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1. SPECIFICATIONS FREE x OX X 0 X 0 0 0 OR 0e 0 06 06 0X Ke KK X CARD 1 NENDF UNIT FOR ENDF B TAPE NPEND UNIT FOR PENDF TAPE CARD 2 LABEL 66 CHARACTER LABEL FOR NEW PENDF TAPE DELIMITED WITH ENDED WITH CARD 3 MAT MATERIAL TO BE RECONSTRUCTED NCARDS NUMBER OF CARDS OF DESCRIPTIVE DATA FOR NEW MF1 DEFAULT 0 NGRID NUMBER OF USER ENERGY GRID POINTS TO BE ADDED DEFAULT 0 ERR FRACTIONAL RECONSTRUCTION TOLERANCE USED WHEN RESONANCE INTEGRAL ERROR CRITERION SEE ERRINT IS NOT SATISFIED TEMPR RECONSTRUCTION TEMPERATURE DEG KELVIN DEFAULT 0 NDIGIT NO SIGNIFICANT DIGITS DEFAULT 6 ERRMAX FRACTIONAL RECONSTRUCTION TOLERANCE USED WHEN RESONANCE INTEGRAL ERROR CRITERION IS SATISFIED ERRMAX GE ERR DEFAULT 20 ERR ERRINT MAXIMUM RESONANCE INTEGRAL ERROR IN BARNS PER GRID POINT DEFAULT ERR 10000 CARD 5 CARDS NCARDS OF DESCRIPTIVE COMMENTS FOR MT451 EACH CARD DELIMITED WITH ENDED WITH CARD 6 ENODE USERS ENERGY GRID POINTS CARDS 3 4 5 6 MUST BE INPUT FOR EACH MATERIAL DESIRED MAT 0 TERMINATES EXECUTION OF RECONR X X 0X 0 0 0 0X HHH 0 HEH 0 0 0 HEH HH HH KKH KH HHH KEKE A sample input for processing two isotopes from ENDF B IV tape 407 follows RECONR 20 21 PENDF TAPE FOR U 235 AND PU 239 FROM T407 1261 2 0 005 0
2. Incoherent cross sections are computed by integrating the incoherent matrix for consistency Free incoherent scattering is normalized to the Doppler broadened elastic scattering cross section in order to provide an approximate representation of resonance scattering and to preserve the correct total cross section Discrete angle representations are used to avoid the limitations of Legendre expansions A Coherent Elastic Scattering The thermal coherent scattering from a powdered crystal may be represented as follows gt t t 2 max 24 2 2M t oC ESE uu o Eus 2 Ie e D lu u E E 1 79 where Tnax ni 2 T o n 1 AM 3 and where is the incident neutron energy E is the secondary neutron energy is the scattering cosine in the laboratory reference system is the char acteristic coherent scattering cross section for the material M is the target mass Vo is the volume of the unit cell N is the number of atoms per unit cell F is the form factor Wp is the Debye Waller coefficient and t is one of the reciprocal lattice wave vectors The sum can be simplified by lumping all terms with the same value of together and defining a single factor f t Then coh rhe V max 07 Eg Z2 fu Et 4 i0 This sum is easily performed for any E if a sorted list of precomputed and f t values is available As gets large the values of get more and more
3. 92 U 235 FROM T407 PROCESSED WITH NJOY 1200 2 0 005 0 94 PU 239 FROM T407 PROCESSED WITH NJOY 0 39 The resulting PENDF tape will contain the desired TAPEID card followed by U235 a MEND card PU239 a MEND card and a TEND card G Error Messages RUINA ILLEGAL NDIGIT Value must be between 1 and 15 Any value above 7 will be ineffective on a short word computer RDFIL2 STORAGE IN ENODE EXCEEDED Too many energy nodes including the user s nodes and the energies from MF2 Increase NODMAX in RECONR RDFIL2 STORAGE IN A EXCEEDED Too much resonance data The main container array 15 too small Increase STORE and JX in RECONR or decrease buffer sizes NBUFG NBUFR or NBUF ANLYZD TOO MANY REDUNDANT REACTIONS Increase the size of MTR 10 and MTRT 10 in RECON and increase NMTMAX 10 in RECONR LUNION EXCEEDED STACK Increase length of linearization stack NDIM currently 20 RESXS STACK EXCEEDED Increase length of reconstruction stack NDIM currently 20 CSMLBW NOT CODED FOR T GT O DEG The wx Doppler broadening option is only coded for single level Breit Wigner and Adler Adler resonance parameters Use TEMPR 0 on input CSAA 1 Error in format of evaluation RECOUT FOR MF MT Indexing and pair count for this section do not make sense H Input Output Units The following logical units are used 40 10 NSCR1 in RECONR NOUT in LUNION and NIN in EMERGE C
4. c Qa Y 5 he Unite Sta 9s artment e Ener un ontract W 7405 ENG 36 To ajay IR So A a RLS xls pk T EU NIOY Nuclear Data Pro Lhe NIOY RECO squad FEA E ORATORY LOS ALAMOS NATIONAL LAB Los Alamos An Affirmative Action Equal Opportunity Employer a This work was supported by the US Department of Energy Division of Reactor Research and Technology and the Electric Power Research Institute DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government Neither the United States Government nor any agency thereof nor any of their employees makes any warranty express or implied or assumes any legal liability or responsibility for the accuracy completeness or usefulness of any information apparatus product or process disclosed or represents that its use would not infringe privately owned rights References herein to any specific commercial product process or service by trade name trademark manufacturer or otherwise does not necessarily constitute or imply its endorsement recommendation or favoring by the United States Government or any agency thereof The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof LA 9303 M Vol Il ENDF 324 Manual Issued May 1982 The NJOY
5. defined such that the heating rate in a mixture is given by Ti34 H E gt Z CE 0 E 1 ij 57 22 N GAMMA FLUX y P d prompt gammas 27 delayed gammas prompt and prompt delayed delayed local local non local heating heating heating Fig 1 Components of nuclear heating HEATR treats the prompt local neutron heating only where is the number density of material i is the kerma factor for material i and reaction at incident energy E and is the neutron or photon scalar flux at is used just like a microscopic reaction cross section except that its units are energy x cross section eV barns for HEATR The direct method for computing the kerma factor is E 3E E a 2 2 132 where the sum is carried out over all charged products of the reaction including the recoil nucleus and is the total kinetic energy carried away by the 2th species of secondary charged particle Unfortunately ENDF B does not include the detailed spectral information needed to evaluate Eq 2 58 For this reason NJOY computes most kerma factors by the energy balance method 2 The energy allocated to neutrons and photons is simply subtracted from the available energy to obtain the energy carried away by charged particles where Qij is the mass difference Q value for reaction j E is the total energy of secondary neutrons including multi
6. A calculation of both free and graphite cross sections for ENDF B IV carbon would go as follows THERMR 0 23 24 0 1274 8 3 1 0 1 201 0 300 900 1200 02 3 7 THERMR 26 24 25 1065 1274 3 3 4 1 1 209 0 300 900 1200 2 402 3 7 The output tape on unit 25 will contain the following new sections MF3 MT201 free carbon incoherent xsec 209 graphite incoherent xsec 210 graphite coherent cross section 201 free carbon incoherent matrix 209 graphite incoherent matrix 210 graphite coherent MF6 AMMA Ww Ww These reactions could all be averaged using GROUPR Subsequent formatting modules could then be used to select the desired scatterer and merge it with the static data Error Messages THERMR TINC 2 or 3 NOT PROGRAMMED These are future options THERMR MODE CONVERSION NOT ALLOWED NIN and NOUT must both be binary or both be coded 91 THERMR NIN 0 An input PENDF tape is required THERMR ILLEGAL REFERENCE MT Restricted to MT201 250 THERMR MAT AND TEMP NOT ON TAPE Check input instructions against contents of thermal tape COH TOO MANY LEGENDRE ORDERS The code currently computes only Pa but NL 1 in COH can be changed if desired Code is currently limited to 6 PL If more coefficients are desired increase NLMAX and the dimensions f the variables S EJ and EX in COH CALCEM and PEND SIGCOH STORAGE EXCEEDED Not enough room for lattice factors Increase STORE and
7. 46 The H functions are the 9 10 lt d 11 These functions satisfy a recursion relation that can be used to obtain FgCa 5 erfc a 1 a 12 2 n sted 1 F a 2 2 gt where erfc a denotes the complementary error function 2 2 2 erfc a fe Zaz 13 4n However when F a F b the difference in Eq 10 may lose significance In such cases H a b can be computed by a direct Taylor expansion of the de fining integral 2 Write 47 b 228 _ H a b 25 S ze dz 2 S ze 0 G b G a 14 But by Taylor s Theorem G b G 8 6 rad GM Edi 15 Also m 1 2 2 eo 0767 Po 16 dx where P x is a polynomial with recursion relation p nC zx P liy 2xP x 17 with x From this point it is straightforward to generate terms until the desired number of significant figures are obtained When interpreting BROADR output it is useful to remember several important features of the Doppler broadening process 1 v cross section remains un changed Contrary to popular knowledge the area under a resonance does not remain unchanged unless gt gt kT A In fact each resonance develops a new 1 v tail Finally a constant cross section for example elastic scattering develops a 1 v tail at low energies after Doppler broadening T
8. Argonne National Laboratory report ANL 8144 239 1976 XI BROADR BROADR generates Doppler broadened and thinned cross sections in PENDF format starting from piecewise linear cross sections in PENDF format The input Cross sections can be from RECONR or from a previous BROADR run The code is based on 16 1 0 Cullen of Lawrence Livermore National Laboratory The method is often called kernel broadening because it is based on a detailed integration of the integral equation defining the effective cross section It is a fully accurate method treating all resonance and nonresonance cross sec tions including multilevel effects BROADR differs from SIGMA1 in the following ways An alternate calculation is used for low energies and high temperatures that corrects a numerical problem of the original code Variable dimensioning is used which allows the code to be run on large or small machines with full use of whatever storage is made available All low threshold reactions are broadened and thinned in parallel on a union grid This makes the code run several times faster than the original SIGMA Binary input and output can be used This roughly halves the time required for a typical run The summation cross sections total nonelastic and sometimes fission MT18 or n2n are reconstructed to equal the sum of their parts The file dictionary is updated A Doppler Broadening Theory The
9. closely spaced In order to save storage and run time a range of t values can be lumped together to give a single effective and f t This device washes out the Bragg edges at high energies while preserving the proper average cross section and angular dependence The current grouping factor is 5 see EPS in SIGC Lattice constants given in SIGC for graphite Be and Be0 form factor formulas see FORM and methods for computing reciprocal lattice vectors were borrowed directly from HEXSCAT 80 The energy grid for is obtained adaptively see A panel extending from just above one Bragg edge to just below the next higher edge is subdivided by successive halving until linear interpolation is within a specified frac tional tolerance TOL of the exact cross section at every point This pro cedure is repeated for every panel from the first Bragg edge to the specified maximum energy for the thermal treatment EMAX The code actually computes and writes out the average over of Eq 5 that is the Po cross section Subsequent codes can deduce the correct dis crete scattering angles HLT from the location of the Bragg edges and the factors f t from the cross section step at the Bragg edge see GROUPR A typical coherent elastic cross section is shown in Fig 1 10 Graphite 300 K Coherent cross section barns 10 Energy eV Fig 1 Typical behavior of the coherent elastic scattering from a crystalline mate
10. indicated as a subtraction are printed For MF12 MT102 the print is a little different It shows the photon induced recoil and damage energy as EGAM and EDAM and the corrected heating as HEATING and DAMAGE rather than the change due to capture photons as in other reactions Also for MF12 MT102 a check is made of the total photon energy computed from MF12 and MF15 versus the approximate available energy E Q and the percent difference ERR is printed if greater than 1 modest differences are expected for the light iso topes due to the neglect of recoil This percent difference will appear as an energy balance error in a heating calculation for a large system Finally a summary print of the partial kerma factors and damage energy cross section on the coarse grid is printed On option the kinematic limits are included in this summary print The coarse energy grid is chosen in NHEAT during the pro cessing of the first reaction At present decade steps are used below 1 eV factor of two steps from 1 eV to 100 keV quarter lethargy steps above 100 keV and 1 MeV steps above 2 MeV The kinematic checks are intended for evaluators and other people familiar with ENDF B photon representations The MT301 total column always makes sense but partial kermas are only defined for reactions that appear in File 12 or 13 even then some energy ranges may not be defined As an example many files use MT4 and MT102 to represent the photons at low energies an
11. 27 where z x iy The wx method is not as accurate as kernel broadening see BROADR because the backgrounds which are sometimes quite complex are not broadened and terms important for energies less than about 16kT AWRI are neglected however the wy method is less expensive than BROADR The current version of RECONR includes Doppler broadening for the single level Breit Wigner representation only The Lubitz Rose method used for calculating multilevel Breit Wigner cross section CSMLBW is formulated as follows oC 5 opg 28 30 2 A E ojo CE e 2 gj 1 Ug CE 1 and 29 21 2 nr U e 2 _ 30 ER TE 1P 2 where the symbols are the same as those used above Expanding the complex operations gives the actual formula used i3 gA gt ps xs 31 2 J J 2 r 1 2 2 r Pr 1 2 IpglE where the sums over limited to resonances in spin sequence 2 J fission and capture cross sections are the same as for the single level option The allowed values of J for this sum are limited to the range IS 2 01514598 where S is the magnitude of the channel spin 1 5 and I is the target spin SPI The multilevel Adler Adler representation is defined for 2 0 only The total cross sections are given by 5 12 TE 21 E sin 2 v G cos209 H sin209 y 0 x 52 Gsin2oy 2 3 2 A A
12. A 11 where um is the characteristic bound cross section and W is the Debye Waller integral The energy grid of the elastic cross section is used for E and the average cross section and equally probable angles are computed using e Y 12 where W is interpolated from tables given in reference 3 and N 2 1 41 Hi Le GEM 1 2 1 _1 2EW y 1 1 1 where 85 Ee 14 is the upper limit of one equal probability bin and is the selected discrete cosine in this bin Here N is the number of bins and 18 71 D Coding Details The procedure begins in THERMR with the reading of the user s input The required ENDF tape NENDF is only used for MF7 data it can be set to zero if only free scattering is needed Similarly MATDE is the material number on the MF7 tape and can be set to zero for free problems The ENDF MF7 format only gives the product of the free scattering cross section for the prin ciple scatterer and the number of principle scatterer atoms in the molecule As a result THERMR needs the parameter NATOM to obtain the effective microscopic cross section for example for H in H 0 use NATOM 2 THERMR then finds the desired material on the input PENDF and ENDF tapes It will automatically loop over NTEMP materials on NIN The input tape must have been through BROADR The elastic cross section at the current temperature is saved
13. DISAPPEARANCE MT102 THRU 120 CARDS 4 AND 5 FOR NQA GT 0 ONLY 0X 0 OR 0X 06 OX 0X 0 Ke EH HHH TEO EEES X X X X X X X X 0 0X 0X 0 O X 0X X CARD 4 MTA MT NUMBERS FOR USERS Q ONLY CARD 5 QA USER SPECIFIED Q VALUES EV C2 75 As an example consider a HEATR run for ENDF B IV U 235 with partial kermas and user specified Q values 20 21 22 1261 4 3 303 304 318 402 19 20 21 172 65E6 172 65 6 172 6556 The list of partial kermas is obtained by seeing which reactions appear in MF12 and MF13 The total MT301 is provided automatically The PENDF tape will have partial kermas for 301 303 304 318 and 402 but the values will not be printed H Error Messages HEATR REQUESTED TOO MANY KERMA MTS 8 values in addition to MT301 are allowed with kinematic checks otherwise 26 can be requested HEATR REQUESTED TOO Q VALUES Limited to 30 only HEATR MODE CONVERSION NOT ALLOWED BETWEEN NIN AND NOUT Both units must be BCD positive or blocked binary negative NHEAT NEUTRON BINDING ENERGY FOR SEQUENTIAL N2N MISSING Q S SHOULD BE ENTERED ON A DATA CARD AS A NEG NO IN EV Self explanatory Reflects a problem in the ENDF B evaluation for 9 NHEAT STORAGE EXCEEDED Insufficient storage for diagnostic energy grid See ELIS
