S. Ganesan. Theoretical Physics Division. Bhabha Atomic Research Centre. Trombay, Mumbai INDIA

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1 EXPERIENCES IN PROCESSING OF BASIC EVALUATED NUCLEAR DATA FILES: LINEARIZATION, RESONANCE RECONSTRUCTION, DOPPLER BROADENING AND CROSS SECTION AVERAGING By S. Ganesan Theoretical Physics Division Bhabha Atomic Research Centre Trombay, Mumbai INDIA Abstract This paper presents some interesting experiences in processing of basic evaluated nuclear data files with special emphasis on some experiences in linearization, resonance reconstruction, Doppler broadening and multigroup averaging of neutron induced cross section data bases available in ENDF/B format. 1. INTRODUCTION The subjects of linearization, resonance reconstruction, Doppler broadening and multigroup averaging of neutron induced reaction cross sections in ENDF/B format [1] have been extensively covered in an excellent manner in the manual of the NJOY code system [2] and in an excellent review article by D. E. Cullen [3]. Presented in the Fortran source codes of the IAEA pre-processing code (PREPRO) system [4] and of the NJOY code system [2] are also useful comments and hints to guide the users. In addition, the outputs of these code systems also provide warning messages where necessary in order to help the users in physical interpretation of outputs. The purpose of this paper is to share some thoughts of the author on the use and application of some modules of the NJOY and the PREPRO code systems. The author has very high regards for the evaluators of the ENDF/B system and the authors of the processing codes and pre-processing codes mentioned in this paper. The discrepancies which are pointed out and discussed in these notes are from an educational point of view and are not in any way intended to scare the users away from processing and using the ENDF/B formatted nuclear data files for application calculations. The material of the lecture notes is organised as follows. In the main text, we review some interesting aspects of processing of basic evaluated nuclear data files in ENDF/B format [1] with special emphasis on some experiences in linearization, resonance reconstruction, Doppler broadening and multigroup averaging of cross sections. To focus attention on the main subject, we shift some general background material to the Appendices. In Appendix A, a few remarks on the philosophy and evolution of the subject of cross section processing are presented to provide some background matter in proper perspective. This is followed in Appendix B by some comments on the production of new working libraries for application calculations. Although hand-written and informal transparencies covered some mathematical derivations during the author s lecture at this

2 ICTP Workshop, this paper does not include them to save space as such material is readily available in the literature [2, 3]. The lecture notes of Prof. F. H. Fröhner provide all the mathematical formulae of various resonance formalisms [5]. The formulae for average cross sections are presented in the lecture notes of Prof. A. Trkov [6] distributed at this Workshop. 2. ON THE NJOY AND THE IAEA PRE-PROCESSING CODE SYSTEMS Presented below are a few general remarks on the NJOY [2] and the IAEA preprocessing code systems [4] from the point of view of the users. The NJOY code system [2] has been widely used around the world in many leading laboratories and has served successfully as a general-purpose link between ENDF-formatted evaluated nuclear data files and important applications such as shield design, thermal reactor core design, fusion reactor blanket design, radiotherapy facility design and many others. The NJOY system has been under continuous development in Los Alamos National Laboratory since During the last 22 years it has gone through a number of revisions, in response to the development of the new ENDF formats, in order to add new processing capabilities, in response to changing computer systems and in order to fix errors. It should be noted that the NJOY code system is, by necessity, complex and large with over lines of Fortran instructions. It has a comprehensive approach to interfacing ENDF/B formatted data to application codes. The ENDF/B pre-processing codes (PREPRO), developed by D. E. Cullen [4] are, by design, in the nature of utility codes which have been successfully used at the classical nuclear data centres. Some of the PREPRO codes performs functions such as linearization of File 3 data, reconstruction of resonance cross sections, Doppler broadening of resonance cross sections, multigroup averaging of cross sections etc. See Ref. [4] for more details. The PREPRO codes are not designed by D. E. Cullen to produce a comprehensive working library for reactor applications. They have also played and will continue to play, in the opinion of the author of this paper, an important role in Quality Assurance studies in pre- processing. In fact both the pre-processing codes and the NJOY serve useful purposes in certifying processability of the newly created basic evaluated data files. Simple and higher-order physics consistency checks can be performed on the basic evaluated data file using these codes. See for instance, Section 3 and Section 8. The comparisons and discrepancies discussed in this paper have obviously been seen with the older versions of these codes and are meant for educative and illustrative purposes only. It is recommended that the latest versions of these codes should be used as the older versions have been superseded by many improvements based on feedback from the users around the world. SOME EXPERIENCES IN LINEARIZATION OF ENDF/B CROSS SECTIONS. Following Ref. [7], we present some general remarks below: The Evaluated Nuclear Data File, version B (ENDF/B) format [1] is now used throughout the world by nuclear data evaluators to define the evaluated data, and by nuclear data users as a starting point from which the evaluated data is processed in the form in which it will be used in applications, e.g. temperature -dependent, self-shielded multigroup cross sections. See Figure A.1.

