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USER MANUAL OF UNF CODE - International Atomic Energy Agency

1. 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0221367 0 0186576 0 0125273 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0119846 0 0120059 0 2184E 01 0 2165E 01 0 2097E 01 0 2095 01 0 2079 01 0 2068E 01 for 00 for n a 00 for n He3 00 for n d 00 for n t 00 1 00000 1 00000 1 00000 1 00000 1 00000 1 00000 0 0155722 0 0204185 0 0096659 0 0047348 0 0008074 0 0003275 0 0001329 0 0000549 0 4280819 0 1976483 0 0740087 0 0198466 0 0415829 0 0259373 0 0124646 0 0181689 0 0154548 0 0200238 0 0093231 0 0044802 0 0007564 0 0003051 0 0001233 0 0000510 0 0019584 0 0000278 0 0121352 0 0106863 0 0018456 0 0000261 0 4258114 0 1965816 0 0724323 0 0193576 0 0122169 0 0418192 0 0248752 0 0121726 0 0180247 0 0153894 0 0198528 0 0091922 0 0043842 0 0007374 0 0002967 0 0001197 0 0000495 0 4173139 0 1925760 0 0666574 0 0176713 0 0425481 0 0211277 0 0111132 0 0174476 0 01
2. 302312 0 0 00 1 0 96 1 0 82 3 0 35 50 17 40 40 0 2 0 99 4 1 00 6 0 07 3 0 17 3028 20 10 7 8 60 08 10 10 97 5 20 91 8 000 0 10 56 5 1 0 29 N 3 0 36 oo 10 02 10 302712 40 56 12 2 0 03 4 0 09 0 0 0 20 11 3 0 53 4 0 32 3 0 98 7 0 17 00 00 0 00 00 0 00 00 4 20 04 5 7 20 08 7 8 40 06 9 10 30 7010 0 00 00 0 10 02 5 30 04 7 10 07 9 50 2110 00 00 0 2 0 98 4 0 06 2 0 63 7 0 09 0 0 00 23 2 FOR N 2P 64 Ni 0 11 00 3 10 96 3 20 04 4 FOR N 3N 63 CU 10 18 0 7457460 0 2568850 0 2568850 0 7457460 1 1855790 1 4129900 1 4129900 1 1855790 1 0000000 0 845861 0 2384280 0 0000000 11 00 3 0 22 1 0 48 20 48 7 0 02 11 4 0 57 13 1 1 00 15 6 0 04 15 20 14 16 1 0 93 18 DW 11 00 4 10 84 4 10 76 6 20 02 6 20 22 8 3026 8 1 1 00 3 0 16 3022 5 0 02 5 7 8 60 3610 10 38 10 302410 10 08 11 30 49 11 10 65 13 20 0313 10 07 15 20 0415 70 04 15 80 0415 30 02 16 50 0217 0 580 0 900 0 7200 0 360 0 8800 0 8800 0 800 0 360 1 0000 1 0000 0 800 0 650 0 7200 0 7200 0 5000 1 250 1 2000 1 2000 1 0500 1 250 1 4000 1 4000 1 4300 1 250 1 0000 1 0000 1 0000 1 250 1 2000 1 2000 0 7500 1 2500 1 3000 1 3000 1 2 700 0 0000 0 0000 0 2200 0 0000 0 0000 0 0000 0 0000 0 0000 55 563385 55 38500 151 90 151 90 0 457278 0 3200 0 1700 0 1700 0 0017920 0 000 0 0
3. The theoretical improvements have been made in the unified Hauser Feshbach and exciton model The angular momentum conservation is considered in whole reaction processes for both equilibrium and pre equilibrium mechanism The recoil effects in varied emission processes are taken into account strictly so the energy balance can be held exactly A method for calculating double differential cross sections of composite particles is proposed Based on this theoretical frame the UNF code 2001 version for calculating neutron induced reaction data of structure materials below 20 MeV was issued The functions of the UNF code are introduced Introduction For fast neutron reaction data calculations there are several widely used computer code such as GNASH Refs 1 and 2 and TNG Ref 3 which are useful for fast neutron evaluation The equilibrium and the pre equilibrium statistical mechanism are employed in both codes but in different approach In the theoretical description of the model there are still some thing could be improved The first point is about the emissions of the first outgoing particles there should be three types of emission mechanisms i e direct emission pre equilibrium emission and equilibrium emission In particular the emission from compound nucleus to the discrete levels of the residual nuclei each of which has 31 its individual spin and parity Therefore the angular momentary conservation and parity conse