14. ER is the primary recoil energy Ep E 3 31 1 2 2 3 2 3 30 724 202 Zp A A 32 rm 2 3 1 2 3 2 _ 0 0793 Zp 2 Ap A gius 33 L 2 3 273 374 3 2 172 Zp ZU An A L and Z and A refer to the charge and atomic number of the lattice nuclei L and the recoil nuclei R The function behaves like Ep at low recoil energies and then levels out at higher energies Therefore the damage energy produc tion cross section is always less than the heat production cross section For elastic and two body discrete level inelastic scattering ERC 1 am 34 where the effective mass is given by 35 and is the center of mass scattering cosine damage energy production cross section is then obtained from 69 1 DCE o E FCE M PCERLE pI dp 36 where f is the angular distribution from the ENDF B File 4 This integration is performed with a 20 point Gaussian quadrature Discrete level reactions with LR flags to indicate for example n n a reactions are treated in the same way at present The additional emitted particles are ignored Continuum reactions n n give a recoil spectrum El MEET E 37 where E is the secondary neutron energy is the laboratory cosine and the photon momentum has been neglected The damage becomes 1 D E o E dE f du f E u g E gt E P Ep E E u
15. Kgl Dansk Vidensk Selsk Mat Fys Medd 33 1963 7 R Kinsey ENDF 102 Data Formats and Procedures for the Evaluated Nuclear Data File ENDF Brookhaven National Laboratory report BNL NCS 50496 ENDF 102 October 1979 8 ibid p 5 13 9 R Sher S Fiarman and C Beck Fission Energy Release for 16 Fissioning Nuclides unpublished data October 1976 78 XIII THERMR The THERMR module generates pointwise neutron scattering cross sections in the thermal energy range and adds them to an existing PENDF tape The cross sections can then be group averaged plotted or reformatted in subsequent modules Elastic cross sections are generated for hexagonal lattices using an extended version of the method of 5 and for noncrystalline materials such as CH and ZrH by direct evaluation using the incoherent approximation In elastic cross sections and energy to energy matrices can be produced for free scatterers or for bound scatterers when ENDF B scattering functions are avail able This function has previously been performed using FLANGE 11 THERMR has the following advantages over HEXSCAT and FLANGE II The energy grid for coherent elastic scattering is produced adaptively so as to represent the sharp Bragg edges to a specified tolerance using linear interpolation The secondary energy grid for inelastic incoherent scattering is produced adaptively so as to represent all structure with linear interpolation
16. NUMBER 4 OR 5 ONLY CARD 3 245 MOPT SIX CHARACTER MODULE NAME DELIMITED WITH x Es X E G RECONR ONLY FIRST FOUR CHARACTERS ARE EE USED REPEAT FOR EACH MODULE DESIRED USE X C STOP TO TERMINATE PROGRAM 5 SEE THE COMMENTS AT THE START OF EACH MODULE FOR di C lt ITS SPECIFIC INPUT INSTRUCTIONS C The example in Table I clarifies their use B Interface Files Another requirement of a good modular system is that the input and output files be in a common format so that modules can work with each other s output in a flexible way Since NJOY is basically an ENDF B processing code ENDF B com patible formats see Sec X D were chosen for linking modules together put and output modules see Fig 1 can be specified to communicate with other formats the outside world However if the user desires the RECONR PENDF tape can be run through BROADR to produce a new Doppler broadened PENDF tape for GROUPR Many other combinations are possible These common format files also provide for convenient restarts at many points in the calculational sequence For example if a user is trying to produce pointwise cross sections at 300 K 600 K and 900 K and runs out of time while working on 900 K he can save the partially completed PENDF tape and restart from 600 K Multigroup modules use specially constructed groupwise ENDF formats GENDF that are com patible with the multigroup output modules A
17. Nuclear Data Processing System Volume 11 The NJOY RECONR BROADR HEATR and THERMR Modules D W Muir R M Boicourt i ue Et da o i lt 9 E 8 0 ES E a O ii ds 5 2 od Los Alamos ordi tenio THE NJOY NUCLEAR DATA PROCESSING SYSTEM VOLUME II THE NJOY RECONR BROADR HEATR AND THERMR MODULES by R E MacFarlane D W Muir and R M Boicourt ABSTRACT The NJOY nuclear data processing system is a compre hensive computer code package for producing cross sections and related nuclear parameters from ENDF B evaluated nuclear data This volume provides detailed descriptions of the NJOY module which contains the executive program and utility subroutines used by the other modules and it dis cusses the theory and computational methods of four of the modules used for producing pointwise cross sections RECONR BROADR HEATR and THERMR VIIT INTRODUCTION TO VOLUME II The NJOY nuclear data processing system is a comprehensive computer code package for producing pointwise and multigroup cross sections from ENDF B IV and V evaluated nuclear data A concise description of the code system and refer ences to the ancestors of NJOY are given in Vol I of this report This volume provides more detailed discussions of the theory and methods used in four of the modules that prepare pointwise cross section data
18. continues to the next panel This procedure is continued until all panels are converged The result is a tape NOUT containing the energy grid in the resonance region and the total elastic fission and capture cross sections at each energy point Unionization is obtained automatically in the resonance region since the three partials are computed simultaneously in SIGMA This routine calls CSNORP if there are no resonance parameters CSSLBW for single level Breit Wigner parameters CSMLBW for multilevel Breit Wigner parameters CSAA for Adler Adler parameters and CSUNRI or CSUNR2 for unresolved resonance param eters A new feature of NJOY is the ability to reconstruct the cross sections at TEMPR by wx broadening if single level Breit Wigner SLBW or Adler Adler AA parameters are given The Doppler broadened resonance shapes are obtained using QUICKW see description in UNRESR in CSSLBW or CSAA and the linearization procedure proceeds as before The resonance cross sections on NGRID are merged with the ENDF B cross sections in EMERGE First the background grid from LUNION is merged with the 37 resonance grid from RESXS and written onto the LOADA FINDA file which will accumulate the total cross section and any other redundant reactions required IOLD INEW A loop is then set up over all nonredundant reactions For each grid point the ENDF cross section is obtained by interpolation If this grid point has a resonance contribution on NR
19. cross sections Since the A and are expensive to compute the code computes them only once for the points of a unionized energy grid see RECONR The sum of Eq 7 is accumulated for all the nonthreshold reactions simultaneously This trick makes BROADR several times faster than the original SIGMA1 C Coding Details The code begins by reading the user s input see Section D Storage is then allocated for the LOADA FINDA buffers IBUFO and IBUFN and for the scratch storage ISCR The buffer length NBUF can be changed at will currently NBUF 1000 The input PENDF tape is searched for the desired material MAT1 If the restart option is set ISTART 1 the temperatures less than or equal to TEMPI MATL are assumed to have been broadened previously and they are copied to the output file In either case the files for TEMP1 are copied to a scratch file on unit NSCR1 currently set to 10 Next NSCR1 is rewound and examined reaction by reaction The energy grid from the total cross section MT1 is saved on scratch storage using LOADA If the input tape has not been through RECONR the BROADR module will still run but at possibly reduced accuracy The next low threshold reaction less than EMIN 1 eV is located on NSCR1 The energy points are retrieved from scratch file IOLD 12 or 13 using FINDA the cross sections for this reaction are computed on this grid and the results are stored on scratch file INEW 13 or 12 using LOADA
20. energy nodes is copied to binary scratch storage LOADA FINDA This 36 storage system consists of the buffers BOLD and BNEW and the scratch units IOLD and INEW The energy grid points will ping pong back and forth between units 14 and 15 as the union grid is built up LUNION now starts with MT 2 and checks each reaction in sequence to determine whether the current grid on IOLD 15 sufficient to represent the reaction to within the desired tolerance using linear interpolation If not RECONR uses ISLIN1 to select the optimum points to be added to the new grid on INEW INEW and IOLD are swapped and the next MT is processed When all nonredundant reactions have been examined the list of energies in LOADA FINDA storage is the desired linearized and unionized grid The storage used is released This grid is used as the starting point for resonance reconstruction in RESXS RESXS first reserves space for the LOADA FINDA buffers BUFR and BUFG the linearization stack X and Y and the partial cross sections SIG The length of the stack NDIM determines the smallest possible subdivision of a panel between two nodes energy points as close as 2 NDIM times the panel width can be generated RESXS then examines the grid on NGRID IOLD from LUNION panel by panel Grid points are added and cross sections computed until the convergence criteria discussed in Section C are satisfied The cross sections are copied to NOUT through LOADA FINDA and RESXS
21. g in MF5 using E U BCE f E GC 11 0 where U is defined in MF5 If g is tabulated LAW 1 LAW 5 the integral is carried out analytically for each panel by making use of the ENDF B interpola tion laws For the simple analytic representations LAW 7 9 11 the average energies are known 8 64 The neutron cross sections required by Eq 8 are obtained from an exist ing PENDF file see RECONR and BROADR When the neutron sum in Eq 7 is complete the code processes the photon production files If the evaluation does not include photon data HEATR returns only the first sum This is equivalent to assuming that all photon energy is deposited locally consistent with the fact that there will be no contribution to the photon transport source from this material Discrete photon yields and energies are obtained from MF12 or MF13 Con tinuum photon data are obtained from MF15 and the average photon energy and E are computed For radiative capture the photon term becomes 2 1 Y Y 12 where Yy is the capture photon yield from MF12 This corrects the capture contribution from Eq 8 by conservation of momentum For other reactions Eq 8 is sufficient and the product of Ey Sy is subtracted from the neutron contribution Note that if there are no photon files for the evaluation the resulting kerma factors are equivalent to assuming that a
22. gt is the integral over the angular variable of Eq 5 The angular dependence is obtained by adaptively subdividing the cosine range until the actual angular function see SIG is represented by linear interpolation to within a specified tolerance The inte gral under this curve is used in calculating the secondary energy dependence as described above Rather than providing the traditional Legendre coeffi cients THERMR divides the angular range into equally probable cosine bins and then selects the single cosine in each bin which preserves the average cosine in the bin These equally probable cosines can be converted to Legendre coeffi cients easily when producing group constants and they are suitable for direct use in Monte Carlo codes For strongly peaked functions such as scattering for E gt gt kT when the result begins to look elastic all the discrete angles will be bunched together near the scattering angle defined by ordinary kinematics This behavior cannot be obtained with ordinary Legendre coefficients Con versely if such angles are converted to Legendre form very high orders can be used If a direct calculation of Legendre components is desired reverse the sign of NNL in CALCEM The incident energy grid is currently stored directly in the code see EGRID in CALCEM The choice of grid for gi E is not critical since the cross section is a slowly varying function of E Of course ci Es for one value of E is a ver
23. in ANADAM Tabulated data are interpolated from the MF5 table using TABBAR or integrated using trapazoidal and Gaussian quadratures in TABDAM If the ENDF B material includes photon production data the energy carried away by photons is subtracted from the accumulating kerma factors in GHEAT The damage cross section is also corrected for photon momentum First a scratch 73 file is prepared containing MF12 and 13 Transition probability arrays are verted using CONVER if present A loop is set up over all reactions in MF12 and 13 Tabulated energy distributions are integrated using GAMBAR both E and ES are computed for MT102 In order to avoid requiring MF3 MT3 pointwise data the code uses MT1 MT2 to compute the nonelastic neutron cross section if required The final steps are accomplished in HOUT The partial kermas and damage from the LOADA FINDA file are recast into 1 records and written onto the new PENDF tape using MT numbers from the 300 series for kerma that is capture kerma 300 102 402 and a special 444 series for damage 444 total damage 445 elastic 446 inelastic and 447 disappearance The material dictionary is updated to include the new sections If the long print is requested the Q values o heating and damage are printed for each neutron reaction on a special coarse energy grid Simi larly the average photon energy EBAR yield cross section and the photon part of the heating
24. is 6 MT 0 E 0 0 NL 2 NEP NL 2 t E fa 1 Enep 11151 where E is the incident energy NL is the number of discrete angles currently 8 and is the number of secondary energy E values For each E value the normalized scattering function is given where FE gt 21 15 This is followed by the NL discrete cosines The table continues for each of the other values This format also works for Legendre coefficients set NNL positive in CALCEM except that in this case NL is the Legendre order that is 3 for distributions fi is 1 and the p are replaced by the Pi Legendre coefficients 2 Fari The format for LTT 6 is the same as above except NEP 1 because E E for elastic scattering The normalized distribution reduces to fi 1 The format for LTT 7 is just provided to hold position in File 6 because all the necessary information is implicit in File 3 The structure used is 87 MAT 6 MT ZA AWR O LTT O OJHEAD MAT 6 MT ZA AWR 0 0 0 NBRAGG CONT where NBRAGG is the number of Bragg edges used in the cross section calculation In subroutine COH the energy grid is determined adaptively and stored onto the same LOADA FINDA scratch file used for the elastic cross section The elastic cross section is converted to the coherent grid using Lagrange interpo lation see TERP The structure of the record stored on the scratch file is energ
25. production for specified reactions and adds them to an existing PENDF tape The heating and damage numbers can then be easily group averaged plotted or reformatted for other purposes An option of use to evaluators checks ENDF B files for neutron photon energy balance consistency The advantages of HEATR include Heating and damage are computed in a consistent way All ENDF B neutron and photon data are used Kinematic checks are available to improve future evaluations A Theory of Nuclear Heating Heating is an important parameter of any nuclear system It may represent the product being sold as in a power reactor or it may effect the design of peripheral systems such as shields and structural components Nuclear heating can be conveniently divided into neutron heating and photon heating see Fig 1 The neutron heating at a given location is proportional to the local neutron flux and arises from the kinetic energy of the charged products of a neutron induced reaction including both charged secondary parti cles and the recoil nucleus itself Similarly the photon heating is propor tional to the flux of secondary photons transported from the site of previous neutron reactions It is also traceable to the kinetic energy of charged par ticles for example electron positron pairs and recoil induced by photoelectric capture Heating therefore is often described by the KERMA Kinetic Energy Re lease in MAterials factors