3 The ENDF/B "tapes" [1] are subdivided internally into "materials" (MAT), "files" (MF) and "sections" (MT). A given MAT contains all data for a particular evaluation for an element or isotope (for example, MAT 9640 is an evaluation for 245 Cm 96 in JEF-2). A "file" contains a particular type of data for that MAT: MF=2 contains resonance parameters; MF=3 contains cross sections versus energy data. A "section" refers to a particular reaction for example, MT = 2 represents elastic scattering cross section data and MT=102 the neutron induced capture reaction cross section. In file 2, the resonance data is contained in the form of resolved and/or unresolved resonance parameters. In order to obtain the total cross section (MT=1), the radiative capture cross section (MT=102), fission cross section (MT=18) and elastic scattering cross sections (MT=2), the cross sections which are calculated from these parameters using the recommended formalism must be added to the background cross sections for neutron energies within the energy ranges specified for the resolved and/or unresolved resonance parameters. Thus, within the ENDF/B format, in the resonance region, cross sections are defined by resolved and unresolved resonance parameters plus a "background" cross section. For use in applications the contributions of the resonance parameters and "background" cross section must be combined in order to calculate temperature-dependent, self shielded multigroup cross sections. Several steps are involved in creating tabulated (energy, cross section) pairs which define cross section at any energy by linear interpolation at a specified temperature and each step will introduce an uncertainty due to cross section processing. Generally the running time of the computer codes used in each step will increase when we attempt to decrease the uncertainty due to processing. It is therefore important to balance the need for accurate results with available computer resources. Since one objective of this lecture is to point out the importance of controlling and limiting the uncertainty due to cross section processing, we will briefly describe each processing step and recommend practical uncertainties that can be used. The first step in creating a tabulated, linearly interpolable cross sections is to linearize all tabulated "background" cross sections. The ENDF/B format allows tabulated cross sections to have any combination of five interpolation laws associated with the table. Since in applications the user will be interested in the integral of cross sections over energy, the processing codes take care to use the evaluator specified interpolation laws to uniquely define the cross sections at all energies of interest; failure to use the correct interpolation laws can lead to large cross section errors. Although the use of ENDF/B interpolation laws can be very convenient to use for evaluation (e.g. a 1/v cross section can be exactly represented by logarithmic interpolation in energy versus cross section ) they can create problems when used in applications. One of the problems [8-10] that arise in linearization of the evaluated data is due to inconsistent definitions of sum cross sections such as the total. For example, a 1/v capture cross section and constant elastic cross section can each be represented using the ENDF/B interpolation law which can be used to represent the total cross section, which in this case is a sum of the 1/v capture + the constant elastic. Mechanically, the total can be made equal to the sum of its parts at the energies at which the cross sections are tabulated. However, unless the cross sections are tabulated on a very fine energy grid the use of non linear interpolation can lead to significant inconsistencies at energies between tabulated values; unfortunately, this often occurs with ENDF/B evaluations. Only by reducing all cross sections to a form which obey linear interpolation is it possible to consistently represent sum cross section, such as the total, at all energies. The interested reader can find in the literature [9, 10] a large number of

4 very interesting comparison graphs illustrating the magnitude of this apparently simple linearization problem revealing significant inconsistencies at energies between tabulated values of total cross sections for several cases of evaluations. It is educative and interesting to reproduce here what Red Cullen pointed out [8] in a private communication to S.Ganesan in 1991: " Indeed this is an old problem with the ENDF/B evaluation. Bob Seaman from Los Alamos National Laboratory pointed out that depending on whether one started out from the total or from the parts one could calculate very different resonance integral. He also pointed out that with the five allowed ENDF/B interpolation schemes it is impossible to represent sum cross section e.g. the total cross section using any interpolation scheme but linear-linear. The basic problem is then an inconsistency in the ENDF/B-VI evaluated file and what the RECONR module and the RECENT/FIXUP do is merely one possible way to deal with this problem and this is not necessarily the best way to deal with it". Presented in this paragraph is an interesting experience reported recently by Trkov [11] which provides an example of a practical impact on integral result: of the use of ENDF/B-VI, Rev. 2 versus ENDF/B-VI, Rev. 3 cross sections for aluminium: Trkov has reported [11] that he retrieved the basic evaluated nuclear data file for aluminium from the IAEA on-line nuclear data services at the end of August 1995 and performed analysis of thermal reactor lattices TRX, BAPL and DIMPLE. In this paragraph we will limit our review to his experience with the cross sections for Al-27 as it throws light on the pitfall associated with data in linearized form in the evaluation. His calculations showed that the effect of replacing the aluminium data from ENDF/B-VI, Rev. 2 by Rev. 3 data was to decrease the multiplication factor by more than 0.2% deltak/k. Such a decrease is in contradiction with the statement in the evaluation description, which says that the total cross section below 20 MeV and the radiative capture cross section below 100 kev remain the same. The aluminium data from the ENDF/B-VI Rev. 2 and Rev. 3 were processed with the Pre-Processing codes [4] LINEAR-94/1, RECENT -94/1 and compared with COMPLOT-94/1. The results of graphical inter-comparison [11] showed wiggles in the Rev. 3 data which are typical of an inadequate interpolation, giving rise to differences in excess of 50% in the cross sections. Indeed it was found that the request for a log-log interpolation in the first three data points of the total cross section and the first ten points of the radiative capture cross section in Rev. 2 data have been changed to linear-linear interpolation in Rev. 3, without changing the energy grid and the cross section values. The evidence presented by Trkov [11] indicates that the interpolation law for the total, the non-elastic and the radiative capture cross sections for aluminium data of ENDF/B-VI, Rev. 3 was incorrect. After some changes to the interpolation law flags, the overall effects on the thermal lattice integral parameters due to the replacement of the aluminium data were also small. Considering the magnitude of influence of the incorrect interpolation law, the data for aluminium should be corrected before general distribution and application. A corrected ENDF/B-6 file is expected [11] within the 1996 update of the ENDF/B-6 database. As pointed out in [3] and [7], the integral of the cross sections using non-linear interpolation can often be defined in analytical form. Unfortunately the resulting analytical expressions can be surprisingly numerically unstable when used on a computer. Considering all the five possible ENDF/B interpolation laws and attempting to identify and eliminate all the situations which lead to numerical instabilities requires consideration of many limiting situations which are often difficult to identify and analyse.