4. do M N LE and f e the third 2 de FETO 1 1 m 1 1 using fde term in Eq B36 is reduced into ig 27 fde JE St f E The second term in can reduced by S Jag 92 do de d 26 poe ee Je C En En A TE E J Je de dE M AEn x m asc 44 dE f E oae 5 E n a M r do 1 2 dz de B39 M Thus energies carried second emitted particle is obtained by do r E p RIS AMES jde 3 M Dm m c c 2 fde f e e In terms of the same procedure for energy carried by its residual C 40 nucleus M can be obtained by _ m M E LE de f de PACA JE M 2 41 m m M ii The y de excitement energy is obtained by the averaged residual excitation energy g 9 46 r p p e e E fie ae aQ aQ de 40 de dQ RADY E B B e f e jde Je de where B43 r m fde 0 mm Je Jde 2 2 2 M m m JE fo de acd de f e 44 Therefore 45 M M M fde es es dE et 45 E
5. i de It is easy to see that 1f the recoil effect is not taken into account the residual nucleus is static in CMS in this way the energy carried by the second emitted particle only has the second term in Eq B43 while the first term is the energy gain by recoil effect From Eq B43 one can see that the recoil effect increases with the decreasing of the mass of residual nucleus and with the increasing of the mass of emitted particles The total released energy can be obtained by summing over Eqs B36 B40 B41 and B45 E E E E E E Q B46 Q B B B is the reaction Q value in the two particle emission process Therefore the energy balance is held exactly in the analytical form From the afore mentioned formulation one can see that the quantity of the Legendre expansion coefficient with 1 f g gt 0 plays an important role the energies carried by different kinds of emitted particles which is caused by the forward emission of the first emitted particle in the pre equilibrium process If f increases then the energy carried by the first emitted particle increasing in LS while the recoil effect reduces the energies of the second particles emitted from the recoil residual nuclei due to the motion of the center of mass system Meanwhile the shape of TEL can also influence the energy distributions between the emitted particles the residual nucleus and de excitation y energy The harder of the
6. 3 o b 6 b 0 5 0 4371 0 5629 3 586E 02 3 871E 02 15 0 5928 0 4072 7 173E 02 7 412 02 2 5 0 6722 0 3278 1 263E 01 1 112E 01 3 5 0 7236 0 2764 1 684E 01 1 191E 01 4 5 0 7620 0 2380 1 711E 01 1 489E 01 5 5 0 7929 0 2071 2 053E 01 4 345E 02 6 5 0 8175 0 1825 5 649E 03 5 070E 02 7 5 0 8372 0 1628 6 456E 03 7 689E 04 8 5 0 8519 0 1481 1 032E 04 8 651E 04 9 5 0 8623 0 1377 1 146E 04 1 347E 05 10 5 0 8676 0 1324 1 721E 06 1 482E 05 11 5 0 8681 0 1319 1 877E 06 2 160E 07 12 5 0 8611 0 1389 0 000E 00 2 340E 07 As an example the occupation probabilities at incident neutron energy 12 MeV for different j are given in Table to show the angular momentum conservation effect For low j region the pre equilibrium state is dominant part while for high j region the equilibrium contributions become important which 37 means that the components with high j in compound nucleus need multi step intrinsic collision processes Averaged by the absorption cross section the pre equilibrium emission occupies the percentage of 28 86 while the equilibrium emission occupies 71 14 95 B2 Recoil Effect and Energy Balance The energy balance for whole reaction processes must be taken into account to set up neutron data file for application For each reaction channel with a reaction Q value the released total energy includes the energies of the outgoing particles the recoil nucleus and the gamma decay energy The energy balance nee
7. Substituting the maximum value into Eq B51 the maximum energy of the second emitted particle is obtained by B53 For a given value of 6 from condition of 1 cosO lt 1 one can get the integration area of as follows 1 AS GU ey 1 41 XU y B54 p M M M M pM where R 24 2 U RE e M Mm M m 1 1 1 1 1 The minimum energy of second emitted particle c max corresponds to the opposite direction of the first outgoing particle m Ho ZE B55 XN i M m k There is zero point at 48 Ei BEC B56 There are three cases for the maximum values of the second emitted particle m c r pc ME Bu m V E n sk if Eu lt 1 2 40 if E E lt E B57 c m M min M M max x m E ox n F E if Ese lt E 1 The expression of the double differential cross section of the residual nucleus can be obtained by replacing m and 6 with M and E Eq B49 respectively One can prove that the f 7 is also normalized By means of exchanging nm the integration order the integration limits of are J E for a value of By using Eq B49 he des f E dE 1 B58 When the final state
