. The insert is the same plot with the x-axis in linear scale. V.B. Adjustment of 239 Pu Nuclear Data Once the choice of the best random file is made, the most probable values for the nuclear data ~cross sections and others! are set. For the selected file, the cross sections, n-bar, angular distributions, etc., need to be in agreement with differential data. It is also interesting to check whether they deviate from the conventional evaluations. Figures 9 to 12 present different nuclear quantities ~cross sections, n-bar, fission neutron NUCLEAR SCIENCE AND ENGINEERING VOL. 169 SEP. 2011 239 Pu ADJUSTMENT 77 Downloaded by [Tufts University] at 03:21 27 October 2017 Fig. 8. Benchmark results for the best random file ~run 307!, compared to the benchmark results with the JEFF-3.1 library. Fig. 9. 239 Pu n-bar for the ENDF0B-VII.0, JEFF-3.1, and JENDL-3.3 libraries compared with the present adjusted file. Fig. 10. 239 Pu fission neutron spectrum at thermal energy and at 14 MeV for the ENDF0B-VII.0, JEFF-3.1, and JENDL-3.3 libraries compared with the present adjusted file. spectra! for run 307, compared with differential data and from other evaluations. In cases where measurements exist, almost all evaluations are within experimental uncertainties. In the case NUCLEAR SCIENCE AND ENGINEERING VOL. 169 SEP. 2011 of the capture cross section, our evaluation and the one of ENDF0B-VII.0 are lower than experimental data above 1 MeV, but there is no strong evidence ~based on differential measurements! that this cross section should be 78 ROCHMAN and KONING Downloaded by [Tufts University] at 03:21 27 October 2017 Fig. 11. 239 Pu fission cross section in the thermal and fast range for the ENDF0B-VII.0, JEFF-3.1, and JENDL-3.3 libraries compared with the present adjusted file. 1 Fig. 12. 239 Pu capture cross section in the fast range for the ENDF0B-VII.0, JEFF-3.1, and JENDL-3.3 libraries compared with the present adjusted file. higher. For other nuclear quantities, even though the evaluated data of run 307 do not strongly deviate from other evaluations, the changes are significant enough to improve the agreement with the integral benchmarks. To better understand which parts of the nuclear data file play a critical role, a sensitivity study is necessary. Together with the current approach, we have developed a sensitivity method based on the Monte Carlo adjustments. With the full random files, partial random files are also being produced, in which only parts are changed ~n-bar, resonance parameters, inelastic cross sections, etc.! and the rest of the file is kept unchanged and equal to the file with unperturbed model parameters. By benchmarking these partial random files, sensitivities to n-bar, cross sections, or the fission neutron spectrum can be obtained. Although more exact than traditional sensitivity approaches based on perturbation theories, the principal drawback of this sensitivity method is ~for the time being! that the needed computational resources are large. This method was successfully applied to the study of a few criticality benchmarks,22 and we plan to scale up this type of study for more benchmarks. VI. CONCLUSION AND FURTHER IMPROVEMENTS We have presented in this paper an unconventional way to approach nuclear data adjustment. First, through detailed evaluation work a complete data file is made, after which the data are randomly varied within the uncertainty bands. By applying this methodology to 239 Pu and its integral validation, we have shown that considerable improvements can be obtained regarding the agreement between nuclear data evaluations and benchmark results. This method of work was made possible with a high degree of automation for the production of the evaluated file and its benchmarking. But, regardless of the success of this approach, some criticism can be raised. From the author’s point of view, a nonexhaustive list is given as follows: 1. Choice of model parameters: Even if not confined to this approach, the initial choice of model parameters is crucial. It is much more efficient to start from an educated selection of model parameters rather than from NUCLEAR SCIENCE AND ENGINEERING VOL. 169 SEP. 2011 239 Pu ADJUSTMENT Downloaded by [Tufts University] at 03:21 27 October 2017 blind parameters. In the present work, we have spent a considerable amount of time to adjust these parameters. But even so, initial parameters can still be more accurate, and0or the nuclear models can be improved. Again, this problem should not be narrowed to this method only but to all evaluation processes. 