5 As in the case of resonance contribution, it is not possible to exactly replace a table of cross section versus energy where non- linear interpolation is specified by a new table of cross section versus energy where linear interpolation is specified. However it is possible to do this within any required accuracy. The program LINEAR of the PRE-PRO [4] is used to convert ENDF/B cross sections to a form which obey linear interpolation. This program requires very little computer time even when the data is linearized to higher precision. It is therefore recommended that "background" cross sections be linearized to 0.1 % accuracy (which is negligible) compared to the uncertainty in virtually any cross section. Presented below are a few remarks following Ref. [7] on combining resonance and "background" contributions. One of the tasks performed by the RECENT code [4] or the RECONR module of the NJOY code system [2] is to define "cold" (0 K) tabulated, cross sections which obey the law of linear interpolation. Using an iterative procedure program RECENT first calculates the resonance contributions as a tabulated cross sections which obey linear interpolation to within any user specified uncertainty. Once the resonance and "background" contributions are both in tabulated form each obeying linear interpolation they are added together to define the real cross sections in tabulated form obeying linear interpolation. It is worth noting here again the importance of using cross sections that obey linear interpolation; unless the resonance and "background" cross sections are both in this form they cannot be simply added together to define real cross sections which obey any of the ENDF/B interpolation laws. It should be noted that the size of the databases have become very large and the representation of the data in terms of physics has become increasingly complex leading to the requirement of specialised skills in electronic access, storage, retrieval, management and processing. For instance, the ENDF/B-VI file for U-238 has now 801 s-wave and 1,112 p- wave i.e., a total of 1,913 resolved resonances in the multilevel Reich-Moore formalism. To compute the cross section data from such a large number of resonances with the code LINEAR/RECENT at 0.1% accuracy the author required in 1991, 19.5 hours of CPU time on a multi-processing IBM 3081 mainframe (14 MIPs) computer, and the resulting data file containing the U-238 cross sections as a function of energy had a size of records, that is 75.2 MB. When the same problem was solved with the reduced accuracy of 0.5% and the code RECONR/NJOY89.31, 156 minutes CPU time were required, and the resulting cross section data file had a size of 148,353 records = 12 MB. A Pentium 100 MHz computer at BARC, Mumbai was able to run in 1996, in a dedicated mode, in about 150 minutes the same LINEAR/RECENT run with 0.1% resonance reconstruction tolerance for U-238 thus giving confidence that a dedicated PC can now-a-days perform most of the processing tasks on a desktop. Of the series of PREPRO codes which we will discuss at this Workshop, program RECENT requires the longest running time. Therefore when using the RECENT code in order to balance the required computer time to accuracy requirements it may be necessary to somewhat compromise the accuracy of the results. This is particularly true when dealing with heavy even-even nuclei such as 232 Th, 238 U or 240 Pu which have a rather large number of isolated resonances. A comparison of the results of a CRAY run for the RECONR of the NJOY code system with 7 digits accuracy for energies with the result of the RECENT code which outputs energies up to 9 digits for energies for a p-wave resonance in Th-232 with a resonance reconstruction tolerance of 0.1% is available in Ref. [10]. For Ni-60, intercomparison results of using single and double precision versions of the NJOY outputting the energy points in 7 and 9 digits respectively using an IBM mainframe computer are available in Ref. [10] for total, elastic and capture illustrating the effect of precision in energy on the cross section line shapes for sharp resonances. In cases where the cross section behaviour