8. 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 notation the second incident energy 1 00000 0 00000 0 2768671 0 0000057 0 0000013 0 0000028 0 0000000 0 0430051 0 0071451 0 0000005 0 0000016 0 0000031 0 0000007 0 0000018 0 0000036 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0021647 0 0000009 0 0000022 0 0000040 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 000
9. iE E excitation energy c B binding energy of incident neutron in compound nucleus masses of target and compound nucleus respectively mass of the first and the second emitted particle respectively energy of the first and the second emitted particle respectively M M mass of residual nucleus after the first and the second emitted particle respectively energies of residual nuclei after the first and the second particle emissions respectively B binding energy of the first and the second emitted particle in its compound nucleus respectively E 2 level energy with the level order number k reached by the first and the second emitted particle respectively Legendre expansion coefficient of the first emitted particle in CMS J Legendre expansion coefficient of the second emitted particle CMS B2 1 Double Differential Cross Section from Continuum State to Continuum State Based on the relation of the double differential cross sections between CMS 39 and RNS Uo que B18 dQ de dO The Jacobian is given by de dQ qe de dQ B19 E The normalized double differential cross section in the standard form reads 21 1 lt ET ud 0 20 where P cos refers to the Legendre polynomial Averaged by the double differential cross section of the residual nucleus after
10. 15 in the discrete level states with analogy procedure all of the released energies can be obtained If the residual nucleus isin level which is just the energy of gamma de excitation The energy carried by the second emitted particle is obtained by 1 m m c c V E TEL Jotes e fe B59 49 M se E E JEE fE 86 Substituting Eqs B49 B50 into Eqs B59 B60 and carrying out the integration with the integration limits of as the same as that used in Eq B58 the energies carried by m and M can be obtained in the case from continuum state to discrete levels respectively The energy carried by the second emitted particle in LS is given by mp E B B E M M M M mm c c c c HC o B61 M VE e Aen esae and M BE 2 2 M m mM c c Ex B62 1 m c c Ex JE 7 e de The energy carried by the first emitted particle in LS is already given in Eq B34 the total released energy is given by Q B B E E E Q B63 Obviously in the case of the second particle emission from continuum state to discrete state the energy balance is still held exactly in the analytical form The formulation given above is employed in UNF code to set up files 6 with full energy balance in the neutron data library The prec
11. Particle Emissions Chin J Nucl Phys 1996 18 28 MANTZOURANIS G WEIDENMULER H AGASSI D Generalized Exciton Model for the Description of Pre equilibrium Angular Distribution Z Phys A 1976 276 145 SUN Z WANG 5 ZHANG 1 ZHOU Y Angular Distribution Calculation Based on the Exciton Model Taking into Account of the Influence of the Fermi Motion and the Pauli Principle Z Phys A 1982 305 61 ZHANG J S YAN S WANG C The Pickup Mechanism in Composite Particle Emission Processes Z Phys A 1992 344 251 ZHANG J S A Method for Calculating Double Differential Cross Sections of Alpha Particle Emissions Nucl Sci Eng 1994 116 35 ZHANG J S A Theoretical Calculation of Double Differential Cross Sections of Deuteron Emissions Chin J Nucl Phys 1993 15 347 CHADWICK M B OBLOZINSKY P Particle Hole State Densities with Linear Momentum and Angular Distribution in Pre equilibrium Reaction Phys Rev C 1991 44 1740 KIKUCHI K KAWAI M Nuclear Matter and Nuclear Reaction North Holland Amsterdam 1968 44 OBLOZINSKY P Pre equilibrium y Rays with Angular Momentum Coupling Phys Rev C 1987 35 407 59 18 GRIMES S M et al Charged Particle Emission in Reactions of 15 MeV Neutron with Isotopes of Chromium Iron Nickel and Copper Phys Rev C 1979 19 217 19 ZHANG J S LIU T G ZHAO Z X The Current Status OF CENDL 2 Proc Int Conf Nuclear Data for Science and Technology Gatlinburg Tennesses May 9 13