2. Choice of benchmarks: For this study, an arbitrary choice of 120 criticality benchmarks was made. All benchmarks have equal weight. This can be legitimately criticized, and different choices can be made to suit special demands, such as putting a large weight on a few important benchmarks. But again, the present method is independent of the choice of benchmarks, and one can imagine a very different selection, using shielding, burnup, or activation benchmarks. In addition, one should include even different ~deterministic! codes in the loop for the same goodness-of-fit estimator, realizing that reactor physics codes and user-friendly software are two different things. 3. Strong correlation of calculated quantities: As a result of the use of the TALYS system and theoretical models, energy-energy correlations for a given cross section are quite strong ~without the mathematical inclusion of experimental differential data, energy-energy correlations are above 50%!. It affects the benchmark results in the sense that the cross section in the fast range will move up or down from one random file to another, keeping a rigid shape. Even if correlations are not basic physical quantities as cross sections, reflecting only the method used to obtain cross sections, it is generally believed that experimental differential data should be mathematically included in the process, and therefore, correlations will be weaker. As a consequence the shape of cross sections will become less rigid and the benchmark results could vary more. We are currently studying solutions to that problem, such as using the “Unified Monte Carlo” presented in Ref. 23 or by randomly changing nuclear models ~such as different level density models! from one calculation to another. Despite these points of critics, more possibilities can be foreseen with the current approach as follows: 79 provement! of the TENDL library, as presented in Ref. 24. There are basically two ways to randomly search for the best nuclear data solution: ~a! The most general approach is to randomly vary all isotopes together and to benchmark each combination, and ~b! less general and certainly more efficient is to vary only one isotope at a time, starting with the most sensitive one ~ 235 U and0or 238 U! and keeping the optimal nuclear data file, and use this when the next relevant isotope is to be optimized. With the current and future computer technology, and the accumulated amount of knowledge in the nuclear data community, we believe that this methodology is technologically condemned to succeed. A limited factor is its acceptance by the nuclear data community, which is more used to accepting a definition of “evaluation work” as a long, tedious, nonreproducible, and repetitive process. It would be a misunderstanding to see a random nuclear data search as a low-cost, low-quality evaluation procedure. A huge amount of knowledge is already included in the TALYS system, its adjusted model parameters, and the selection of differential measurements. As mentioned before, this method will be used for the improvement of the TENDL library, and we are considering applying it to the next generation of the European Activation library. REFERENCES 1. M. B. CHADWICK et al., “ENDF0B-VII.0: Next Generation Evaluated Nuclear Data Library for Nuclear Science and Technology,” Nucl. Data Sheets, 107, 2931 ~2006!. 2. A. SANTAMARINA et al., “The JEFF-3.1.1 Nuclear Data Library,” OECD0NEA JEFF Report 22, Organisation for Economic Co-operation and Development0Nuclear Energy Agency ~2009!. 3. A. J. KONING and D. ROCHMAN, “Towards Sustainable Nuclear Energy: Putting Nuclear Physics to Work,” Ann. Nucl. Energy, 35, 2024 ~2008!. 4. A. J. KONING, S. HILAIRE, and M. C. DUIJVESTIJN, “TALYS-1.0,” Proc. Int. Conf. Nuclear Data for Science and Technology (ND2007), Nice, France, May 22–27, 2007; www.talys.eu ~current as of September 14, 2010!. 1. Virtually unlimited random variation: If applied today to a limited number of random files, it is very easy to extend it almost forever. With today’s computer power, one can start the production of random files with benchmarking, leave it running for months and regularly look at the results. As the probability distribution of the benchmark results follow a law of x 2 ~or a lognormal probability distribution!, there is always a possibility to obtain a better solution. 