6 exhibits steep variations as in the case of sharp resonances at higher energies, interesting interplay between accuracy specified by the user in linearization and available precision of the computer can occur. The current international trend is to set the resonance reconstruction tolerance to 0.1 % as powerful desktop computers with large disk capacity have become available. Nuclear data centres may be able to calculate results to high precision, say 0.1% and distribute the results for wider use. Therefore, before investing large amounts of computer time in cross section reconstruction, the users who lack computer resources may wish to contact the Nuclear Data Centre to determine if the resonance reconstructed data is already available. 4. PARAMETER VERSUS CROSS SECTION INTERPOLATION IN THE UNRESOLVED RESONANCE REGION The treatment of unresolved resonance region is one of the most interesting problems in processing [1-5, 12, 15, 16]. It may be noted that, as explained in the documentation for the code RECENT, the RECENT only interpolates unresolved resonance parameters. The ENDF/B document [1] states that the evaluators should include enough energy points so that the difference between the results obtained using cross section or parameter interpolation are negligible. These differences can be removed either by the evaluators correcting their results or by the user by assuming that the uncertainty is as large as the differences that we are finding. In Ref. [9] and Ref. [10], Ganesan and Muir reported differences in the average "point" cross sections calculated from the same basic data file by the two processing modules RECONR and RECENT at zero Kelvin in the unresolved resonance region for some isotopes in the period with the versions of the codes available at that time. In this paragraph, we briefly point out an interesting study by J. L. Rowlands [13] concerning interpolation in the unresolved resonance region. Rowlands [13] has reported that comparisons between NJOY/THEMIS and CALENDF have indicated significant differences, in the unresolved resonance region for several isotopes in the jef-2 evaluation. The cross section calculated for 245 Cm from JEF-2 at the nodes at 3000 ev is 45.9 barns using UNRESR and interpolation of cross sections calculated at the nodes. However, the value of the calculated cross section using the average parameters was 9.2 barns at the same energy. The differences were thus up to a factor of 5 in the case of 245 Cm. The problem which has been traced by Rowlands [13] is due to the use of a single energy set of unresolved parameters for the whole energy range which is leading to large uncertainties due to interpolation. It is due to the fact that in the NJOY the interpolation is linear in energy between cross section values calculated at the points where the resonance parameters are tabulated, or at the ends of the range if there is a single set of parameters for the unresolved resonance region, as is the case in the JEF-2 evaluation for 245 Cm. Rowlands [13] provides also a prescription for the required energy spacing in the ENDF/B tabulation. For a 1% accuracy, he finds [13] that we must have an energy spacing of a factor of 1.5 or less. A better procedure according to Rowlands [13] is to specify the infinite dilution cross-section values, then the error will only be in the shielding factors at intermediate values of the energies and the variations in this are smaller. However, the infinite dilution cross-sections must be specified on a fine energy mesh, and the mean parameters should not be on a widely spaced mesh. As pointed out in [12], the procedure used in the unresolved resonance region in the ENDF/B system is not satisfactory from a physics point of view. Going to too fine an energy mesh at the time of evaluation invokes the assumption that the statistical properties change rapidly with energy. Ideally the energy mesh in the unresolved resonance region

7 should be sufficiently widely spaced so that the there are enough resonances in each mesh to make the statistical assumption valid. 5. REMARKS ON NUMERICALLY DOPPLER BROADENING In order to define tabulated cross sections that obey the law of linear interpolation at each required temperature, the SIGMA1 method [14, 3, 4, 7] or the BROADR module of the NJOY [2] uses the free atom Doppler broadening equation and a tabulation of values of "cold" cross sections. In order to analytically define the cross section at any energy, at any higher temperature, the SIGMA1 method assumes that the "cold" cross sections are available as a tabulation obeying the law of linear interpolation. The present day version of SIGMA1 or BROADR runs much faster due to the fact [7] that the original algorithm by Cullen and Weisbin [14] calculated the "hot" cross section at all of the energies at which the "cold" cross sections were tabulated, whereas the new algorithm calculates the "hot" cross section only at energies where the "hot" cross section is required. Since generally the "hot" cross section is smoother and requires considerably fewer energy points to accurately represent the cross sections, the new algorithm [7] calculates the "hot" cross section at fewer energies resulting in the reduction of running time. The running time of the code SIGMA1 or that of the BROADR will depend on the number of points used to represent the "cold" cross sections. At each temperature of interest. starting from a tabulation of cross section values obeying the linear interpolation law and smooth weighting functions (e.g. Maxwellian, 1/v, fission spectra at successively higher energies), and using the Bondarenko self-shielding model, it is analytically possible to define self-shielded cross sections By only considering linearly interpolable data it is rather straight forward to identify and eliminate all cases where the analytical expression could potentially become numerically unstable and implement the resulting algorithms in program GROUPIE [4]. Since this integration can be performed exactly it does not introduce any uncertainty due to cross section processing. 6. COMPARISON OF Ψ -χ METHOD WITH KERNEL DOPPLER BROADENING Currently, cross section processing codes use one of the two methods of calculation to process evaluated data into a multigroup form. One method uses the J* - method of Hwang [5, 15, 16] in which the familiar line shape broadening functions Ψ -χ are used to define the temperature dependence of the resonance line shape, and the required group averages are in turn directly defined in terms of integrals involving these Ψ -χ functions. This method has the advantage that it can be used in the resolved and unresolved resonance region and it is very economical in terms of computer time. It has the disadvantage that, strictly speaking, the Ψ - χ method can only be used with single-level Breit-Wigner resonances and it uses the narrow resonance approximation in order to define the multigroup integrals involving these functions. The SIGMA1 method, also adopted in the BROADR module of the NJOY codes system, combines the resonance and "background" contributions to define the "cold" (0 K) cross sections in tabular form in which linear interpolation in energy and cross section can be used to define the cross section at energies between the energies at which the cross sections are tabulated. This "cold" cross section is then numerically Doppler broadened [14, 3, 4, 7] to define the cross sections at higher temperatures in a tabular form that obeys linear