26. reactions for example total or inelastic are reconstructed to be exactly equal to the sum of their parts at all energies The resonance parameters are removed from File 2 and the material dictionary is corrected to reflect all changes Resonance reconstruc tion uses methods based on RESEND and linearization uses the method developed for MINX 2 RECONR has the following advantages over the RESEND module of MINX Efficient use of dynamic storage allocation and a new stack structure allow large problems to be run without the use of secondary overlays The unionized grid improves the accuracy usefulness and ENDF B compat ibility of the output s A correct material dictionary is provided Approximate wx Doppler broadening may be used to speed up reconstruction for narrow resonance materials A resonance integral criterion is added to the normal linearization cri terion in order to reduce the number of points added to the tabulation to represent unimportant resonances A ENDF B Cross Section Representations A typical cross section derived from an ENDF B evaluation is shown in Fig 1 The low energy cross sections are smooth They are described in File 3 see IX D for a review of ENDF B nomenclature using cross section values given on an energy grid with a specified law for interpolation between the points In the resolved resonance range resonance parameters are given in File 2 and the cross sections for resonance re
27. searches that it makes NJOY often has to match two numbers that are different only in the few least Significant bits This routine is intended to make such numbers exactly equal to each other by truncating the numbers to a given number of digits and removing any low significance junk resulting from nonterminating binary fractions This problem is not so common on short word length machines but it might still be necessary to con vert this routine for some machines I Error Messages NJOY ILLEGAL ENDF B VERSION NUMBER Only 4 and 5 are allowed ENDF B III data can be processed with IVERF 4 NJOY TLLEGAL OPTION Use 0 for card image input or 1 for TTY NJOY TLLEGAL MODULE NAME Check spelling and check for missing or incorrect item counts in the preceding module Only the first four characters of each name are used OPENZ ILLEGAL UNIT NUMBER CLOSZ ILLEGAL UNIT NUMBER Units less than 10 are reserved for the system TOMEND MODE CONVERSION NOT ALLOWED TOFEND MODE CONVERSION NOT ALLOWED TOSEND MODE CONVERSION NOT ALLOWED Input and output units must both be binary or both be BCD FINDF MAT MF MT NOT ON TAPE Desired section cannot be found STORAG STORAGE EXCEEDED There is not enough storage allocated to hold even the directory table 17 RESERV STORAGE EXCEEDED NEED MORE WORDS FOR ID Container array is not large enough to hold desired data even after re packing The message gives an es
28. small for the temperature difference requested Increase total storage available or repeat the calculation with smaller temperature steps and ISTRAP 1 The normal maximum size of is 4 0 and A is in versely proportional to 5 1 Input Output Units 10 NSCR1 in BROADR Contains the ENDF B data at the initial temperature 12 13 IOLD INEW in BROADR Contains union energy grid and low threshold reactions 20 26 User s choice for NIN and NOUT to link with other modules Units 12 and 13 will always be binary Unit 10 will have the same mode as NIN and NOUT binary mode is recommended G Storage Allocation All storage used is divided in the most efficient way possible The tainer array in STORE and NAMAX should be made as large as possible NBUF can be increased or decreased at will large values will give faster execution NWSCR depends on the size of the ENDF B dictionary and 1000 words is sufficient for all current evaluations 55 H References for BROADR 1 D E Cullen Program SIGMA1 Version 77 1 Doppler Broaden Evaluated Cross Sections in the Evaluated Nuclear Data File Version B ENDF B Format Lawrence Livermore National Laboratory report UCRL 50400 Vol 17 Part B 1977 2 Abramowitz and I Stegun Handbook of Mathematical Functions Dover Publications New York 1965 56 XII HEATR The HEATR module generates pointwise heat production cross sections and radiation damage energy
29. tape Note that the elastic cross section in MT2 and the total cross section in 1 are not changed from their static values nor is the union grid updated As a result MT200 250 must be con sidered supplemental Subsequent modules could ignore them or use them in place of the static values Also note that it is possible to run THERMR several times with different values of MTREF The result would be one PENDF tape containing static cross sections and several different binding states that can be selected at will for example MT2 static hydrogen MT201 free hydrogen MT202 hydrogen in water and 203 hydrogen in polyethylene all on one PENDF tape File 6 matrices are read from a scratch tape NSCR in ENDF format normal ized and written back onto the final tape Since free incoherent scattering was set equal to elastic scattering in CALCEM the approximate resonance tion of the matrix is now complete Input Instructions The following input instructions have been copied from the comment cards in HEATR see also Vol I User s Manual 89 INPUT SPECIFICATIONS FREE FORMAT CARD 1 NENDF ENDF B TAPE FOR MF7 DATA NIN OLD PENDF TAPE NOUT NEW PENDF TAPE CARD 2 MATDE MATERIAL DESIRED ON ENDF TAPE MATDP MATERIAL DESIRED ON PENDF TAPE NBIN NUMBER OF EQUI PROBABLE ANGLES NTEMP NUMBER OF TEMPERATURES IINC INELASTIC OPTIONS 0 NONE 1 COMPUTE AS FREE GAS 2 RESERVED 3 COMPUTE
30. weak high energy resonances which do not need to be treated accurately in many applications As an example the capture and fission resonance integrals important for thermal reactors must be computed with a 1 E flux weighting If the resonance reconstruction tolerance is set high say 1 to reduce the cost of processing the resonance integrals will be computed to only 1 accuracy However if the high energy resonances whose importance is reduced by the 1 E weight and the 1 v trend of the capture and fission cross sections are treated with less accuracy than the low energy resonances then it is likely 24 that one can achieve an overall reduction in the number of points hence com puting cost or increased accuracy in computed resonance integrals or both Since 1 E weighting is not realistic in all applications for example in fast reactors user control of this thinning operation must be provided Based on these arguments the following approach was chosen to control the problem of very large files First panels are subdivided until the elastic and capture cross sections are converged to within ERRMAX where ERRMAX gt ERR These two tolerances are normally chosen to form a reasonable band such as 10 and 0 5 to ensure that all resonances are treated at least roughly for example for plotting If the resonance integral 1 E weight in a particular panel is large the panel is further subdivided to achieve an accuracy of ERR sa
31. 38 where g is the secondary energy distribution from ENDF B File 5 In the code the angular distribution is defaulted to isotropic and a 4 point Gaussian quadrature is used for the angular integration For analytic representations of g an adaptive integration to 5 accuracy is used for E for tabulated File 5 data a trapezoidal integration is performed using the energy grid of the file The same procedure is used for n 2n n na etc with no account being taken of the extra emitted particles The recoil for radiative capture must include the momentum of the emitted photon below 25 100 keV giving 70 2 2 E E Eg ea NR tC 39 2 A 1 mc 2 A 1 mc where Q is the angle between the incident neutron direction and emitted photon direction If subsequent photons are emitted in a cascade each one will add an 2 additional term of E and an additional angle A complete averaging of Eq 39 with respect to P Ep would be difficult and would require angular correlations not present in ENDF B However damage calculations are still fairly crude and an estimate for the damage obtained by treating the neutron kick and all the photon kicks independently should give a reasonable upper limit because 2 1 E E D E d coso lt D zD L 40 Finally for the n particle reactions the primary recoil is given by E 1 x E 2 En cos aE 4 41 where a is the mass ratio of the emit
32. ATR 77 I Storage Allocation Variably dimensioned dynamic storage allocation is used for most data Storage requirements are dominated by the length of MF5 or MF15 for the evalua tion The size of common STORE and the parameter NAMAX in HEATR may be ad justed accordingly The LOADA FINDA buffer size NBUF may be decreased or in creased at will The code is currently dimensioned as follows 100 coarse grid points 30 auxiliary values 26 partial kermas 8 when kinematic limits are requested 12000 total storage J References for HEATR 1l M A Abdou C W Maynard and R Q Wright MACK A Computer Program to Calculate Neutron Energy Release Parameters Fluence to Kerma Factors and Multigroup Reaction Cross Sections from Nuclear Data in ENDF Format Oak Ridge National Laboratory report ORNL TM 3994 July 1973 2 D W Muir Gamma Rays Q Values and Kerma Factors Los Alamos Scien tific Laboratory report LA 6258 MS March 1976 3 T A Gabriel J D Amburgy and N M Greene Radiation Damage Calcula tions Primary Knock On Atom Spectra Displacement Rates and Gas Produc tion Rates Nucl Sci Eng 61 21 1976 4 D G Doran Neutron Displacement Cross Sections for Stainless Steel and Tantalum Based on a Linhard Model Nucl Sci Eng 49 130 1972 5 M T Robinson in Nuclear Fusion Reactors British Nuclear Energy Society London 1970 6 J Lindhard V Nielsen M Scharff and P V Thomsen
33. BLOCKED BINARY INPUT Test BCD BB 235 Doppler broadening 169 72 1 235 elastic matrix 10 9 4 99 2350 n 2n matrix 4 51 838 Iron Doppler broadening 139 46 5 Sometimes it is necessary to find a particular part of the buffered data In such cases use 5 IP NP NA NTAPE BUF NBUF 12 where E is a value for the first of the NA words and IP points to part of the data whose first word is either equal to is the first value less than _ Dynamic Storage Allocation In many large computer codes storage requirements may change continually throughout the execution of a problem If maximum use is to be made of the available memory it is necessary to reallocate and repack storage in response to the requirements of the calculation In NJOY these functions are handled by the STORAG package of 4 subroutines STORAG IAMAX NIDMAX IPR A Initialize variably dimensioned dynamic storage allocation system for the container array A IAMAX length of container array NIDMAX maximum number of data identifiers that will be needed at one time IPR print flag normally 0 use 1 to suppress most routine messages RESERV ID NWORDS INDEX A Reserve NWORDS in A for the data set identified by ID ID can be a left adjusted Hollerith name or a number less than or equal to 9999 Space will be allocated at the top of A if possible If insufficient space is available A will be repacked and another attempt to reserve sp
34. Contains the scatter ing matrix before normalization 13 NSCR2 in THERMR and TPEND Contains data from NIN that are to be simply copied to NOUT 20 99 User s choice for NENDF NIN NOUT and NREAD IINC 2 only to link with other modules No mode conversion between NIN and NOUT allowed Units 10 and 11 are always binary Units 12 and 13 have the same mode as NIN and NOUT The user can choose the modes for NENDF NIN and NOUT except NIN and NOUT must have the same mode H Storage Allocation The storage allocated in THERMR is for the LOADA FINDA buffers and a scratch array NBUF may be changed at will larger values increase I 0 effi ciency NWSCR controls the maximum size of the TAB1 records of o E E versus E for incoherent scattering Hence it interacts with TOL The linearization stack STK in COH is controlled by IMAX and the number of Legendre components requested always 1 in the standard version The current value of IMAX 20 93 is sufficient to divide each panel into parts as small as one millionth of the panel size The length of the list of lattice factors FL in SIGCOH is trolled by the size of the ENDF B File 7 and STORE must be big enough for the problem 1 References for THERMR 1 Y D Naliboff and J U Koppel HEXSCAT Coherent Scattering of Neutrons by Hexagonal Lattices General Atomic report GA 6026 1964 2 Kinsey Ed ENDF 102 Data Formats and Procedures for the Evaluated Nuclea
35. ES it is added The resulting net cross section at this point is added into the appropriate redundant cross tions on IOLD INEW and also saved on NGRID When all the energies for this reaction have been processed the cross sections on NGRID are converted into a TAB1 record and written onto NSCR This loop is continued until all reactions have been processed When EMERGE is finished NSCR contains cross sections for all the nonredundant reactions and IOLD contains the redundant summation cross sections Control now passes to RECOUT which writes the new file 1 comments and dic tionary It then steps through the reactions on NSCR and IOLD Redundant re actions are converted to 1 records and inserted in the correct order Non redundant reactions are simply copied Finally a MEND record 15 added and control is returned to RECONR RECONR either directs that this process be repeated for another isotope or writes a TEND record and terminates The result is a new tape in ENDF format containing the desired pointwise cross sections Note that only files 1 2 3 and 13 are included for neutron tapes Only 1 and 23 are included for photon tapes Input Instructions The input instructions for each module are given in the code as comment cards at the beginning of each module They are reproduced here for the con venience of the reader see also Vol I User s Manual 38
36. GENDF tape from GROUPR can be saved in the NJOY data library run through CCCCR to produce one output format and then run through MATXSR for another output format In NJOY unit numbers from 20 through 99 are used for storing results or linking modules units 10 through 19 are reserved for scratch files which can be destroyed after a module has completed its job and units below 9 are re served for the system There are special utility routines to open close and reposition files These routines can be modified to adapt NJOY to a particular operating system OPENZ LUN NEW Open the unit ABS LUN If LUN gt 0 use coded formatted mode and if LUN lt 0 use binary mode Destroy on close or job termination if 10 lt LUN lt 20 If NEW 1 destroy the file on this unit if it exists and open a new file CLOSZ LUN Close the file with unit ABS LUN REPOZ LUN Reposition rewind the unit ABS LUN SKIPRZ LUN NREC Skip NREC records forward or backwards Caution Some systems have a call for this option others can use loops of backspace and dummy reads as given in the NJOY code Both these operations work well for systems that use linked list data structures for I O files On some systems however backspace is implemented as a rewind followed by forward dummy reads to the desired location In such cases for example VAX SKIPRZ must be recoded to avoid calling BACKSPACE repeatedly This strategy is similar to the app
37. It also describes the execu tive program that controls the order of execution of the various modules and it discusses the library of utility routines that are available to all of the pro cessing modules NJOY is a very modular system In fact each module is essentially a free standing code The organization of this report reflects the structure Each module is described in a separate chapter In order to allow for easy revision 1 each chapter uses independent numbering of figures tables equations and pages and each chapter contains its own references The next chapter describes the overall structure of the NJOY system the executive program and the utility subroutines available to the processing modules This is followed by chapters describing four of the modules that pro duce pointwise ENDF PENDF libraries RECONR reconstructs pointwise cross sections from ENDF resonance parameters and interpolation laws BROADR Doppler broadens these cross sections to any desired temperature HEATR generates heat and radiation damage production cross sections and THERMR adds elastic and in elastic thermal cross sections for free and bound scatterers IX NJOY The modular structure of NJOY is shown in Fig 1 The term module 15 used here in a very restrictive sense a module is a block of coding that communicates with other modules only through logical units the terms tape and file will be used interchangeably in this report T