12. and 135 deg The results are in good agreement with the measured data 55 o b 0 001 o b 56 0 01 T T T TTTTTT T T 16 Gd n Y Theory L R Fawcett 72 K G Broadhead 67 R G Wille 60 M Valkonen 76 J L Perkin 58 S Joly 81 J Voignier 86 V N Kononov 77 M V Bokhovko 96 0 01 0 1 1 10 T T T TTTIT N E MeV Fig B1 The n y cross section of n Gd reaction 2 5 15 Nd n 2n Theory 2 0 1 5 71 R G Wille 60 M P Menon 67 J Frehaut 80 S M Qaim 74 ILKumabe 77 S Gmuca 83 AN Jongdo 84 1 0 0 5 9 X b OB 0 0 8 10 12 14 16 18 E MeV Fig B2 The reaction cross section of n 2n of nt Nd Fig B3 The deuteron energy angular spectra of n Fe at 14 8 MeV The data are taken from Ref 17 B6 Summary The first version of the UNF code was completed in 1992 The code has been developed continually since that time and has often been used as an evaluation tool for setting up CENDL and for analyzing the measurements During these years many improvements have been made The Hauser Feshbach model with the width fluctuation correlation is a very successful theory used for low incident energies With the increasing of incident energy the pre equilibrium mechanism needs to be involved by using angular momentum dependent exciton model The frame o
13. book entitled NEUTRON PHYSICS Principle Method and Application published by China Atomic Energy Press in 2001 The code can handle a decay sequence up to n 3n reaction channel The total reaction channels are 14 0 13 as shown in the Table 1 In fact the reaction channels n np and n pn as well as nno and should be treated as one channel respectively Thus the total reaction channels are 12 0 11 Table 1 14 reaction channels considered UNF code No Channels No Channels No Channels 0 n y 5 n d 10 n pn 1 n n 6 n t 11 n 2p 2 n p 7 n 2n 12 nom 3 n Q 8 n np 13 n 3n 4 n 9 n na The physical quantities calculated by using UNF code contain 1 2 3 4 5 6 Cross sections of total elastic scattering non elastic scattering and all reaction channels in which the discrete level emissions and continuum emissions are included Angular distributions of elastic scattering both in CMS and LS The energy spectra of the particle emitted in all reaction channels Double differential cross sections of all kinds of particle emissions neutron proton alpha particle deuteron triton and He as well as the recoil nuclei Partial kerma factors of every reaction channel and the total kerma factor Gamma production data gamma spectra gamma production cross sections and multiplicity including the gamma production cross
14. dpa cross sections if 1 in the ODH DAT file 6 Guide for Running UNF Code In order to calculate the fast neutron data some preparations need to be set down in advance 1 2 3 4 5 6 At first set the UNF DAT file If the data of the direct inelastic scattering and direct reaction are available from other codes then input the data in the file DIR DAT with the proper format See 4 2 If 1 direct reaction data are not taken into account the user must put a 0 in this channel of file DIR DAT Set the OTH DAT in advance After set down the preparations mentioned above the users can start the neutron data calculation After adjustment procedure of parameters users set KENDF 1 in general KTEST 0 and run UNF code The physical results output in file UNF OUT and the ENDF B 6 output in file B6 OUT If the running is stop and some information occurs on the screen which informs the user there are some errors in the input data file then the user needs to correct them accordingly When set KTST 1 and NOE gt 0 for performing one incident neutron energy calculation the threshold energies of every reaction channels as well as that of inelastic scattering of the discrete levels are given in UNF OUT file which are useful for the calculation to set up the ENDF B 6 outputting file Meanwhile checking the normalization of the de excitation ratios some other information will be g