8 interpolation. The tabular cross sections at each temperature are then analytically integrated to define temperature-dependent self-shielded cross sections. This method has the advantage that it can be used with any resonance formalism, to define the "cold" cross sections e.g. single or multilevel Breit-Wigner, Reich- Moore or Adler-Adler. In addition, in principle it can be used with any self-shielding model, e.g. the intermediate resonance method, to define the self-shielded cross sections. As such this method should be potentially most versatile and accurate. It has the disadvantage that compared to the J* method, this method requires a large amount of computer time and it can only be used in the resolved resonance region. Note that in the NJOY code system, the Ψ -χ method can be invoked in the RECONR module. An interesting comparison study was carried out numerically for 232 Th from JEF-1 by Riyanto Raharjo [17] while he underwent an IAEA fellowship training in 1991 at the Nuclear Data Section of the IAEA. The interesting graphical results of comparison of Ψ -χ method with kernel Doppler broadening using the NJOY codes system for 232 Th from JEF-1 are available in the unpublished IAEA Fellowship report of Raharjo [17]. The kernel broadening technique adopted by the BROADR module required 2.21 times more computing time than the Ψ -χ method. The Ψ -χ method does not Doppler broaden the 8.34 ev resonance as the basic file of JEF-1 for 232 Th is in the form of a tabulation and not in the form of a Single Level Breit Wigner resonance parameter for this particular resonance. The Ψ -χ method does not Doppler broaden the non-resonance regions away from the resonance such as the constant scattering cross section in the thermal energy region. There are also notable differences in the way the scattering cross sections are Doppler broadened at the interference minima [17]. 7. REMARKS ON UNCERTAINTY DUE TO CROSS SECTION PRE-PROCESSING In the resolved resonance region, in principle, the contribution to each cross section from File 3 should be Doppler broadened, but in practice many codes in the past ignored this effect. See Ref. [7]. It is therefore recommended that the evaluator keeps File 3 contributions in the resolved resonance range and the unresolved resonance range small enough and/or smooth enough so that the omission of Doppler broadening does not "significantly " alter the combined File 2 plus File 3 results for Doppler broadening to the required temperatures. It is not possible to exactly represent the resonance contribution to the cross sections in tabulated form following the law of linear interpolation. However it is possible to represent the cross section in this form to any required accuracy; in particular, the uncertainty introduced due to cross section processing can be made small compared to the uncertainties in the cross sections. Therefore from a practical view point it is possible to represent the resonance contributions to the cross sections in an "equivalent" tabulated form which obey the linear interpolation law; "equivalent" in the sense that the two will differ only by the uncertainty due to cross section processing. The uncertainties due to : (a) linearizing "background" cross sections; (b) combining the resonance and "background" cross sections; and (c) numerically Doppler broadening will combine to define the total uncertainty due to cross section processing. As mentioned above, the final integration to define temperature dependent self-shielded cross sections does not introduce any uncertainty. In principle, the uncertainties introduced by steps (a)-(c) could simply add linearly to produce a total uncertainty. In practice, the uncertainties introduced are

9 independent and therefore we can consider a quadratic combination. The current international trend is to (a) linearize the basic data to 0.1% tolerance (b) combine resonance and background contributions to 0.1% (c) Doppler broaden with a numerical accuracy of 0.1%. In such a combination, we expect the total uncertainty in the energy dependent cross sections at each temperature due to pre-processing not to exceed ( ) 1/2 = 0.173% When we use these energy dependent cross section to integrate to define self-shielded multigroup cross sections the results will have an uncertainty not exceeding 0.173%, and in most cases due to cross-cancellation uncertainties will be much less, e.g. contributions to the integral from energy points where the cross sections is up to 0.173% too high will be compensated for by the contribution from points where the cross section is down to 0.173% too low. 8. INFLUENCE OF FILE-3 ON CALCULATED SELF-SHIELDING FACTORS IN THE UNRESOLVED RESONANCE REGION The unresolved resonance parameters are specified in the ENDF/B formatted files [1] in order to calculate the self-shielding factors for various temperatures and dilution cross sections in the unresolved resonance region. While processing the basic nuclear data file for 181 Ta from JENDL-2 using the UNRESR module of the NJOY system, the author observed [18] negative self-shielded cross sections for the temperature 300 K at the background dilution cross sections =25, 50 and 100 barns in the energy groups up to 5000 ev in the unresolved resonance region These self-shielded cross sections became more negative at lower dilution cross sections. The physical reason for the appearance of negative selfshielding factors for the broad groups in the unresolved resonance region was traced to be due to the fact that the unresolved parameters in File 2 were the result of poor fitting of unresolved resonance parameters to the average cross sections in the unresolved resonance region, leading to the presence of large negative background cross sections at some energy points in File 3 in this case for 181 Ta in JENDL-2. As background cross sections in File 3 for 181 Ta in JENDL-2 were large negative values and the File 3 values are not Doppler broadened in the unresolved resonance region in any case by the processing module such as the UNRESR of the NJOY code system, the "effective" self-shielded cross sections became negative at some dilution cross sections and temperatures in the output of UNRESR. This defect in JENDL-2 evaluation has been removed by the evaluators in JENDL-3 evaluation by providing fitted unresolved parameters that reproduce perfectly the average total and partial reaction cross sections, thereby necessitating only zero background corrections in File 3. The self-shielding factors in the broad energy groups in the unresolved resonance region for 181 Ta in JENDL-3, consequently come out positive at all background dilution cross sections in the unresolved resonance region when processed using the UNRESR module of the NJOY code system. The above mentioned experience demonstrates that the negative cross sections which are present in the File 3 in the energy range of the unresolved resonance energy region can pose problems by leading to unphysical values of self-shielding factors in the unresolved resonance region. The evaluators of the unresolved resonance region can make a higher order physical check whether the evaluated unresolved resonance parameters produce unphysical (negative) self-shielded cross sections by using the processing code system such as the NJOY. Note that the production of non-negative self-shielded cross sections by itself does not automatically imply the correctness of the calculated self-shielding effects [12].