5. A. J. KONING and D. ROCHMAN, “TENDL-2008: Consistent Talys-Based Evaluated Nuclear Data Library Including Covariances,” OECD0NEA JEF0DOC-1262, Organisation for Economic Co-operation and Development0Nuclear Energy Agency ~Nov. 2008!; http:00www.talys.eu0tendl-2008 ~current as of September 14, 2010!. 2. Virtually unlimited isotopic variation: The method can also be applied to more than a single isotope. It can be applied to a complete library. In the near future, we plan to use this method for the random search ~and im- 6. A. J. KONING and D. ROCHMAN, “TENDL-2009: Consistent Talys-Based Evaluated Nuclear Data Library Including Covariances,” OECD0NEA JEF0DOC-1310, Organisation for Economic Co-operation and Development0Nuclear Energy NUCLEAR SCIENCE AND ENGINEERING VOL. 169 SEP. 2011 80 ROCHMAN and KONING Agency ~Nov. 2009!; http:00www.talys.eu0tendl-2009 ~current as of September 14, 2010!. 7. D. ROCHMAN, A. J. KONING, and S. C. VAN DER MARCK, “Uncertainties for Criticality-Safety Benchmarks and k eff Distributions,” Ann. Nucl. Energy, 36, 810 ~2009!. 8. D. ROCHMAN, A. J. KONING, and S. C. VAN DER MARCK, “Exact Nuclear Data Uncertainty Propagation for Fusion Neutronics Calculations,” Fusion Eng. Des., 85, 669 ~2010!. Downloaded by [Tufts University] at 03:21 27 October 2017 9. D. ROCHMAN, A. J. KONING, D. F. DA CRUZ, P. ARCHIER, and J. TOMMASI, “On the Evaluation of 23Na NeutronInduced Reactions and Validations,” Nucl. Instrum. Methods A, 612, 374 ~2010!. 15. P. TALOU, “ Prompt Fission Neutrons Calculations in the Madland-Nix Model,” LA-UR-07-8168, Los Alamos National Laboratory ~2007!. 16. D. G. MADLAND and J. R. NIX, “New Calculation of Prompt Fission Neutron Spectra and Average Prompt Neutron Multiplicities,” Nucl. Sci. Eng., 81, 213 ~1982!. 17. A. C. WAHL, “Systematics of Fission-Product Yields,” LA-13928, Los Alamos National Laboratory ~2002!. 18. R. E. MACFARLANE, “NJOY99—Code System for Producing Pointwise and Multigroup Neutron and Photon Cross Sections from ENDF0B Data,” RSIC PSR-480, Los Alamos National Laboratory ~2000!. 19. J. F. BRIESMEISTER, “MCNP—A General Monte Carlo N-Particle Transport Code, version 4C,” LA-13709-M, Los Alamos National Laboratory ~2000!. 10. A. J. KONING, M. C. DUIJVESTIJN, S. C. VAN DER MARCK, R. KLEIN MEULEKAMP, and A. HOGENBIRK, “New Nuclear Data Libraries for Lead and Bismuth and Their Impact on Accelerator-Driven Systems Design,” Nucl. Sci. Eng., 156, 357 ~2007!. 20. J. B. BRIGGS, “International Handbook of Evaluated Criticality Safety Benchmark Experiments,” NEA 0NSC0 DOC~95!030I, Organisation for Economic Co-operation and Development, Nuclear Energy Agency ~2004!. 11. A. J. KONING and J. P. DELAROCHE, “Local and Global Nucleon Optical Models from 1 keV to 200 MeV,” Nucl. Phys. A, 713, 231 ~2003!. 21. M. ABRAMOWITZ and I. A. STEGUN, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Chapter 26, p. 940, Dover, New York ~1965!. 12. H. HENRIKSSON, O. SCHWERER, D. ROCHMAN, M. V. MIKHAYLYUKOVA, and N. OTUKA, “The Art of Collecting Experimental Data Internationally: EXFOR, CINDA and the NRDC Network,” Proc. Int. Conf. Nuclear Data for Science and Technology, Nice, France, May 22–27, 2007, p. 737 ~2007!. 22. D. ROCHMAN, A. J. KONING, S. C. VAN DER MARCK, A. HOGENBIRK, and D. VAN VEEN, “Nuclear Data Uncertainty Propagation: Total Monte Carlo vs. Covariances,” Proc. Int. Conf. Nuclear Data for Science and Technology (ND2010), Jeju, Korea, April 26–30, 2010 ~to be published!. 13. S. F. MUGHABGHAB, Atlas of Neutron Resonances: Thermal Cross Sections and Resonance Parameters, Elsevier Publisher, Amsterdam ~2006!. 14. D. ROCHMAN and A. J. KONING, “ Pb and Bi Neutron Data Libraries with Full Covariance Evaluation and Improved Integral Tests,” Nucl. Instrum. Methods A, 589, 85 ~2008!. 23. R. CAPOTE and D. L. SMITH, “An Investigation of the Performance of the Unified Monte Carlo Method of Neutron Cross Section Data Evaluation,” Nucl. Data Sheets, 109, 2768 ~2008!. 24. D. ROCHMAN and A. J. KONING, “500 Random Evaluations of 239 Pu,” OECD0NEA JEF0DOC-1327, Organisation for Economic Co-operation and Development0Nuclear Energy Agency ~May 2010!. NUCLEAR SCIENCE AND ENGINEERING VOL. 169 SEP. 2011

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