15. in Ref 4 A large number of figures to compare the calculated results with the measured data have been published in Communication of Nuclear Data Progress INDC CRP 041 L to 053 L as technical reports during the evaluations of the nuclei for CENDL 3 Some typical calculated examples are given below The capture radiation cross section of n Gd is shown Fig B1 In UNF code the gamma de excitation has three mechanisms 1 equilibrium gamma emission 2 pre equilibrium gamma emission 3 direct gamma emission The Oblozinsky s formula is employed for the last two terms A small peak occurs at about 14 MeV in the capture radiation cross section which is the contribution from the direct gamma emission The n 2n reaction cross section of Nd is shown in Fig B2 The calculated results agree fairly well with the experimental measurements All of the measured data used in Fig Bl and Fig B2 are retrieved from EXFOR library Only few double differential measurements have been performed for charged outgoing particles For n Fe the double differential measurements of n d reactions were performed by Grimes The comparisons of the calculated results with the experimental data of outgoing alpha particle have been given in Refs 13 and 19 while the comparisons of the calculated results with the measured data of outgoing deuteron are shown in Fig B3 of the Fe n d reaction at 14 8 MeV for outgoing angles 30 45 90
16. limited in UNF code IZT Integer Charge number of target IAT 1 NAB Integer The mass numbers of each isotope FONG 1 NAB Real The abundance of each isotope MAT Integer Material number to mark the element in ENDF B 6 format file MEL Integer Number of incident energies and NOE Integer notation NOE 0 Doing the calculation for all incident energies NOEzO Only doing the calculation for single incident energies with the order number NOE 1SNOESMEL EL I 1 MEL real incident energies in unit of MeV MEL integer energy point type MET I 1 only output cross sections 2 output cross sections and angular distributions MET I 3 besides outputting cross sections and angular distributions the outputting double differential cross section and y production data 15 also issued in ENDF B 6 format Card 9 The 5 angels for the neutron double differential cross sections outputting to fit the measured data in laboratory system Card 10 DLH real Bin size of y spectra B For each isotope the input data are as follows The sequence of the input data is illustrated as below Card 1 AMT real mass of the target in unit of a m u CK real Kulbach parameter in exciton model EF real Fermi energy MeV real adjustable factor in y radiation Card 2 EHF real The energy bound between the Hauser Feshbach model and the unified Hauser Feshbach and exciton model If EL LE EHF th
17. order number of the first excitation level is 2 and so on If NDL I 0 then the content of the J I term is empty Notations 1 for calculation of natural nucleus limited by ENDF B 6 format the total number of the discrete levels included in all isotopes of the inelastic scattering channel could no be over 40 if user want to set up the data file in ENDF B 6 format Notations 2 for the reaction channels of multi particle emissions such as n np n pn n on n 2p and n 3n the number of discrete levels could not be over 20 in the calculation limited by UNF code Since the number of reaction channel n d has identical residual nucleus with n np and n pn so the number of discrete levels could also not be over 20 Card 7 Branching ratio in y de excitation process The branching ratio from I4 level to J level is written in the format 13 F5 2 The number of the lines of the input branching ratios for each residual nucleus is denoted by NUL integer Thus the input order for each residual nucleus is NUL integer 6 13 I3 F5 2 NUL lines There are 6 set data in one line If the branching ratio between two levels is 0 then it does not need in the input file The input sequence is J 0 10 for n y nn n p n He nd n t n 2n n no n 2p and n 3n reaction channels Card 8 Optical potential parameters AR Array 1 6 Diffusivities parameters of real potentials AS Array 1 6 D