38. NAMAX in THERMR SIGCOH ILLEGAL LAT Only three lattices are coded so far To add others insert the constants in SIGC and form factor formulas in FORM IEL UNKNOWN MATERIAL IDENTIFIER Only three options are coded so far To add others insert DATA statements for the Debye Waller integrals and values for the bound cross sections CALCEM NL TOO LARGE FOR BINNING Increase NLMAX now 17 and the dimensions of Y and YT CALCEM DESIRED TEMPERATURE NOT FOUND Requested temperatures do not agree with those on NIN from a previous BROADR run CALCEM STORAGE EXCEEDED Increase NWSCR in THERMR This may cause a STORAG error that requires STORE and NAMAX to be increased SIG ILLEGAL OPTION Only tabulated S a 8 and free gas are coded at this time 92 SIGL NEGATIVE DISCRIMINANT SIGL NO LEGAL SOLUTION Having trouble solving equation for the boundary of a bin TPEND DID NOT FIND TEMP ON NIN Temperatures requested for THERMR are not consistent with those on the input PENDF tape TPEND STORAGE EXCEEDED Increase NWSCR in THERMR TPEND CROSS SECTION 0 Thermal cross section of zero can not be used to normalize the distribution Input Output Units The following logical units are used 10 11 IOLD INEW in THERMR Also used in READEM CALCEM and TPEND Used for the LOADA FINDA scratch file that saves the energy grid and reaction cross sections 12 NSCR in THERMR Also used in CALCEM and TPEND
39. NBUFR 2000 and NBUF 2000 in RECONR The yx broadening option requires 7688 words of additional storage There fore the container array in STORE can be reduced significantly if yx is not required No code changes are needed just avoid TEMPR greater than zero Resonance reconstruction in RESXS uses 5 x NDIM words NDIM determines the smallest subdivision of a panel that can be obtained Using NDIM 20 allows points to be generated with spacing as small as one millionth of the panel size 20 2 41 42 References 0 Ozer RESEND A Program to Preprocess ENDF B Materials With Resonance Files into Pointwise Form Brookhaven National Laboratory report BNL 17134 1972 C R Weisbin P D Soran R E MacFarlane D R Harris R J LaBauve J S Hendricks J E White B Kidman MINX Multigroup Inter pretation of Nuclear X Sections from ENDF B Los Alamos Scientific Lab oratory report LA 6486 MS ENDF 237 1976 R Kinsey Ed ENDF 102 Data Formats and Procedures for the Evaluated Nuclear Data File ENDF Brookhaven National Laboratory report BNL NCS 50496 ENDF 102 2nd Edition ENDF B V 1979 B J Toppel A L Rago and D M O Shea MC2 A Code to Calculate Multigroup Cross Sections Argonne National Laboratory report ANL 7318 1967 Henryson II J Toppel and Stenberg MC2 2 A Code to Calcu late Fast Neutron Spectra and Multigroup Cross Sections
40. O CONTIO LISTIO etc when mode conversion is desired The advantages of the blocked binary mode are demonstrated in Table II for several characteristic processing tasks E Buffered Binary Scratch Storage During the execution of a program there are often times when large amounts of data need to be stored in mass storage temporarily In order to make such 11 scratch storage as efficient as possible NJOY includes a pair of utility sub routines that automatically buffer such data through fast memory to disk and or large core memory LCM LOADACT A NA NTAPE BUF NBUF FINDACI A NA NTAPE BUF NBUF where I data point number I must increase except I 1 causes a rewind and 1 lt 0 flushes the fast memory buffer to mass storage A array containing data to be stored or destination of data to be read NA number of words to be transmitted must be the same for all I NTAPE logical unit number of disk file BUF fast memory buffer array NBUF length of buffer array When a point is to be saved LOADA stores it in BUF When BUF becomes full it is automatically dumped to disk When a point is to be retrieved FINDA checks to see whether the desired point is in BUF If not it reads through the disk until the desired point is in memory It then returns the desired point When is small using LOADA FINDA reduces the number of 1 0 operations dramatically TABLE 11 EXAMPLES OF EFFICIENCY GAINS OBTAINED WITH
41. S A B AND MATRIX 4 READ S A B AND COMPUTE MATRIX ELASTIC OPTIONS 0 NONE 1 GRAPHITE 2 BERYLLIUM 3 BERYLLIUM OXIDE 11 POLYETHYLENE 12 H ZRH 13 ZR ZRH NATOM NUMBER OF PRINCIPAL ATOMS MTREF FOR INELASTIC REACTION 201 250 ONLY IPRINT PRINT OPTION O MINIMUM 1 MAXIMUM 2 MAX NORMAL INTERMEDIATE RESULTS DEFAULT 0 CARD 3 TEMPR TEMPERATURES KELVIN CARD 4 FOR IINC 4 ONLY EFTEMP EFFECTIVE TEMPERATURES FOR SHORT COLLISION TIME DEFAULT FOR EACH TEMPERATURE IS STANDARD VALUE FROM GENERAL ATOMIC REPORT IF AVAILABLE OTHERWISE MATERIAL TEMPERATURE CARD 5 TOL TOLERANCE EMAX MAXIMUM ENERGY FOR THERMAL TREATMENT X 3 OX O6 0 OR 0 06 OR OR 0 0 O6 0 Ob OR 0 X X X 0X 0 0 06 0 0 0 OR OR 0X 0 OR 0 0 OR O0 OR 06 The following sample problem illustrates producing thermal cross sections for hydrogen in water It assumes that a previous RECONR BROADR run prepared a three temperature PENDF tape on unit 23 in blocked binary mode ENDF B III tape 320 was mounted on unit 26 90 THERMR 26 23 24 1002 1269 8 3 4 0 2 201 0 300 500 600 01 2 0 Note that default effective temperatures are used The tape on unit 24 will contain MF3 MT201 and MF6 MT201 which can be requested in GROUPR
42. T 100 and ILMAX CONBAR NKTOT GT NKMAX More than 12 subsections found See NKMAX and 01 D2 El E2 and LOC all dimensioned 12 CONBAR TABULATED SUBSECTION MUST BE LAST Required by organizational problems This situation is satisfied in vers IV and V Other evaluations may need to be modified 76 CONBAR INSUFFICIENT STORAGE FOR RAW ENDF DATA Main container array is too small Increase STORE and NAMAX in HEATR HGTYLD ILLEGAL LND Assumes a maximum of six time groups for delayed neutrons HGTYLD STORAGE EXCEEDED Increase NWMAX in NHEAT currently 2500 TABBAR CODED FOR LF 1 AND LF 5 ONLY Self explanatory Should not occur HGTFLE DESIRED ENERGY ABOVE HIGHEST ENERGY GIVEN Fault in the evaluation HGTFLE NOT ENOUGH STORAGE FOR RAW DISTRIBUTIONS Main container array too small Increase STORE and NAMAX in HEATR GETCO LIMITED TO 21 LEGENDRE COEFFICIENTS Normal ENDF B limit GETCO LAB TO CM CONVERSION NOT CODED Discrete scattering data should be in the center of mass system already HCONVR ENERGY READ IN DOES NOT MATCH PREVIOUS ENERGIES Something is wrong with the data in MF12 LO 2 transition probability arrays GHEAT NOT CODED FOR LO 2 2 Will not occur since 10 2 data has been transformed to 10 1 format by CONVER GAMBAR REQUESTED ENERGY AT HIGHEST GIVEN ENERGY Some fault in MF15 data GAMBAR STORAGE EXCEEDED IN A Increase container array STORE and parameter NAMAX in HE
43. T ecw Ob JE e eff o E E u 10 3 544908 Via where is the effective temperature for the SCT approximation These tem peratures are given in Ref 3 they are usually somewhat larger than the corre sponding Maxwellian temperature T For the convenience of the user the values of Toff for the common moderators are included as defaults see input instruc tions THERMR expects the requested temperature T to be one of the temperatures included on the ENDF B thermal file or within a few degrees of that value 296 K is used if 300 K is requested Intermediate temperatures should be ob tained by interpolating between the resulting cross sections and not by inter polating S a B The secondary energy grid for incoherent scattering is obtained adaptively see CALCEM A stack is first primed with four points a point at the kine matic down scattering limit 1 2 1 2 a point near E or near the ex pected peak E if E KT and a point far out on each wing These inter vals are then subdivided by successive halving until the cross section obtained by linear interpolation is within the specified tolerance of the correct cross 83 section from SIGL The result is easily integrated by the trapazoid rule to find the incoherent cross section at energy E In this way all the extreme energy dependence of this function is accurately represented The cross section for one particular
44. The units for IOLD and INEW are then exchanged and the entire process is repeated for the next low threshold reaction 21 The final result of this process is a list of NREAC low threshold reaction types in usually MT2 MT18 and MT102 the first high threshold or the input value in THNMAX and a scratch file IOLD containing the energy grid and all the low threshold reactions there are N2IN points Now that the number of reactions to be broadened simultaneously is known NREAC storage for data paging can be assigned The total amount of storage available is NAMAX 2 NBUF NWSCR 40 The value of NAMAX should be as large as possible current value is 30 000 This space is divided up into the largest possible page size NPAGE An overflow region NSTACK is also allocated STORAG is used to allocate three pages for energies E three pages for each reaction cross section S one extended page for the broadened energy grid EB and three extended pages for the broadened cross sections SB This system is designed to use the available storage with maximum efficiency The cross sections on IOLD are now broadened and thinned by FILE3 see below and the results are written on scratch unit INEW using LOADA The dictionary from NSCRI actually an index is revised to reflect any thinning and written on the output PENDF tape NOUT Note that the new temper ature is written into the first word of the Hollerith data record to simplify later s
45. ace will be made If NWORDS 1 repack A and assign all available words to this ID INDEX points to the first word for data set ID in A RELEAS ID NWORDS Release all but NWORDS of the space assigned to ID in A NWORDS 0 deletes this ID If NWORDS is less than zero this ID and all ID entries above it are deleted Note that repacking of A only takes place when the released space is really needed see RESERV FINDEXCID INDEX A Find the index for the data set ID Using FINDEX is good practice if there is any chance that A might have been repacked since RESERV was called The NWORDS 1 option in RESERV is useful when the number of words in a data set is not known in advance an example 13 NW 1 CALL RESERV 3HSIG NW LSIG A READ NIN NW A LSIG I 1 1 1 NW CALL RELEAS 3HSIG NW A STORAG prints out routine messages if IPR 0 so that the user can monitor the use of memory The following example from THERMR illustrates several char acteristics of STORAG 1 STORAG 10 20000 2 ID SCR 1 2050 3 ID BUFO 2 3050 4 ID BUFN 3 4050 5 ID STK 4 4110 6 ID FL 5 19963 7 XX FL 406 8 XX STK 1 9 ID E 4 4095 In line 1 STORAG is initialized with 20 000 words of core for up to 10 identi fiers In lines 2 3 4 and 5 space is reserved for SCR BUFO BUFN and STK The number before the slash is the ordinal number assigned to the identifier and the second number is the total amount of storage used so far In line 6 spa
46. action cross section of a reso nance material may require a very large number of energy points For example ENDF B IV U 238 MAT1262 requires 57 400 points for the total cross section for 0 5X precision ERRMAX ERR It is impractical to load all these points into memory simultaneously However the discussion following Eq 5 in the theory section shows that only a limited energy range around the point of interest is required The strategy used is to stage the cross section data into three pages of NPAGE points each Points in the center page can then be broadened using the NPAGE or more points on each side of the point of interest If v 4 fa and 50 4 fa are both included in the three page range accurate broadening can be performed If not a diagnostic warning is printed the user should repeat the calculation with a smaller temperature step or larger page size There are many different reaction cross sections for each material How ever the cross sections for high velocities are normally smooth with respect to 32kT A for any temperatures outside of stellar atmospheres therefore they do not show significant Doppler effects The code uses the input value THNMAX or the lowest threshold typically gt 100 keV below the input THNMAX as a break point No Doppler broadening or thinning is performed above that energy Fur thermore the A and factors in Eq 7 depend only on the energy or veloc ity values and not on the
47. actions have to be obtained by adding the contri butions of all the resonances to backgrounds from MF3 At still higher ener gies comes the unresolved region where explicit resonances are no longer de fined Instead the cross section is computed from statistical distribution of resonance parameters given in File 2 and backgrounds from File 3 Finally at the highest energies the smooth MF3 representation is used again 19 10 ENDF B V U 235 Total Cross Section 1 Cross Section barns 1 mE smooth resolved unresolved smooth 10 i 107 40 40 Energy eV Fig 1 A typical cross section reconstructed from an ENDF B evaluation using RECONR The smooth resolved and unresolved energy regions use different representa tions of the cross sections For medium mass isotopes the unresolved range is usually omitted For the lightest isotopes the resolved range is also omitted the resonance cross sec tions being given directly in the smooth format In addition several differ ent resonance parameter representations are allowed It is the purpose of RECONR to take all of these separate representations and produce a simple cross section versus energy representation such as that shown in Fig 1 B Unionization and Linearization Strategy Several of the cross sections found in ENDF B evaluation are summation cross sections for example total inelastic and sometimes n2n and fission and it is im
48. ave to be made to convert a typical CDC code to an IBM machine Furthermore many of the changes can be made automatically with a simple preprocessing code see Vol I App D NJOY uses the following trick CCDC INTEGER H 5 CCDC CIBM REAL 8 H 5 CIBM The variable H is intended to hold Hollerith data To convert from CDC to IBM simply add in column 1 of every card image bracketed by CCDC cards and move the C from column 1 of every card image bracketed by CIBM cards Machine dependent aspects of free form input and interface 1 0 have been discussed above Several other conversion problems are discussed here BANNER This subroutine prints the NJOY banner on the output file It in cludes a user field LAB which should be changed to properly identify the user s installation It also includes a variable MX which can be used to indicate which machine was used at large computing centers remove CALL MACH MX if a corresponding capability is not available The date and time of day routines used here may have to be replaced with local equivalents ERROR This subroutine should result in a fatal error exit and must be ad justed to reflect the local system Special features such as trace back information or saving files for later analysis can be performed here TIMER This routine will have to be revised in many systems The coding given is appropriate for CDC machines 16 SIGFIG Because of the many comparisons and
49. ce for FL was reserved with NWORDS 1 Therefore 20 000 words less the STORAG table were allocated If repacking had been necessary a REPACKING message would have appeared here The program determined that only 406 words were needed for FL and the remainder of the storage was released in line 7 The maximum storage used to this point was 4110 406 4516 Farther on the code was finished with STK and FL and both were released by a single call with NWORDS 1 as indicated by line 8 Finally line 9 shows a new identifier being assigned Note that position 4 in the STORAG table was reused The STORAG system is compact and easy to use The overhead required to use it is very small unless frequent repacking is required G ENDF B Utility Routines There are several operations performed on ENDF B data that are needed in so many other modules that it is practical to put them into the NJOY level 14 TERP1 X1 Y1 X2 Y2 X Y 1 Interpolate for y x between yo x2 using the ENDF B inter polation law I I 1 means 1 2 means is linear in x 1 3 means y is linear in ln x I 4 means In y is linear in x and I 5 means 1 is linear in 1n x TERPACY X XNET IDIS A IP IR Interpolate for in the 1 structure in array A The routine searches for the correct interpolation range starting from IP and IR initialize to 2 and 1 for first call It returns XNEXT the next x value in the tabulation IDIS is set to 1 if the