10 9. REMARKS ON COLLAPSING OF FINE GROUP AVERAGES INTO BROAD GROUP AVERAGES We describe below an interesting example of the error that can be introduced due to collapsing of fine group cross sections into broad group cross sections. In general collapsing a fine group structure into a coarse one is only allowed when the coarse group boundaries are a subset of the fine group ones [3]. However, the effect of using non coincident boundaries will be small when the number of fine groups per energy interval is much larger than that of the coarse groups or when the original pointwise cross sections do not vary much with energy. Wienke [19], based on his results of calculations and comparisons for the dosimetry reactions, concluded that the generation of VITAMIN-J 175 multigroup cross sections by collapsing SAND-II 640 multigroup data leads to unacceptable errors in the calculated 175 group cross sections. It is recommended, where ever possible, to start directly from the point data to generate multigroup cross sections in the required energy group structure. 10. ON GROUP AVERAGING OF CROSS SECTION LINE SHAPES USING A TABULATED FLUX SPECTRUM Wienke and Ganesan demonstrated [20] that the calculation of group cross sections for resonant materials which exhibit sharp resonances in the high energy region such as for the isotopes of iron, chromium and nickel, needs special caution when one is required to use a tabulation for the flux spectrum to obtain flux weighted group average cross sections using, for example, the GROUPIE code. Care should be taken to provide the tabulation of fluxes at as many points as there are for the description of cross sections obeying the law of linear interpolation [20]. For instance, in the case of averaging of 56 Fe(n,γ ) cross sections from ENDF/B-VI, the number of (energy, cross section) pairs in the output of the RECENT code is around 30,000 at zero Kelvin with 0.1% tolerance in resonance reconstruction. If one wishes to use the GROUPIE code to obtain the "175 groups VITAMIN-J format group cross sections" and the flux spectrum is that of the VITAMIN-J which is not a spectrum available as a standard option in GROUPIE, the user should take care to provide a tabulation of the fluxes not at 175 points but at points. It was found [20] that the group cross sections can be in error by as much a factor of 10 if the flux spectrum of VITAMIN-J is provided at only 175 points instead of at as many fine points as those at which the point cross sections are available in such calculations. Note that the GROUPIE or the GROUPR of the NJOY calculate correctly the group cross sections for cases which invoke the built-in flux weighting spectrum. Care has to be exercised when one uses the option of feeding in a tabulation of fluxes externally to such codes. 11. SUMMARY AND CONCLUDING REMARKS In this paper, we reviewed some interesting aspects of processing of basic evaluated nuclear data files in ENDF/B format. One of the problems that arise in linearization of the evaluated data due to inconsistent definitions of sum cross sections such as the total was mentioned. Several pitfalls encountered in creating tabulated cross sections obeying the law of linear interpolation, at several temperatures were mentioned. An example of the inconsistency arising from "parameter versus cross section interpolation" in the unresolved

11 resonance region was reviewed. It was pointed out that the evaluators of the unresolved resonance region can, by using the processing code system such as the NJOY, make higher order physical checks and examine whether the evaluated unresolved resonance parameters produce unphysical (negative) temperature dependent self-shielded cross sections. It was pointed out that the collapsing of fine group averages into broad group averages can lead to unacceptable errors in some cases. We also pointed out that the calculation of group cross sections for resonant materials which exhibit sharp resonances in the high energy region such as for the isotopes of iron, chromium and nickel, needs special caution when one is required to use a tabulation for the flux spectrum to obtain flux weighted group average cross sections. The accuracy of the processed data should correctly reflect the quality of the basic evaluated data. The gap between the creator and the end-user of the ENDF/B files can be greatly reduced by having some limited processing activities at the classical data centres. It was pointed out that the nuclear data processing tasks performed at the stage of evaluation help perform Quality Assurance studies as part of data evaluation process leading to creation of an acceptable ENDF/B formatted file for the users.

12 Fig. 1 Steps in preparation of working nuclear data library for applications APPENDIX A PHILOSOPHY AND EVOLUTION OF THE SUBJECT OF CROSS SECTION PROCESSING The advanced nuclear reactor analyses is essentially a fundamental approach without depending much on pure empiricism. It originated largely as a result of demanding nuclear