18. sections from level to level 7 Total double differential cross sections of each kind outgoing particles from all reaction channels 8 Cross sections of isomeric states 1f the level 15 a isomeric state of the residual nucleus 9 dpa cross sections used in radiation damage UNF code can also handle the calculations for a single element or for natural nucleus and the target can be in ground state or in its isomeric state Besides the output file the outputting in ENDF B 6 format is also included files3 4 6 12 13 14 15 or files 3 4 5 which are controlled by a flag Meanwhile some self checking functions are designed for checking the errors in the input parameter data if it exist Users can correct them according to the indicating information in advance 1 Spherical Optical Potential In UNF code the spherical optical potential is employed to calculate total cross section shape elastic scattering cross section and its angular distribution absorption cross section as well as the transmission coefficients and inverse cross section of the reaction channels No 1 6 for n p He d t For the reaction channels n 2n and n 3n the transmission coefficients are taken from n n channel The calculated transmission coefficients for the second emitted particles of the reaction channels n pn n pp and with the same parameters as that for these particles in the channels No 1 2 but with different mass numb
19. should be taken into account strictly This kind of accurate kinematics is introduced in Sec B2 The semi empirical model for double differential cross sections of the complex particles emissions is used in GNASH code while in UNF code a method to calculate double differential cross sections of the complex particles with the pickup mechanism is used This method is introduced in Sec B3 This is the third point on the improvements of the theoretical model The functions of UNF code 2001 version are elaborated in Sec B4 and some typical calculated results are shown in Sec B5 with some discussions A summary is given in Sec B6 33 Angular Momentum Coupling Effect in Pre Equilibrium Particle Emission To consider the angular momentum and parity conservation the angular momentum J and parity should be addressed in the master equation of exciton model so the master equation of jz channel reads dg di n 2 q n 2 t A 2 4 n 2 1 4 n A n W n q n t B3 where Af is the internal transition rate and W is the total emission rate of the exciton state in channel The dependent internal transition rate can be written in the form AT n v 0 B4 Where n is the internal transition used in the usual jz independent exciton model while 7 n stands for the angular momentum factor In FKK model the angular momentum conservation was co
20. 0 2750 0 3858 0 4652 0 5908 0 7298 0 8227 1 00 2 0 2 0 3 0 1 0 2 0 40 3 0 2 0 9 1 FOR N N 65 CU 0 0 0 7706 1 1156 1 4818 1 6234 1 7250 2 0943 2 1074 2 2128 2 2785 2 3290 2 4066 2 5257 15 05 2 5 35 25 15 3 5 25 0 5 3 55 5 55 45 12 1 1 FOR N P 65 Ni FOR N A 62 63 FOR N D 64 FOR N T 63 FOR N 2N 64 CU 0 0 0 1593 0 2783 0 3439 0 3622 0 5746 0 6088 0 6630 0 7391 10 20 20 10 3 0 40 20 10 2 0 9 1 FOR N NA 61 Co 0 0 1 0275 1 2051 1 2858 1 6189 35 15 1 5 25 085 5 1 FOR N 2P 64 Co FOR N 3N 63 Cu 0 0 0 6697 0 9621 1 3270 1 4120 1 5470 1 8612 2 0112 2 0622 2 0814 2 0926 2 2079 2 3366 2 3380 2 4048 2 4972 2 5064 2 5120 L5 05 25 35 25 15 3 5 1 5 05 25 3 5 05 25 15 35 15 45 045 22 13 1 1 1 1 1 1 BRANCHING RATIO 0 10 FORNAT 6 213 F5 2 N0 2 FOR N G 66 CU 3 2 1100 3 11 00 6 1095 6 20 01 9 10 61 9 20 04 FOR N N 65 CU 6 2 1100 3 11 00 5 3033 6 10 71 7 4043 7 50 05 8 60 06 9 1037 8 9 11 10 48 11 20 2911 13 4100 0 00 00 FOR N P 65 Ni 0 FOR N A 62 Co 0 FOR N He 63 Co 0 FOR N D 64 Ni 0 FOR N T 63 Co 0 FOR N 2N 64 CU 5 2 1100 3 11 00 6 20 06 6 50 94 8 1032 8 2027 9 3010 9 40 03 0 4 7 8 9 11 10 57 11 20 03 11 FOR N NA 61 Co 1 10 01 40 04 5 0 28 1 0 83 2 0 01 1 0 16 2 0 55 8 9