50. coil energy and ES is the energy of the charged product For absorption followed by particle emission MT103 120 E Ep Emin A 1 X gt 23 2 24 En i 0 25 67 where Q is the C2 field from MF3 and x is the particle mass ratio x 1 gives a minimum for all reactions For neutron continuum scattering MT16 17 22 37 Ep Emin 0 and 26 En T SUBE En 27 where Q is the C2 field from MF3 Finally for fission MT18 21 38 the limits are E Q M 15 MeV and 28 max 7 E R 29 where Q is the prompt fission Q less neutrinos These values are intended to be very conservative Note that Ex is only significant at very low neutron energy In order to reduce unimportant error messages a tolerance band is applied to the above limits If all checks are satisfied the resulting kerma factors should give good local heating results even when 99 8 of the photons escape the local region E Computation of Damage Energy The formulas used for calculating damage energy are derived from the same sources as the heating formulas given above except in this case the effects of scattering angle do not result in simple factors like fa because the Robinson partition function is not linear Instead it is calculated as follows ER 30 1 6 0 402443 c P E 1 F 3 4008 68 if Ep gt 25 0 eV and zero otherwise In Eq 30
51. crease or decrease the errors in their respective columns to get an appro priate balance of accuracy and economy for a particular application 25 D Resonance Representations RECONR uses the resonance formulas as implemented in the original RESEND with three changes a more efficient calculation of multilevel Breit Wigner cross sections developed by C Lubitz of the Knolls Atomic Power Labora tory General Electric Co and coded by P Rose of the Brookhaven National Lab oratory the addition of competitive widths introduced for ENDF B V and a yx Doppler broadening calculation for single level Breit Wigner and Adler Adler resonance shapes An expanded discussion of the following formulas can be found in the ENDF B V format manual The subroutine that computes single level Breit Wigner cross sections CSSLBW uses code Z 2 1 y 8 x 51126 2 3 0 720 h 6 x 3 f pon Te r a z Om p U 0 xX and 4 4n 2 0 X 5 2241 sin 5 P 2 where On Uf Oy and are the neutron elastic fission radiative capture and potential scattering components of the cross section arising from the given resonances There can be background cross sections in File 3 that must be added to these values to account for competitive reactions such as inelastic scattering or to correct for the inadequacies of the single level representation with regard to multilevel
52. d MT3 74 at high energies do not pay attention to 304 and 402 above the breakover point Another example might indicate the care required in interpreting these error flags In Ta some of the proton emission is given as pseudo level n n p reactions in MT51 90 The corresponding photons are given in MT28 Clearly MT328 makes no sense and neither does MT304 G Input Instruction The input instructions that follow are reproduced from the comment cards in HEATR see also Vol I User s Manual INPUT SPECIFICATIONS FREE FORMAT CARD 1 NENDF UNIT FOR ENDF B TAPE NIN UNIT FOR INPUT PENDF TAPE NOUT UNIT FOR OUTPUT PENDF TAPE CARD 2 MATD MATERIAL TO BE PROCESSED NPK NUMBER OF PARTIAL KERMAS DESIRED DEFAULT 0 NQA NUMBER OF USER Q VALUES DEFAULT 0 NTEMP NUMBER OF TEMPERATURES TO PROCESS DEFAULT 0 MEANING ALL ON PENDF LOCAL 0 1 GAMMA RAYS TRANSPORTED DEPOSITED LOCALLY DEFAULT 0 IPRINT PRINT 0 MIN 1 MAX 2 CHECK DEFAULT 0 CARD 3 MT NUMBERS FOR PARTIAL KERMAS DESIRED TOTAL MT301 WILL BE PROVIDED AUTOMATICALLY PARTIAL KERMA FOR REACTION MT IS MT 300 AND MAY NOT BE PROPERLY DEFINED UNLESS A GAMMA FILE FOR MT IS ON ENDF TAPE SPECIAL VALUES ALLOWED 303 NON ELASTIC ALL BUT MT2 304 INELASTIC MT51 THRU 91 318 FISSION MT18 OR MT19 20 21 38 401 DISAPPEARANCE MT102 THRU 120 DAMAGE ENERGY PRODUCTION VALUES 444 TOTAL 445 ELASTIC MT2 446 INELASTIC MT51 THRU 91 447
53. d Y X is the one dimensional tabulation TAB2 MAT MT C1 C2 L1 L2 N1 N2 NBT 1 JNT I I71 N1 where the interpolation table is to be used to control a series of N2 LIST or TAB1 structures that follow and DICT MAT MF MT 0 0 MFS MTS NCS MODS where there is a record for each section in the material MFS MTS giving the card count NCS for that section For ENDF B V MODS indicates the revision number for that section The ENDF B procedure manual explains how these structures are combined to represent various physical quantities In order to make these records practical limits have been established that keep the record length below approximately 10 000 words In BCD mode each structure is broken up into many card images each containing 6 data words followed by MAT MF MT and a line sequence number There is no in trinsic limit to the length of a data structure written in BCD form because a program reading the data can normally be coded to use the data in pages of reasonable size The MINX code was forced to use BCD formats to handle the large tabulations found on PENDF tapes Analysis shows that this code uses more than 50 of its running time coding and decoding BCD formats In order to eliminate this waste a blocked binary format has been developed for the ENDF B data structures A structure is divided up into several logical records of intermediate length typically about 300 words each having the following fo
54. de for the radiative capture reaction n y The difference between the available energy E Q and the total energy of the emitted protons is such a small fraction of E Q that it is difficult to hold enough precision to get reasonable recoil energies Moreover the emitted photons cause a component of recoil whose effect is not normally included in evaluated capture spectra Finally the element problem cited above is especially troublesome for capture because the available energy may change by several MeV between energies dominated by resonances in different isotopes of the element giving rise to many negative or absurdly large heating numbers These problems are more important for damage calculations see below where the entire effect comes from recoil and the compensation provided by later deposition of the photon energy is absent For these reasons HEATR estimates the recoil due to radiative capture using conservation of momentum The recoil is the vector sum of the kick 60 caused by the incident neutron and the kicks due to the emission of all sub sequent photons Assuming that all photon emission is isotropic and that the directions of photon emission are uncorrelated the photon component of recoil depends on the average of E over the entire photon spectrum 2 E E sai 2 E 5 R 1 2 1 where mc is the neutron mass energy The second term is important below 25 100 keV This formula gives an estimate that work
55. dified MF6 format and written onto a scratch file At the same time the incoherent cross section is accumulated by trapazoidal integration interpolated onto the energy grid of the LOADA FINDA scratch file and stored If free scattering has been selected the elastic cross section is stored in the incoherent slot This process is repeated for each energy in the incident energy grid EGRID 88 Incoherent inelastic scattering cross sections and discrete cosines are computed in SIGL The stack for the adaptive reconstruction of the angular dis tribution for a given E gt is primed with p 1 p 1 and the angle for static that is 0 scattering The top interval on the stack is subdi vided by halving until the actual cross section computed by SIG is within a specified tolerance of a linear interpolate As each panel is converged its area is added to the accumulating cross section On convergence the fraction of the cross section corresponding to each equal probability bin is computed and the linearization process is repeated to find the bin boundaries and dis crete cosines Note that Legendre coefficients can be computed in this routine from the discrete cosines Finally PEND is called to prepare the output tape The dictionary is up dated to account for the new sections that are being added File 3 is located and the cross sections stored on the LOADA FINDA scratch file are retrieved formatted and written to the output
56. e examples are given in Table Doppler broadening effects will be impor tant below this energy and for any features such as resonances thresholds or artificial discontinuities in evaluations that are not slowly varying with respect to 2E E As an example for 235y at 100 eV Doppler effects are im portant for features smaller than about 0 8 eV The numerical evaluation of Eq 5 developed for SIGMA1 assumes that the cross section can be represented by a piecewise linear function of energy to acceptable accuracy This is just the form of the NJOY PENDF tapes see RECONR Defining the reduced variables y Jav and x the cross section becomes o 5 02 6 ENERGY PARAMETER FOR EFFECTIVE DOPPLER BROADENING Target Temperature Energy Parameter H 300 K 0 2 eV U 235 300 K 0 0017 eV U 235 1 0 keV 69 eV 45 _ 2 os with slope S 09 41 EA CITAN Xi Equation 5 can now be written as 1 1 2 a x 2 2 x 1 1 0 i _ 2 a 2 gt Ho Hy Ho and y EE 4 2 Bi 2 Ha y H3 6H 4yH y Ho 7 8 and where a is shorthand for 1 The extrapolations to zero and infinity assume a constant cross section sg7sy70 incomplete probability integrals defined by a b These functions can be computed in two ways First H a b F b where
57. earching The broadened cross sections are now converted into ENDF TABI records and merged with the unbroadened cross sections NSCR1 The total cross section and sometimes nonelastic fission and n2n is reconstructed to equal the sum of its parts The new Doppler broadened MAT on NOUT is a legal PENDF file with the same MAT number as the original data but a new temperature The process is now repeated for each of the NTEMP2 final temperature TEMP2 requested Note that after each step INEW contains the new data and IOLD con tains the previous data If the bootstrap option is set ISTRAP 1 these units are interchanged For this option TEMP2 IT is always obtained from TEMP2 IT 1 Because of thinning the broadening runs faster at each step The accumulation of error is usually not a problem For ISTRAP 0 1 is used for the starting temperature every time The broadening and thinning calculations are directed by FILE3 except for the parallel processing and input output this subroutine is taken from SIGMA1 The routine loads data into the appropriate core pages from scratch file IOLD 52 calls BROADN to broaden it calls THINB to thin it and writes the broadened and thinned results onto scratch file INEW BROADN is also nearly unchanged from SIGMA1 The energy grid points just loaded into by FILE3 are converted to the dimensionless variables x and see Eq 6 A loop is then set up over the y values in the center pa
58. effective cross section for a material at temperature T is defined to be that cross section that gives the same reaction rate for stationary target nuclei as the real cross section gives for moving nuclei Therefore pvo v T f dv olv v lo V V P V T 1 where v is the velocity of the incident particle V is the velocity of the target p is the density of target nuclei o is the cross section for stationary 43 nuclei and P v T is the distribution of target velocities in the laboratory system For many cases of interest the target motion is isotropic and the dis tribution of velocities can be described by the Maxwell Boltzmann function 3 2 12 P V T dv 5 OV 2 where a 2 is Boltzmann s constant and is the target mass Equation 1 can be partially integrated in terms of the relative speed V V V to give the standard form of the Doppler broadened cross section 2 atV Sv 25 dV vp 20707 a Im 0 P 3 It is instructive to break this up into two parts av o v 0o v 4 where x a E 2 a V v v 4 f dV o V V e 5 n v 0 The exponential function in Eq 5 limits the significant part of the integral to the range NOS Ja Ja 44 v the integral depends only on velocities satisfying These results can be converted to energy units using y 16 A m Nim 3 m Som
59. effects or missed resonances The sums extend over all the resolved resonances that may belong to different spin sequences 2 J L and AJ in the code Each resonance is characterized by its total neutron 26 ESTIMATED MAXIMUM ERROR DUE TO RESONANCE INTEGRAL CHECK ERRMAX ERRINT AND SIGNIFICANT FIGURE TRUNCATION NDIGIT UPPER ELASTIC PERCENT ERROR CAPTURE PERCENT ERROR ENERGY INTEGRAL RES INT SIG FIG INTEGRAL RES INT SIG FIG 1 55 02 4 96 02 7 45E 00 000 0 000 2 82 02 003 0 000 1 63 403 5 94E 00 000 0 000 1 7 1E O1 002 0 000 2 5 20E 03 4 12 00 000 0 000 6 80E 03 149 0 000 1 73 04 6 49E 00 000 000 1 61E 02 134 C08 5 62E 04 9 66 00 001 000 1 74 02 200 097 1 78E 05 4 20E 00 004 009 1 19 02 216 4 284 4 00 05 3 50E 00 008 007 5 64E 03 257 5 265 POINTS ADDED BY RESONANCE RECONSTRUCTION 12309 POINTS AFFECTED BY RESONANCE INTEGRAL CHECK 6969 POINTS AFFECTED BY SIGNIFICANT FIGURE REDUCTION 1262 POINTS REMOVED BY BACKTHINNING 201 FINAL NUMBER OF RESONANCE POINTS 12749 162 0365 909 Fig 3 Sample of RECONR resonance integral and significant figure error summary fission and capture widths Fe and its maximum value SMAX t in the code _ 4 Sm K 9 T E 6 _ 2J 1 9 412 gt 7 I is the total spin SPI given in File 2 and k is the neutron wave n
60. f the two values do not agree within various criteria the top of the stack is moved up one notch 1 3 and the new value is inserted I 2 The code then repeats the checking process for the new smaller interval at the top of the stack The top of the stack rises until convergence is achieved for the top interval The top energy and cross section are then saved on a scratch file the stack index is decremented and the checks are repeated This process is continued with the top of the stack rising and falling in response to the complexity of the cross section until the entire panel AE has been converged I 1 The stack is then reprimed with the bounds of the next panel The process continues until the entire energy range for linearization or reconstruction has been processed This new stack logic enables a panel to be divided into parts as small as 27 where n is the stack size currently 20 and several different cross sec tions elastic capture fission can easily be stored in arrays of this size By contrast RESEND used several arrays 500 words long and sometimes ran out of storage while subdividing between resonances Intervals are subdivided differently for linearization and resonance recon struction In the latter case the interval is simply divided in half as in RESEND For linearization the method developed by D R Harris for MINX2 is used Analytic formulas are used to choose the optimum intermediate point this point turns out
61. ge Refer ring to Eqs 7 and 8 the sum is accumulated for below y until the terms become insignificant If necessary the cross section is extended to 0 as a constant The H a b functions are produced by FUNKY and HUNKY using either Eq 10 or the alternate method of direct expansion The calculation is ordered to take advantage of previously computed values of A similar loop is performed for X gt y For low energies the term c y is then computed and added to the sum The broadened cross sections are stored in SB and the ener gies are converted back to eV and stored in EB The THINB routine follows SIGMA1 except that no thinning is performed above the minimum threshold THNMAX 11 points in a given interval are tested for their deviation from the straight line connecting the endpoints If all are within tolerance all can be removed the interval is extended to one more point and the test is repeated If any point fails the last point is accepted as an output point The thinned data remain in EB and SB for FILE3 HUNKY has been modified to implement the alternate H a b calculation when necessary see HNABB When using the direct method En values from the pre vious step are used in the difference of Eq 10 and FUNKY is called to get the new values The A and B of Eq 18 are related to the 1 and S2 here FUNKY evaluates F a by the recursion formula of Eq 12 using a rational approximation to the reduced co
62. hese effects are shown in Figs 1 2 and 3 they can be best understood by noting that the Doppler process preserves reaction rate vo v according to Eq 1 and a finite reaction rate is expected for T gt 0 even as v gt 0 48 10 10 1 Cross cuen barns 1 10 10 107 10 10 10 10 10 10 10 Energy eV Fig 1 The n a cross section for 10 from ENDF B V for three different temperatures showing that a 1 v cross section is invariant under Doppler broadening 5 Cross Section barns 1 10 10 10 10 10 1 10 10 10 Energy ev Fig 2 The elastic cross section for carbon from ENDF B V showing that Doppler broaden ing a constant cross section adds a 1 v tail 49 10 Cross Section barns 101 d 10 10 10 10 10 10 10 10 Energy eV Fig The n y cross section for 240p from ENDF B V for several temperatures showing the effects of Doppler broadening on resonances The temperatures are OK solid 30 000 K dotted and 300 000 K dash dot The higher resonances behave in the classical manner even at 30 000 note that the line shape re turns to the asymptotic value in the wings of the resonance 11 resonances at 300 000 K and to a lesser extent the first resonance for 30 000 K show the additional 1 v component that appears when kT A is large with respect to the resonance energy B Data Paging Methodology A piecewise linear representation of a re