13 design requirements to have a firm scientific foundation in the design and safe operation of nuclear reactors and nuclear applications. Internationally, the evolution of the subject of preparation of working nuclear data libraries has included five basic technologies: 1. Cross section measurements 2. Cross-section evaluations 3. Cross section processing 4. Integral experiments 5. Neutron-photon coupled transport calculations and response functions. All these five basic technologies are well known and one or more of these steps are always encountered in the literature. The process of getting the working libraries for design calculations requires an iterative sequence of events to yield a quality assured transport cross section library. See Figs. A.1 for some illustration. The international nuclear data community has, over several decades, efficiently provided state-of-the-art experimental and theoretical data which were needed in applications [21-26]. Several evaluated nuclear data files providing cross sections for neutron induced reactions and photon productions in various important isotopes/elements in the periodic table are available [23, 25, 26]. The first two steps, "cross section measurements" and "cross-section evaluations" lead to the creation of the basic evaluated nuclear data files in the well known ENDF/B format. As illustrated in Fig. A.1, we stress that the recently released basic evaluated nuclear data files [23] such as ENDF/B-VI, JENDL-3.2, BROND-2.2 and CENDL-2.2 etc., available in the computerised ENDF/B format [1] are not directly used as input to neutronics or other applied calculations but are first converted to pre-processed files which are post-processed into multigroup files which are then cast into specially formatted working libraries that are compatible with neutronic codes. Nuclear data processing is the vital link between evaluated data files and the users as discussed well in the literature [27-42]. However, both the developed and developing countries are finding it difficult [30, 31] to sustain and fund adequately the nuclear data processing activities. The processing tasks demand specialised expertise using computer resources committed over a long period of time (several years) to execute the tasks as pointed out for instance by J.E. White [32]. There has been no active common forum to bring the scientists, in particular in developing countries working in this area together. The field of study of nuclear data processing and preparation of processed nuclear data libraries form the connecting bridge between basic evaluated nuclear data files and application calculations. The subject involves development and validation of computer software using knowledge of ENDF/B formats and conventions, numerical reconstruction of resonance line shapes, calculations of Doppler broadening, thermalization effects, selfshielding factors in resolved and unresolved resonance regions, transfer matrices for various Legendre orders etc. The nuclear data processing requirement must satisfy the very important requirement that errors due to processing of the basic data does not introduce unacceptable errors in the processed data which are the results of processing [7, 11, 30, 31]. The accuracy of the processed data should correctly reflect the quality of the basic evaluated data. See for example [7, 38, 40-42]. APPENDIX B

14 REMARKS ON PRODUCTION OF WORKING LIBRARIES FOR APPLICATION CALCULATIONS The task of updating the multigroup library for reactor calculations involves the tasks of processing the computerised ENDF/B formatted [1] basic neutron cross section data files [23] such as ENDF/B-VI.x, JENDL-3.x, BROND-2.x and CENDL-2.x etc., (where x is the revision/update number) using the nuclear data processing code system such the NJOY code system [2], taking care to ensure that the quality of the working library correctly reflects the quality of the basic evaluated data file from which the working library is derived, keeping the conventions and definitions of the group constants as expected by the nuclear design system, without introducing unacceptable errors in processing. In the opinion of the author, there is a basic need to bring out a handbook which will provide comparison of evaluated data from various sources (examples: JENDL3.x, BROND- 2.x, ENDF/B-VI.x, JEF-2.x, CENDL-2.x etc.) with experimental data from EXFOR to highlight existing convergence or non-convergence of basic evaluated data and spread of available experimental data with uncertainties for all isotopes and elements for which evaluations are available. Such a handbook will help every scientist and engineer to appreciate the existing gaps and spread in measurements and in the data of evaluations made by different countries in relation to the experimental uncertainties for each reaction cross section for each isotope/element. In the resolved resonance region such a comparison is presently of limited scope in most of the cases of isotopes and elements as point experimental cross section in the resolved resonance region have not been traditionally compiled into EXFOR thus far except in the case of some isotopes (e.g., Fe-56). The compiled nuclear data in the resonance region, traditionally input into EXFOR [23], have been in the form of resolved resonance parameters extracted from the transmission experiments. This is acceptable if the user is guaranteed that the resolved resonance parameters with its specified resonance formalism as present in EXFOR reproduce exactly the originally obtained experimental point cross section data in the resolved resonance region. Today, for a scientist looking freshly at the status of nuclear data, it is seen that, taking any nuclide as example, one can get [23, 26] the neutron interaction cross section data from various countries in ENDF/B format, for example: ENDF/ B-VI.2 (USA), JEF-2.2 (Europe), BROND-2.2 (Russia), JENDL-3.2(Japan), CENDL-2 (China) etc. Presently, with so many data files for the same isotope for the same physical quantity being available from various countries, it is a complex and time consuming task extending to several years for the poor user team to arrive at a decision as to which data file is better for a specific application. The author sincerely wishes that over the next few decades, many data files existing to provide numerical cross section data for the same physical reaction process will converge and we will hopefully have one unique and internationally accepted numerical data file along with uncertainties for each isotope for use in applications. REFERENCES 1. "ENDF-102-Data Formats and Procedures for the Evaluated Nuclear Data file ENDF-6," by P.F. Rose and C. L. Dunford, US National Nuclear Data Centre, Brookhaven National Laboratory, Upton, NY, USA, IAEA-NDS-76, Rev. 4, Jan. 1992, Vienna, Austria.