63. hine dependent limit for decimal single precision accuracy is reached It clearly makes no sense to continue to add grid points after this limit is reached Through the use of dynamic format construction the energy resolution available for formatted NJOY output is 7 significant figures that is 1 234567 tn rather than the usual 5 or 6 see Section X D On short word machines 32 36 bits per word the limit set by precision is also about 7 significant figures On long word machines typically 60 64 bits per word binary output files can be used and NJOY can produce up to 15 significant figures if necessary Significant figure control is implemented as follows each intermediate energy is truncated to NDIGIT significant figures before the corresponding cross sections are computed and if the resulting number is equal to either of the adjacent values the interval is declared to be converged Thus no identical energies are produced but an unpredictable loss in accuracy results The error in the area of this interval is certainly less than 0 5 Ao AE so this value is added to an error estimate and a count of panels truncated by the significant figure check is incremented for a later informative diagnostic message The second basic problem alluded to above is that a very large number of resonance grid points arise from straightforward linear reconstruction of the resonance cross sections of some isotopes Many of these points come from nar row
64. his means that every module is essentially a freestanding program Figure 1 illustrates the over lay version of the code Here the NJOY level consists of a simple executive program for linking modules together and a set of utility subroutines available to all modules Other structures are possible For example the linking of modules could be handled by the normal sequencing capabilities of the operating system the NJOY utilities would then be made available to the loader as a re locatable library The restrictive definition of the term module used here makes it possible to choose whichever of these two configurations is most suit able for a particular operating system makes it easy to add new modules and protects a module against changes or repairs in another module A The Executive Program This is the main program of the NJOY system It simply reads a module name in free format and calls in the requested module The first card read by any module contains the unit numbers for the various input and output files In this way the output of one module can be assigned to be the input of another module thereby linking the modules to perform the desired processing task Table I gives an example of the linking procedure 2 NJOY ENDF B PENDF GENDF Main program Working Output Module Module MODER RECONR MODER BROADR DTFR UNRESR CCCCR HEATR MATXSR THERMR COVR GROUPR ACER GAMINR POWR ERRORR Modu
65. ill be copied to the new NOUT and broadening will continue for temperature five The bootstrap option speeds up the code by using the broad ened and thinned result for TEMP2 I 1 as the starting point to obtain TEMP2 I The THNMAX parameter can be used to speed up a calculation or to prevent the broadening of inappropriate data such as unresolved cross sections or evalua tions using histogram or sharp triangular representations at high energies for example ENDF B V lead The following example prepares a single output tape containing AM 241 and AM 243 from ENDF B IV at two temperatures each BROADR 20 21 1056 2 0 1 0 001 300 1200 1057 0 Unit 20 contains a RECONR generated BCD PENDF tape containing O K cross sections for the two isotopes Four materials will be generated on unit 21 with 0 1 accuracy The default THNMAX of 1 MeV will be used 54 Error Messages BROADR TOO MANY LOW THRESHOLD REACTIONS The current limit is 9 Check TT MTR and NTT in BROADR TT in FILE3 and SBT in BROADN Too many reactions might also strain the total storage see A and NAMAX in BROADR BROADR INPUT AND OUTPUT MUST BE SAME MODE Use coded to coded or blocked binary to blocked binary The latter is much faster due to the several tape copies performed in BROADR BROADR STORAGE EXCEEDED Insufficient storage to update dictionary Increase NWSCR in BROADR WARNING BROADENING TRUNCATED AT A The is too
66. interference 32 1 0 1200 0 Reconr only Broadr Difference O no amp 2 1 58 A 5 e ANAL Maddern 2 2 lt YN E o0 T 2 Og 2 a 1 8 j Dm 4 57 3 0 20 Energy eV Fig 4 Comparison of Doppler broadened cross sections generated with the method RECONR only and the kernel method BROADR for 2330 at 300 recon struction tolerance was 0 2 2 gi _ 2 o E 0 2 i n msi 35 P D 2 9 o Def TFR 36 K s D S 2g 1 sin e 37 P ge 5 33 where x stands for either fission or capture D are the appropriate average widths and spacing for the 2 J spin sequence and Ri is the fluctuation integral for the reaction and spin sequence see GNRL These integrals are simply the averages taken over the chi square distributions specified in the file for example 1 7 5 nff T x f dx Ap AF f dx FO OT STO 38 where P x is the chi square distribution for u degrees of freedom The inte grals are evaluated with the quadrature scheme developed for Mc 11 giving gta pa eee 39 f 1 1 J j k k FAME av pA n EN 2 Ty i TQ The Qi are the appropriate quadrature weights and values for degrees of freedom and assumed to be constant many degrees of freedom com petitive width re
67. is assumed to effect the fluctuations but a corresponding cross section is not computed The entire competitive cross section is supposed to be in the File 3 total cross section as a smooth background It should be noted that the reduced average neutron width AMUN is given in the file and _ 0 p E JE VO 40 34 where the penetrabilities for the unresolved region are defined as 1 41 2 ae and 42 p m 43 2 BAE Other parameters are defined as for SLBW Unresolved parameters can be given as independent of energy only fission widths dependent on energy or as fully energy dependent The first two options are processed in CSUNR1 and the last one in CSUNR2 The ENDF B V formats specify that cross sections are to be computed at the specified energy points and the cross sections are to be computed for energies between these points by interpolation However this procedure gives unreasonable results for the energy independent evaluations carried over from earlier versions of ENDF B Therefore RECONR is allowed to linearize the unresolved cross section using interpolation on parameters For most applications the numbers in this energy range are replaced by UNRESR where a different strategy is used to select inter mediate points E Code Description The flow of this module is controlled by the RECONR program The first step is to read cards 1 2 and 3 of the user s input The TAPEID record of the inpu
68. le Fig 1 Basic structure of the NJOY code overlay configuration TABLE I EXAMPLES OF LINKING MODULES TOGETHER IN THE OVERLAY CONFIGURATION mount an ENDF B tape on unit 20 0 5 RECONR 20 21 input lines for RECONR GROUPR 20 210 22 input lines for GROUPR DTFR 22 23 21 input lines for DTFR STOP DTF format card images written on unit 23 The main program also sets the page length NPAGE for blocked binary files see below and assigns the unit numbers for system input and output NJOY ex pects these numbers to be less than 10 the normal choice is 5 for input and 6 for output In a time sharing environment it is often helpful to have a short print for the terminal while still preserving the long listing for the system printer Such an option is provided by IOPT 1 This option changes the input and output NSHORT to unit 7 which can be equivalenced to the terminal TTY The final common parameter is IVERF which should be 4 to process ENDF B 1V evaluations and 5 for ENDF B V The input instructions for the NJOY module are given as comment cards at the beginning of the module They are reproduced here for the convenience of the user see also Vol I User s Manual C x INPUT SPECIFICATIONS FREE FORMAT 5 C C CARD 1 INPUT OPTION Go IOPT 0 FOR CARD INPUT AND FULL OUTPUT Qo 1 FOR TERMINAL INPUT WITH SHORT OUTPUT ON TERMINAL C CARD 2 5 C o IVERF ENDF B VERSION
69. ll be called redundant if the partial fission representation MT19 20 21 38 is found Space for the new material dictionary is then reserved MFS MTS NCS Section identification and card counts will be entered into these arrays as they are determined The next step is to read File 2 which contains resolved and unresolved resonance parameters if any The array RES is assigned to contain the File 2 data and RDFIL2 is called to read them While the resonance parameters are being stored RECONR adds each resonance energy to its list of energy nodes ENODE In the unresolved energy range RECONR uses the energies of tabulated parameters or fission widths if available If the evaluation uses energy independent parameters RECONR creates additional node energies with equal lethargy spacing The energy nodes are sorted into order and duplications are removed When control is returned to RECONR any unused space in the RES array is released to be made available for other uses The subroutine LUNION is used to linearize and unionize the ENDF B data Space is reserved for two buffers to be used by LOADA FINDA and for the lineari zation stack Y and X The length of the stack NDIM determines the smallest NDIM times the possible subdivision of each panel energy points as close as 2 panel width can be generated Since the number of energies in the union grid may soon exceed the capacity of any reasonable small core array the existing list of
70. ll photon energy is deposited locally The same result can be forced using the LOCAL input parameter Kinematic Limits As an option provided mainly as an aid to evaluators HEATR will compute the kinematic maximum and minimum kerma factors and compare them with the energy balance result The formulas used are as follows For elastic scatter ing MT2 2 1 2 R QE 13 65 where Ep is the expected recoil energy For discrete inelastic scattering MT51 90 the photon momentum is neglected to obtain 1 _ 2AE E 1 f 1 14 R A 1 2 1 AE 1 where EY C2 from For continuum inelastic scattering MT91 secondary neutrons are assumed to be isotropic in the LAB system giving oL n En 7 15 and A 1 E ADE 16 where E is the average photon energy expected for this representation For radiative capture MT102 ANDE ER Ex gt 17 _ bog UE A 18 where 66 fog ce E Ati 19 K 2 Moc with Mac 939 512 A 1 Q 20 being the mass energy in MeV For two body scattering followed by particle emission MT51 91 LR flag set a minimum and maximum can be defined E ER Emin 7 ER gt 21 ER Emax Ep 0 Emax 22 where Ep is the value from Eq 10 11 or 12 Q is the C2 field from MF3 and is the C2 field from these equations En is the re
71. mber of entries in the dictionary MOREIO is not used MOREIO NIN NOUT NSCR A NB NW Read write continuation records or pages to from the array A Returns NB 0 after processing the last record or page CXFP X F S N This routine is used by some of the other ENDF B routines to prepare formatted output without the normal FORTRAN E Floating point numbers are output as 1 23456tNN or 1 2345674N depending on the size of the exponent In these calling sequences the unit numbers can be positive negative or zero Positive numbers mean BCD mode negative numbers mean blocked binary mode and zero means the file corresponding to this position in the calling sequence is not used All of these routines use one area of labelled common COMMON CONT C1 C2 L1 L2 N1 N2 MAT MF NS NSP NSC where Cl through MT have their usual ENDF meanings NSP is the sequence number for NIN NS is the sequence number of NOUT and NSC is the sequence number for NSCR Two examples may help to make clear the use of these routines Example 1 Read All Data LOC 1 CALL TABIIO NIN 0 0 A 1 NB NW 10 IF NB EQ 0 GO TO 20 LOC LOC NW CALL MOREIO NIN 0 0 A LOC NB NW GO TO 10 20 process data in A Example 2 Paging CALL TABIIO NIN 0 0 A 1 NB NW 10 process this page of data in A IF NB EQ 0 GO TO 20 CALL MOREIO NIN 0 0 A 1 NB NW GO TO 10 20 CONTINUE When NIN is BCD paging is automatic Positive and negative unit numbers can be mixed in TPIDI
72. me mode The data on an ENDF tape are written in 7 different kinds of structures each of which has a binary and a formatted form the words coded formatted and BCD will often be used interchangeably even though the actual representa tion might be ASCII or display code The structures are 1 TAPEID a Hollerith title for the tape 2 CONT a control record includes SEND FEND MEND and TEND 3 LIST a list of data items 4 HOLL a list of Hollerith words 5 TAB1 a one dimensional tabulation of data pairs 6 TAB2 a two dimensional tabulation control record and 7 DICT an index dictionary to the sections found in the MAT It should be noted that HOLL is a special case of LIST and DICT is a special case of CONT In binary mode each structure is written as a single logical record as follows MT A 1 I 1 17 where MAT tape number MF MT 0 and the Hollerith data are 16A4 A2 CONT MAT MF MT C1 C2 L1 L2 N1 N2 LIST MAT MF MT C1 C2 L1 L2 N1 N2 ACI I 1 N1 HOLL MAT MF MT C1 C2 L1 L2 N1 N2 ACI I 1 N1 s In ENDF B manuals the slash is used as a logical divider Replace it with a comma and add parentheses when constructing a FORTRAN I 0 list where MF 1 MT 451 and each line of Hollerith characters is stored in A as 16 4 A2 MT C1 C2 L1 L2 N1 N2 NBT I JNT I I 1 N1 X 1 I 1 N2 where NBT and JNT are the interpolation table an
73. mplementary error function HNABB implements the alternate calculation described by Eqs 14 17 The series expansion is continued until about six significant figures are guaran teed see EPS in HNABB HNABB is called when only four significant figures are reliable in HUNKY see TOLER in HUNKY D User Input The following input instructions have been copied from the comment cards at the start of BROADR and are also given in Vol I User s Manual 53 X INPUT SPECIFICATIONS FREE CARD 1 C NIN INPUT PENDF TAPE 5 5 NOUT OUTPUT PENDF TAPE CARD 2 x MATL MATERIAL TO BE PROCESSED a 5 NTEMP2 NUMBER OF FINAL TEMPERATURES MAXIMUM 6 x ISTART RESTART 0 1 YES 5 C ISTRAP BOOTSTRAP 0 NO 1 YES C 1 STARTING TEMPERATURE FROM NIN 5 ERRTHN FRACTIONAL TOLERANCE FOR THINNING x THNMAX MAX ENERGY FOR BROADENING AND THINNING 5 5 DEFAULT 1 MeV C CARD 3 5 C 5 2 FINAL TEMPERATURES DEG KELVIN x CARD 4 s MAT1 NEXT MAT NUMBER TO BE PROCESSED WITH THESE C PARAMETERS TERMINATE WITH MAT1 0 Note that TEMP1 need not occur on NOUT The restart option enables the user to add new temperatures to the end of an existing PENDF tape This option is also useful if a job runs out of time while processing for example the fifth temperature The job can be restarted from the partial NOUT The first four temperatures w
74. nd kinematic checks if requested Now NHEAT is called After allocating itself some temporary storage it copies MF1 from the ENDF tape to be used for the retrieval of fission v by CONBAR A loop is set up over all nonredundant reactions in MF3 For each reaction the appropriate Q value is chosen the cross sections are retrieved with GETYl and the average neutron energies and damage energies are calculated with DISBAR CONBAR CAPDAM and DISDAM The neutron part of the kerma and the 72 1 1 10 10 10 Damage eV barns 1 10 10 10 10 10 10 10 10 10 10 Energy eV Fig 3 Components of radiation damage energy production for 27A from ENDF B V A jis absorption I is inelastic scattering E is elastic scattering and T is total damage function are computed and added into the appropriate partial reactions being accumulated on the LOADA FINDA file If desired kinematic limits are computed and added onto the LOADA FINDA file This loop is continued for all reactions and all grid energies The DISBAR routine is used by NHEAT to compute the average secondary energy for elastic MT2 or discrete inelastic scattering MT51 90 using the scat tering coefficient from MF4 see GETFLE Similarly CONBAR computes the aver age secondary energy and damage energy for continuous distributions described in MF5 Analytic representations use simple formulas coded into ANABAR or a combination of adaptive and Gaussian quadrature
75. ntal evaluations in ENDF B Isotopic Q values and cross sections are not available in the files It will usually be possible to define quite adequate cross sec tions yields and spectra for the element However it is clear that the available energy should be computed with an effective Q given by 59 2 0 4 2 Po 1 where is the atomic fraction of isotope 1 in the element This number is energy dependent and can be represented only approximately by the single con stant Q allowed in ENDF B For elastic scattering the neutron kerma factor can be directly evaluated without reference to photon data For other reactions conservation of momentum and energy can be used to estimate the kerma or to compute minimum and maximum limits for the heating HEATR includes an option that tests the energy balance kerma factors against these kinematic limits thereby providing a valuable test of the neutron photon consistency of the evaluation If the energy balance heating numbers for a particular isotope should fail these tests and if the isotope is important for a small system an improved evaluation is probably required The alternative of making ad hoc fixes to improve the local heat production is dangerous because the faults in the neutron and or photon data revealed by the tests may lead to significant errors in neutron transport and or photon dose and nonlocal energy deposition In practice an exception to this conclusion must be ma
76. ocumented elsewhere 1 but for the convenience of the reader some features of the format will be described here ENDF B tapes are subdivided internally into materials MAT files MF and sections MT A MAT contains all data for a particular evaluation for an element or isotope for example MAT1276 is an evaluation for 8 0 16 A file contains a particular type of data for that MAT MF 3 is cross section versus energy data MF 15 contains secondary photon energy distributions A section refers to a particular reaction for example MT 2 is elastic scatter ing and MT 107 is the n a reaction Every record contains the current MAT MF and MT values Two materials are separated by a record with MAT 0 the mate rial end or MEND record Two files are separated by a record with MF 0 the file end or FEND record Two sections are separated by a record with 0 the section end or SEND record Finally the tape is terminated with a record with MAT 1 tape end or TEND record NJOY has a set of utility subroutines for locating desired positions on an ENDF tape FINDF MAT MT NIN Search NIN backward or forward for the first record with this MAT MT TOSEND NIN NOUT1 NOUT2 A TOFEND NIN NOUT1 NOUT2 A TOMEND NIN NOUT1 NOUT2 A TOTEND NIN NOUT1 NOUT2 A Skip forward past the next SEND FEND MEND or TEND Card on NIN If NOUT1 and or NOUT2 are nonzero copy the records Input and output files must be in the sa
77. on a LOADA FINDA scratch file to be used for normalizing free scatter ing if necessary On option THERMR computes elastic and or inelastic cross sections by calls to COH IEL and CALCEM The results are written onto the output PENDF tape by PEND li Some alteration of ENDF B formats and conventions was required to accommo date thermal cross sections The incoherent inelastic cross sections fit wel into MF 3 using MTREF see user input The coherent or incoherent elastic cross section if present uses MTREF 1 Other modules of NJOY expect that thermal MT numbers will be between 200 and 250 The incoherent energy to energy matrix is stored in MF6 coupled angle energy distributions The orig inal ENDF formats are not well suited to this application because secondary angle and energy are not tightly coupled as required by the physics of the These are tapes in the 320 series available from the National Nuclear Data Center at Brookhaven National Laboratory 86 problem Three new options have been defined LTT 5 for reordered discrete angle inelastic transfer cross sections LTT 6 for discrete angle elastic data and LTT 7 for coherent elastic reactions The format for LTT 5 is in standard ENDF B notation 6 MT ZA AWR O LTT O OJHEAD MAT 6 MT TEMP O 0 NNR NNE E TAB2 lt subsections for each of the NNE values of incident energy E 6 0 0 0 0 0 0 0 JSEND The structure of a subsection for LTT 5
78. ontains copy of nonredundant sections from original ENDF B tape 11 NSCR2 in RECONR NGRID in LUNION RESXS and EMERGE Contains union grid for ENDF B tape not counting resonances 12 NSCR3 in RECONR NOUT in RESXS and NRES in EMERGE Contains resonance grid and cross sections 13 NSCR4 in RECONR is used for two separate purposes In RESXS it is a binary scratch file NSCR used for the unthinned resonance data In EMERGE and RECOUT it is NMERGE and contains the nonredundant reactions on the union grid 14 15 IOLD INEW in LUNION Used locally only to accumulate union grid for ENDF B cross sections 14 15 IOLD INEW in EMERGE Used locally only to accumulate summation cross sections on union grid 20 99 User s choice for NENDF and NPEND to link RECONR with other modules 5 6 7 System I 0 units see NJOY Note that 11 12 14 and 15 are always binary Unit 10 has the same mode as NENDF Unit 13 is binary when used in RESXS and it has the same node as NPEND elsewhere NPEND can have a different mode than NENDF Storage Allocation Storage allocation in RECONR is sensitive to 1 the amount of resonance parameter data 2 the size of the resonance reconstruction stack 3 the use of broadening and 4 the sizes of LOADA FINDA buffers Other storage re quirements are minor Buffer sizes can be reduced or increased at will The result is a storage speed tradeoff with no change in capability or accuracy See NBUFG 2000
79. photon partials in J The total kerma is well defined but partial kermas should be used only with caution HEATR loops through all the neutron reactions on the ENDF B tape and com putes the neutron contributions needed for the first term These are n oe E Qi Ei 210 0 8 The 0 value is zero for elastic and inelastic scattering For n n particle reactions represented by scattering with an LR flag set Q is the ENDF C1 field from For all other reactions Q is the C2 field from MF3 In the case of fission the component of delayed fission energy from File 63 1 MT 458 is subtracted from Q to give a prompt result HEATR allows the user to override any Q value with his own number The E value is defined to include multiplicity in Eq 8 The multi plicity is either implicit for example 2 for n2n or is retrieved from the ENDF B file fission v The average energy per neutron is computed differently for discrete two body reactions and continuum reactions For elastic and discrete inelastic scattering MT2 51 90 1 arf n 1 9 where fi is the center of mass average scattering cosine from MF4 and r is the effective mass ratio For elastic scattering r A but for threshold scatter ing AES 10 where S is the negative of the C2 field from MF3 For continuum scattering the average energy per neutron is computed from the secondary neutron spectrum
80. plicity and E is the energy of secondary photons including photon yield This method is well suited for use with ENDF B which contains neutron and photon spectral data but not the particle spectra required by the direct method The disadvantage of this method is that the kerma factor sometimes depends on a difference between large numbers In order to obtain accurate results extreme care must be taken with the evaluation to ensure that photon and neutron yields and average energies are consistent In fact the lack of consistency in ENDF B IV often reveals itself as negative kerma factors However this is not always the defect it seems to be It must be remem bered that heating has both neutron and photon components A negative kerma might indicate that too much energy has been included with the photon production in the evaluation This will result in excessive photon heating if most of the photons stay in the system However the negative kerma will have just the right magnitude to cancel this excess heating The energy balance method guar antees conservation of total energy in large homogeneous systems In this context large and homogeneous means that most neutrons and photons stay in their source region It is clear that energy balance errors in the evaluation affect the spatial distribution of heat and not the total system heating when the energy balance method is employed A final problem with the energy balance method occurs for the eleme
81. portant that each summation cross section be equal to the sum of its parts However if the partial cross sections are represented with nonlinear interpolation schemes the sum cannot be represented by any simple interpolation 20 law A typical case is the sum of elastic scattering MT2 interpolated linearly to represent a constant and radiative capture MT102 interpolated log log to represent 1 v The total cross section cannot be represented accurately by either scheme unless the grid points are very close together This effect leads to significant balance errors in multigroup transport codes and to splitting problems in continuous energy Monte Carlo codes Furthermore the use of linear linear interpolation that is o linear in E can be advantageous in several ways The data can be plotted easily they can be integrated easily cross sections can be Doppler broadened efficiently see BROADR and finally linear data can be retrieved efficiently in con tinuous energy Monte Carlo codes Therefore RECONR puts all cross sections on a single unionized grid suit able for linear interpolation As described in more detail below RECONR makes one pass through the ENDF B material to select the energy grid then a second pass to compute cross sections on this grid Each cross section on the PENDF tape except for the redundant summation cross sections is exactly equal to its ENDF B value The summation cross sections are then obtained by adding
82. r Data File ENDF Brookhaven National Laboratory report BNL NCS 50496 ENDF 102 1979 3 J U Koppel and D Houston Reference Manual for ENDF Thermal Neutron Scattering Data General Atomic report GA 8774 revised and reissued as ENDF 269 by the National Nuclear Data Center Brookhaven National Labora tory 1978 4 Honeck and D Finch FLANGEII Version 71 1 A Code to Process Thermal Neutron Data From an ENDF B Tape Savannah River Laboratory report DP 1278 ENDF 152 1971 5 Williams The Slowing Down on Thermalization of Neutrons John Wiley and Sons New York 1966 94 Y U S GOVERNMENT PRINTING OFFICE 1982 0 576 020 101 Los Alamos
83. re is a discontinuity at XNEXT it is zero otherwise GETY1 X XNEXT IDIS Y1 ITAPE A GETY2 X XNEXT IDIS Y2 ITAPE A Find in a TAB1 structure starting at the current location on ITAPE by paging the data through array A GETY1 and GETY2 are iden tical for occasions when two different tapes are being searched at the same time XNEXT and IDIS behave as in TERPA The array A must be at least NPAGE 50 words in length These routines are normally used to retrieve cross sections from MF 3 GRAL XL YL XH YH X1 X2 1 This function returns the integral from to Xo of an ENDF B function with interpolation law I see TERP1 XL YL XH and YH are the low and high limits of the interpolation panel INTEGA F X1 X2 A IP IR Integrate the TAB1 function stored in A from to Xo The routine automatically determines the correct interpolation law for each panel or fraction of a panel and uses GRAL to compute each part of the in tegral Set IP 2 and IR 1 on the first call to INTEGA In subsequent calls the previous values of IP and IR will usually provide a good starting point for searching in the 1 structure Code Conversion Standardization of the computer industry has not yet reached the point where it is possible to write a truly machine independent FORTRAN code How ever by using fairly simple commands and isolating some functions in utility 15 subroutines it is possible to minimize the number of changes that h
84. rial as computed by THERMR 81 B Incoherent Inelastic Scatterin In ENDF B notation the thermal incoherent scattering cross section is given by 1 gt Je 67872 sap b MIA E 5 where is the initial neutron energy is the energy of the scattered neu tron u is the scattering cosine in the laboratory system 95 is the character istic bound incoherent scattering cross section for the nuclide T is the Kelvin temperature B is the dimensionless energy transfer BR i a is the dimensionless momentum transfer E 7 is Boltzmann s constant and A is the ratio of the scatterer mass to the neutron mass The bound scattering cross section is usually given in terms of the characteristic free cross section Ors ae us 8 The scattering law S a B describes the binding of the scattering atom in material For a free gas of scatterers with no internal structure 82 5 8 8 L e 92 82 4 4na 9 For binding in solids and liquids 5 for several materials has been com puted and written in ENDF B File 7 format 2 The scattering law is given as tables of S versus a for various values of B Any desired values of S can be obtained by interpolation If the a or B required is outside of the range of the table in File 7 the differential scattering cross section can be computed using the SCT approxima tion 181 2 SC
85. rm MF NB NW ACT I 1 NW where NB is the number of words remaining in the data structure the last record has NB 0 This type of record is compatible with the official ENDF binary record but is also adaptable to paging methods The page size can be chosen to optimize input output rates for a particular computer system A set of utility subroutines has been devised to handle both blocked binary and paged BCD input and output 10 TPIDIO NIN NOUT NSCR A NB NW Read write the Hollerith tape identification record to from array A NB 0 NW 17 CONTIO NIN NOUT NSCR A NB NW Read write a control record to from A NB 0 NW 6 Uses ACONT for END cards ACONT NOUT NSCR Write an end record on the desired units LISTIO NIN NOUT NSCR A NB NW Read write the first record or page of a list record to from A If NB is not zero continue with MOREIO as illustrated in Examples 1 and 2 below HOLLIO NIN NOUT NSCR A NB NW Read write the first record or page of the Hollerith descriptive data MF1 MT451 to from A taking account of the 16A4 A2 format needed in BCD mode If NB is not zero use MOREIO TAB1IO NIN NOUT NSCR A NB NW Read write the first record or page of TAB1 structure If NB is not zero use MOREIO TAB210 NIN NOUT NSCR A NB NW Read write a TAB2 structure NB 0 DICTIO NIN NOUT NSCR A NB NW Read write the entire material dictionary really an index to from A On entry NW is the nu
86. roach standardized for FORTRAN 77 If call able open and close operations or the equivalent are not available on the target system a fixed set of units can be defined on a program card CDC or job control deck IBM and these routines can be replaced with versions that simply return to the calling program Caution some units may be used for binary I 0 in one part of the program and coded formatted 1 0 in another C Free format Input For a card input program free form input is convenient but in a time sharing environment it is almost essential Therefore a subroutine FREE has been included among the NJOY utilities to provide a simple free format input capability This routine contains a machine dependent subroutine PACK that may have to be adapted to local conditions FREE NIN Z NZA NCW NIN input logical unit containing free format card images Z 1 dimensioned variable containing numbers decoded from input cards NZA on call number of words desired on return number of words found NCW number of Hollerith characters to be loaded in each word blank fill to right All numbers read from the input cards are returned as real in Z The calling program can convert selected numbers to integer mode as required Hollerith variables are returned in integer form using the internal N bit code of the machine If NCW is larger than the number of characters per word successive locations of Z will be used Fields on the input cards are delimi
87. s for both isotopes and elements and has no precision problems However it does not explicity con serve energy and isotopes with bad capture photon data can still cause problems B Theory of Damage Energy Damage to materials caused by neutron irradiation is an important design consideration in fission reactors and is expected to be an even more important problem in fusion power systems There are many radiation effects that may cause damage for example direct heating gas production for example helium embrittlement and the production of lattice defects A large cluster of lattice defects can be produced by the primary recoil nucleus of a nuclear reaction as it slows down in a lattice It has been shown that there is an empirical correlation between the number of displaced atoms DPA and various properties of metals such as elasticity The number of dis placed atoms depends on the total available energy Ea and the energy required to displace an atom from its lattice position Ey Since the available energy is used up by producing pairs E DPA 6 d 61 The values of Ey used in practice are chosen to represent the empirical corre Jations and a wide range of values is found in the literature see Table I for some examples The energy available to cause displacements is what HEATR calculates It depends on the recoil spectrum and the partition of recoil energy between electronic excitations and atomic motion The par