15 2. R.E. MacFarlane, "NJOY94, A Code System for producing Pointwise and Multigroup Neutron and Photon Cross Sections from ENDF/B Evaluated Data," PSR-171, Radiation Shielding Information Centre, USA (1994). 3. D. E. Cullen, "Nuclear Cross Section Preparation," pp in CRC HANDBOOK ON NUCLEAR REACTOR CALCULATIONS, Yigal Ronen, (Editor), CRC Press Inc. (1988). 4. D.E. Cullen, "The ENDF Pre-processing Codes," IAEA-NDS-39, Rev. 8, January 1994, Nuclear Data Section, International Atomic Energy Agency, Vienna (1994). 5. F. H. Fröhner, "Reactor Safety Coefficients and Neutron Resonances," Lecture note presented at this Workshop on Nuclear Reaction Data and Nuclear Reactors-Physics, Design and Safety, 15 April-17 May These Proceedings (1996). 6. A. Trkov, "Processed Evaluated Data for Reactor Calculations," Lecture note presented at this Workshop on Nuclear Reaction Data and Nuclear Reactors-Physics, Design and Safety, 15 April-17 May These Proceedings (1996). 7. S. Ganesan, V. Gopalakrishnan, M. M. Ramanadhan and D. E. Cullen, "Verification of the Accuracy of Doppler Broadened, Self-Shielded Multigroup Cross Sections for Fast Power Reactor Applications," Annals of Nucl. Energy, Vol. 15, No.3, pp (1988). 8. D. E. Cullen (1991). communication to S. Ganesan. 9. S. Ganesan and D. W. Muir, "First results of intercomparison of NJOY89.31 with the IAEA pre-processing codes for FENDL materials for zero Kelvin and 300 Kelvin cross section line shapes of ENDF/B-VI. May 10, 1991, Unpublished. 10. S. Ganesan and D.W. Muir, "IAEA Activities in Nuclear Data Processing for Thermal, Fast and Fusion Reactor Applications using the NJOY System," pp , in Proceedings of the OECD / NEA Seminar on NJOY-91 and THEMIS, OECD/NEA Data Bank, Saclay 7-9 April 1992 (1994), OECD, Paris. 11. A. Trkov, "The Impact of ENDF/B-VI Rev. 3 Data on Thermal Reactor Lattices," INDC(SLN)-002, IAEA Nuclear Data Section, Vienna, Austria (October 1995). 12. S. Ganesan, Annals of Nucl. Energy, Vol 9, p. 481 (1982). See also S. Ganesan, Nucl. Sci. Engg. Vol. 74, p.49 (1980). 13. John L. Rowlands, "Interpolation in the Unresolved Resonance Region," pp , in Proceedings of the OECD / NEA Seminar on NJOY-91 and THEMIS, OECD/NEA Data Bank, Saclay, 7-9 April 1992, OECD, Paris (1994). 14. D.E. Cullen and C. R. Weisbin, Nucl. Sci. Engg. 60, 199 (1976). 15. R. N. Hwang, Nucl. Sci. Engg. 21, 523 (1965). 16. R. N. Hwang, Nucl. Sci. Engg. 52, 157 (1965).

16 17. R. Raharjo, "Brief Report on Activities during in-house group fellowship training programme in computer based nuclear data processing for reactor physics applications," 1 March - 15 June Unpublished document (1991). 18. S. Ganesan, "Observation of negative self-shielding factors in the energy groups in the unresolved resonance region for 181 Ta from JENDL-2," Unpublished (1988). 19. H. Wienke, "A Study into the Reliability of Collapsing SAND-II 640 Multigroup data into VITAMIN-J 175 Multigroup Cross Sections," Report: INDC(NDS)-337, (July 1995). Nuclear Data Section, International Atomic Energy Agency, Vienna. 20. H. Wienke and S. Ganesan, Unpublished (December 1994). 21. Papers presented at the International Conference on Nuclear Data for Science and Technology, Gatlinburg, Tennessee, May 9-13, 1994, J. K. Dickens (Editor), American Nuclear Society (1994). 22. C. L. Dunford and T. W. Burrows, "Online Nuclear data Service," IAEA-NDS-150 (1995) Nuclear Data Section, International Atomic Energy Agency, Vienna, Austria. 23. H. D. Lemmel, "Index of Nuclear Data Libraries available from the IAEA Nuclear Data Section," IAEA-NDS-7 Rev. 96/4 (April 1996), International Atomic Energy Agency, Vienna, Austria. 24. "National Nuclear Data Needs of the 1990's. "A report by the Nuclear Science Advisory Committee of the U.S. DOE. Unpublished document (1994). See also, "A Strategic View on Nuclear Data Needs," Report by the NEA Secretariat, OECD, Paris, September (1993). 25. S. Ganesan, "IAEA Nuclear data Services," in A. Gandini, S. Ganesan and J. J. Schmidt (Editors), "Proceedings of the Workshop on NUCLEAR REACTORS: PHYSICS, DESIGN AND SAFETY, ICTP, Trieste, Italy, 11 April-13 May 1994," World Scientific (1995). 26. P. Oblozinsky, "Nuclear data Libraries and On-Line Services," Lecture notes presented at this Workshop on Nuclear Reaction data and Nuclear Reactors-Physics, Design and Safety, 15 April-7 May 1996, ICTP Informal report(1996). 27. V. Gopalakrishnan (Editor), "Activity Report of Reactor Physics Division-1994," Report IGC-165, Indira Gandhi Centre for Atomic Research, Kalpakkam (1995). 28. S. Ganesan (Compiler), "Progress Report on Nuclear Data Activities in India for the Period July 1992 to March 1995," BARC/1995/E/005(1995), Bhabha Atomic Research Centre, Bombay. 29. R. E. MacFarlane, "TRANSX 2: A Code for Interfacing MATXS Cross Section Libraries to Nuclear Transport Codes," LA MS (1992). See also J. Stepanek, "TRAMIX: A Code for Interfacing MATXS Cross Section Libraries To Nuclear Transport Code for all Types of Fission Reactors, Fusion Blankets as well as Shielding Analysis," Paul Scherer Institute (Draft ).