88. t tape NENDF is read and printed then the new TAPEID record is written on the output tape NPEND RECONR is now ready to enter the loop over desired materials For each material STORAG is used to allocate space for the energy nodes and for scratch storage ENODE SCR and RUIN 1 called to read cards 4 through 7 of the user s input RUIN automatically adds the ENDF B energy limits of 1x 107 eV 20 MeV and the thermal energy 0 0253 eV to any energy grid 35 points entered by the user If the reconstruction temperature TEMPR is greater than zero a table of y and functions is generated the W table see WTAB and QUICKW The FINDF utility subroutine 15 then used to find the first card of file 1 MF 1 MT 451 for the desired material File 1 on the input ENDF B tape is examined to obtain certain constants and flags and to analyze the dictionary ANLYZD The dictionary is really an index to all the files and sections reactions appearing for the MAT ANLYZD determines which reactions should be considered redundant that is the sum mation reactions that will be included on the PENDF tape The total cross sec tion MT 1 for neutrons MT 501 for photons will always be included the non elastic cross section MT 3 will be included if it is needed for photon pro duction that is MF12 is found the inelastic cross section MT 4 will be included if MT51 through MT91 occurs and the total fission reaction MT18 wi
89. ted by any character not used for an other purpose number E H R For exponent fields the E must be present and spaces are not allowed before the E Decimal points are not re quired after numbers Hollerith fields may use nHstring or string character terminates the input for one call to FREE it may involve more than one card leaving any unread variables unchanged This feature is often used to default variables from the right The nR specification causes the number fol lowing R to be repeated n times Some input examples follow legal illegal 12 12 1 2E1 lo2tl 1 2 El U235 4HU235 4RU235 does not right justify 581 0 1 1 6 Other examples will be found in input samples throughout this report FREE contains several parameters that may have to be changed when convert ing between different machines NBPC is the number of bits per character for Hollerith data 6 on CDC 8 on IBM MACHWD is the number of Hollerith charac ters in a machine word 10 on CDC 4 on IBM and RNDOFF is a constant that should be approximately equivalent to one bit in the last place for the target machine The rest of the machine dependence is incorporated into FUNCTION PACK which inserts characters into words Two versions are supplied one is based on masking for CDC machines and the other uses one byte variables and equiva lencing for IBM systems D Input Output The ENDF B evaluated nuclear data files are well d
90. ted particle to the neutron E is given by _ A 1 a o Co and the particle energy is approximated as being equal to the smaller of the available energy 71 5431 43 or the Coulomb barrier energy 1 029 x 10 27 1 3 41 3 in eV 44 a where z is the charge of the emitted particle and Z is the charge of the target A more reasonable distribution would be desirable but this one has the advan tage of eliminating an integration and most results are dominated by the kick imparted by the incident neutron anyway The angular distribution for the emitted particle is taken as isotropic in the lab At high incident energies direct interaction processes would be expected to give rise to a forward peaked distribution thereby reducing the damage However the importance of this effect is also reduced by the dominance of the neutron kick Figure 3 gives a typical result of a damage energy production calculation showing the separate contributions of elastic inelastic and absorption pro cesses Coding Details The main program starts by reading user input assigning storage pointers and locating the desired material on the PENDF tape INIT is called to examine the dictionary Flags are set if MF12 or 13 is present and if MT18 or 19 is used This subroutine also saves the grid of the total cross section MT1 on the LOADA FINDA scratch file that will be used to accumulate the kerma factors damage a
91. timate of the additional storage required RESERV ID ALREADY DEFINED An ID must be released before being reassigned RESERV POINTER SEQUENCE ERROR The directory at the start of the container array has probably been clobbered RESERV EXCEEDED MAXIMUM NUMBER OF ID S See NIDMAX in STORAG RESERV REQUESTED RESERVE OF ZERO WORDS Check coding that called RESERV RELEAS ID NOT DEFINED Check coding and spelling RELEAS ATTEMPT TO RELEASE MORE WORDS THAN STORED Self explanatory Check coding FINDEX ID NOT DEFINED Check coding and spelling 4 References for NJOY 1 R Kinsey ENDF 102 Data Formats and Procedures for the Evaluated Nuclear Data Files ENDF Brookhaven National Laboratory report BNL NCS 50496 ENDF 102 2nd Ed ENDF B V October 1979 2 Weisbin P D Soran E MacFarlane D Harris J LaBauve J 5 Hendricks J White and Kidman MINX Multigroup Inter pretation of Nuclear X Sections from ENDF B Los Alamos Scientific Labora tory report LA 6486 MS 237 1976 18 RECONR The RECONR module is used to reconstruct resonance cross sections from resonance parameters and to reconstruct cross sections from ENDF B nonlinear interpolation schemes The output is written as a pointwise ENDF tape PENDF with all cross sections on a unionized energy grid suitable for linear interpo lation to within a specified tolerance Redundant
92. tition function used was given by Robinson based on the electronic screening theory of Lindhard see Fig 2 The results are suitable for metals only The damage output from HEATR is the damage energy production cross section eV barns As in Eq 1 multiplying by the density and flux gives eV s Dividing by 2 gives displacements s TABLE I TYPICAL VALUES FOR THE ATOMIC DISPLACEMENT ENERGY NEEDED TO COMPUTE DPA displacements per atom Material Energy eV Aluminum 33 82 37 5 Stainless Steel 50 0 33 Titanium 37 54 Vanadium 50 0 b Tantalum 68 Niobium 75 08 pRef 3 with an efficiency of 0 8 Ref 4 as given C Computation of Kerma Factors The ENDF B files do not usually give photon production data for all partial reactions Redundant reactions such as nonelastic and inelastic MT4 are often used It is still possible to compute partial kerma factors for these redundant reactions by reordering Eq 3 as follows 7 RSE 7 62 10 3 0 gt SN gt ap E amp ap ES lt a Q o 0 0 2 0 4 0 6 0 8 0 10 0 Primary Recoil Energy eV Sic Fig 2 Examples of the portion of the primary recoil energy that is available to cause lattice displacements in metallic lattices The remaining energy leads to elec tronic excitations where j runs over all neutron partials contained in J and 2 runs over all
93. to be the energy value where the slope of the actual inter polation function equals the slope of the linear interpolate Formulas are pro vided for each of the nonlinear ENDF B interpolation laws is linear in In E 0 is linear in E and In o is linear in 1n E 22 Stack Version 1 2 13 14 Numbers above energy markers indicate location in the stack Cross Section Energy Energy Grid Now Stored in Stack stack may be as large as 20 Fig 2 Result of Convergence Test on Lowest Energy Segment Not converged add midpoint Converged write lowest E to disk n Not converged add midpoint Converged write lowest E to disk Not converged add midpoint Converged write lowest to disk Finished Read energy of next resonance and repeat Total length of Inverted stack method used in LUNION and RESXS 23 The convergence criterion used for linearization is that the linearized cross section at the intermediate point is within the fractional tolerance ERR of the actual cross section specified by the ENDF law More complicated cri teria are used for resonance reconstruction There are two basic problems that arise if a simple fractional tolerance test is used to control resonance reconstruction First as points are added to the energy grid adjacent energy values may become so close that they will be rounded to the same number when a formatted output file is produced or when the mac
94. umber that depends on incident energy E and the atomic weight ratio to the neutron for the isotope AWRI as follows 27 3 AWRI 2 196771 x 10 7 JE 8 The neutron width in these equations is energy dependent due to the penetration factors that is E PCE ips 9 Po Po 10 o 11 4 and ic 5 12 9 3p p where En is the resonance energy and p ka depends on the channel radius RA 1 3 0 123 AWRI 0 08 13 The phase shifts are given by gt p 14 FRU 1 91 and 15 p tan 26 16 3 28 a where ka depends the scattering radius given in the file The final components of the cross section are the actual line shape functions y and x At zero temperature j 17 1 4 18 l x 2 E E 19 t S IEI S CE a 2 r 2 TES POE 20 in terms of the shift factors 970 21 MO 17 2 and 22 l p 18 302 223 9 3p p To go to higher temperatures define 24 29 where k is the Boltzman constant and T is the absolute temperature The line shapes y and x are now given by y 35 3 25 110 9 0 2 2 5 26 in terms of the complex probability function see QUICKW WTAB and W which came from the mc code W z e erfc iz i m J dt
95. up the partials at each grid point While RECONR is going through the reactions given in the ENDF B evaluation it also checks the reaction thresholds against the Q value and atomic weight ratio to the neutron AWR given for the reaction If the condition AWR 1 threshold gt e 0 1 is not satisfied the threshold energy is moved up to satisfy the condition and an informative message is printed if the change exceeds 0 1 If desired the unionized grid developed from the ENDF B file can be sup plemented with user grid points given in the input data The code auto matically adds 1 E 5 eV 0 0253 eV and 20 MeV to the grid if they are not already present 21 C Linearization and Reconstruction Methods Linearization LUNION and resonance reconstruction RESXS both function by inserting new energy grid points between the points of an original grid using an inverted stack The general concepts involved are illustrated with a simple example shown in Fig 2 The stack is first primed with two starting values For linearization they will be two adjacent points on the original grid For reconstruction they will usually be the peaks of two adjacent resonances The stack is said to be inverted because the lower energy is at the top 1 2 This interval or panel is now divided into two parts and the cross section computed at the intermediate point is compared to the result of linear interpolation between the adjacent points I
96. y static elastic incoherent inelastic coherent elastic Coherent cross sections at a given energy E are computed by SIGC If this is the first entry E 0 the appropriate lattice constants are selected Then the reciprocal lattice wave vectors and structure factors are computed sorted and stored for later use On a normal entry E50 the stored list is used to accumulate the sums of Eq 4 Incoherent elastic cross sections are computed in subroutine IEL The appropriate Debye Waller integrals are given in data statements and adjusted to the specified temperature using TERP The bound cross sections are also set in the coding The angle integrated cross section is computed analytically on the grid of the static elastic cross section and written back onto the LOADA FINDA scratch file in the same slot used for coherent elastic as described both never occur in the same material The discrete equally probable cosines are cast into LTT 7 format and written onto a scratch tape for use by TPEND Incoherent cross sections and matrices are generated in CALCEM On the first entry the ENDF B scattering law is read in or parameters are set for free scattering On subsequent entries the adaptive loop to determine the secondary energy grid is carried out The required cross sections and discrete cosines are returned by SIGL which uses SIG to compute the differential cross sections As each c versus E curve is computed it is put directly into the mo
97. y 0 5 However if the contribution to the resonance integral from any one interval gets small the interval will be declared converged and the local value of the cross section will end up with some intermediate accuracy Once again the contribution to the error in the resonance integral should be less than 0 5 Ao AE This value is added into an accumulating estimate of the error and a count of panels truncated by the resonance integral check is incremented The problem with this test is that RECONR does not know the value of the resonance integral in advance so the tolerance parameter ERRINT is not the actual allowed fractional error in the integral Instead it is more like the resonance integral error per grid point barns point Thus a choice of ERRINT ERR 10000 with ERR 0 001 would limit the integral error to about 0 001 barn if 10000 points resulted from reconstruction Since important resonance integrals vary from a few barns to a few hundred barns this is a reasonable choice The integral check can be suppressed by setting ERRINT very small or ERRMAX ERR When resonance reconstruction is complete RECONR provides a summary of the possible resonance integral error due to significant figure reduction and the integral check over several coarse energy bands see Fig 3 The last band covers the unresolved range if present The parameter NDIGIT and the param eters ERRMAX and ERRINT taken together should be considered as knobs that can in
98. y strongly energy dependent function However this strong energy dependence is partially an artifact of looking at a given E The shape of the secondary energy distribution changes slowly whereas the peak tends to follow the line E E This behavior implies that a relatively coarse incident energy grid might prove adequate if a suitable method is used to interpolate between adjacent E values One such interpolation scheme is implemented in GROUPR The use of discrete angles is especially suitable for this interpola tion scheme The scattering law for free gas scattering given in Eq 9 is strictly applicable to scatterers with no internal structure However many materials of interest in reactor physics have strong scattering resonances in the thermal 84 240 135 range for example Pu and Xe The Doppler broadened elastic cross sec tion produced by BROADR is formally correct for a gas of resonant scatterers but the cross section resulting from Eq 9 is not In order to allow for the resonance scattering in a way that at least provides the correct total cross section HEATR renormalizes the free scattering to the broadened elastic cross section The secondary energy distribution will still be incorrect C Incoherent Elastic Scattering Materials such as polyethylene and zirconium hydride exhibit a component of elastic scattering that is E that can be treated in the incoherent approximation 2EW 1 14 o E u 7 e
99. z E A E BQE iu 32 31 where 33 and where Vn is the resonance half width corresponds to 2 in the Breit Wigner notation Hy is the resonance energy Gr is the symmetric total parameter is the asymmetric total parameter and the are coefficients of the total background correction The fission and capture cross sections both use the form oC ME _ 6 r lt 2 4 2 17 A E Az E A E BoE b 34 1 where the values of G H Ajs and appropriate for the desired reaction are used Doppler broadening can be applied as for the SLBW case except note that in Eq 24 must be replaced with 2 Doppler broadened Adler Adler cross sections are more accurate than SLBW cross sections because the background is smoother However cross sections below about 16 will still be in accurate An example of the agreement between broadening and the more accurate kernel broadening see BROADR is shown in Fig 4 Infinitely dilute cross sections in the unresolved energy range are com puted in CSUNR1 or CSUNR2 using average resonance parameters and probability distributions from File 2 With the approximations used these cross sections are not temperature dependent therefore the results are a good match to re solved resonance data generated using TEMPR gt 0 The formulas used are based on the single level approximation with

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