21. 00 0 000 27 03870 14 00 50 00 50 00 40 38 11 10 62 10 72 10 55 60 02 40 26 5 0 05 30 2013 50 07 30 3015 4024 9 0 04 15 10 0 04 40 2717 70 40 20 07 0 00 00 0 00 00 0 00 00 OPTICAL MODEL PARAMETERS 0 5000 3000 0 0000 0 0000 0 0000 91 130 0 00 0 000 0 000 0 0000000 0 40000 0 0000 0 0000 2 2000 3 4130000 3 1000 1 2500 1 2500 16 076340 11 8000 41 7000 41 7000 10 6200 0 352875 0 2500 0 3300 0 3300 0 000 35 46683 12 000 44 000 44 000 0 700 24 0 700 3 500 0 000 0 410 0 500 0 500 1 0000 1 6400 1 0000 1 6400 1 0000 1 3000 1 3500 0 0000 0 0000 45 00 0 00 0 000 0 000 0 4000 0 000 0 0000 0 0000 0 000 5 7 9 40 38 2 0 06 3 0 45 1 0 16 10 60 10 12 30 43 13 70 05 15 50 15 16 10 82 17 11 0 33 0 00 00 DIR DAT FILE FOR 63 18 20 notation 18 incident neutron energies and Lmax 20 01 1110100000000000 1 0000 notation the first incident energy 0 8623E 02 1 00000 0 2656345 0 0468745 0 0090906 0 0035008 0 0002518 0 0000129 0 0000003 0 0000007 0 0000008 0 0000011 0 0000012 0 0000016 0 0000017 0 0000021 0 0000023 0 0000028 0 0000029 0 0000036 0 0000037 0 0000045 0 9840E 03 1 00000 0 1790060 0 0104250 0 0006112 0 0000498 0 0000007 0 0000005 0 0000004 0 0000009 0 0000006 0 0000013 0 0000009 0 0000019 0 0000013 0 0000026 0 0000017 0 0000034 0 0000022 0 0000043 0 0000027 0 0000
22. 00 0 1700 0 1700 0 00 0 00 0 0017920 0 000 0 000 0 000 0 000 0 000 27 03870 14 00 50 00 50 00 0 000 0 000 0 0000000 0 40000 0 0000 0 0000 2 2000 0 4000 3 4130000 3 1000 1 2500 1 2500 3 500 0 000 16 076340 11 8000 41 7000 41 7000 10 6200 0 0000 0 352875 0 2500 0 3300 0 3300 0 000 0 0000 35 46683 12 000 44 000 44 000 0 000 0 000 0 700 0 700 M T CK EF 64 9277890 500 0 32 0 1 0 ENERGY BOUND BETWEEN HF AND MULTI STEP REACTION MODEL 6 5 BINDING ENERGIES 0 13 0 0 7 0666570 8 4154700 7 1495978 19 320060 12 286783 15 688714 9 9046581 7 444753 6 7703842 6 0959410 12 312772 6 6874434 7 9160919 LEVEL DENSITY PARAMETERS 0 10 8 472 8 057 8 361 8 804 9 112 8 232 7 937 7 765 8 195 9 539 7 161 PAIR CORRECTION VALUES 0 10 1 5 14 028 14 2 7 1 02 0 18 1 20 0 20 1 30 PARAMETERS OF GIANT RESONANSE MODEL CSE EE GG 0 075 0 075 0 034 0 026 0 026 0 034 0 034 0 075 0 026 0 026 0 075 0 0 0 0 0 05 0 04 0 04 0 05 0 05 0 0 0 04 0 04 0 0 16 7 16 7 16 3 16 37 16 37 16 3 16 3 16 7 16 37 16 37 16 7 0 0 0 0 18 51 18 9 18 9 18 51 18 51 0 0 18 9 18 9 0 0 6 89 6 89 2 44 2 56 2 56 2 44 2 44 6 89 2 56 2 56 6 89 21 0 0 0 0 6 37 7 61 7 61 6 37 6 37 0 0 7 61 7 61 0 0 PARAMETER OF DIRRECT GAMMA DGAM 0 25 DISCRETE LEVEL NUMBER FOR ALL RESIDUAL NUCLEI No 2 9 13 0 0 0 0 0 9 5 0 18 FOR N G 66 CU 0 0 0 1859 0 2378
23. 0000 0 0000000 0 0000000 0 0000000 0 0001294 0 0000011 0 0000024 0 0000045 0 0000000 27 0 0000 00 0 0000 00 0 0000 00 0 0000 00 0 0000 00 0 0000 00 20 0000 0 2270 01 0 2231E 01 28 0 00000 0 00000 0 00000 0 00000 0 00000 0 00000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 notation the 19 incident energy 0 4375999 0 2021357 0 0807721 0 0403190 0 0308124 0 0136942 0 0156058 0 0207292 0 0099966 0 0049840 0 0020706 0 0008582 0 0003499 0 0001426 0 0000589 0 0000294 0 4333668 0 2001342 0 0777346 0 0210633 0 0131504 0 0184715 0 0116601 1 00000 1 00000 0 0409454 0 0285432
24. 053 0 0000E 00 0 00000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000E 00 0 00000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000E 00 0 00000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 2 0000 notation the second incident energy 20 0000 notation the 18 incident energy 0 2199E 01 1 00000 0 4345621 0 2013494 0 0768496 0 0207795 0 0133181 0 0420165 0 0287509 0 0141307 0 0196234 0 0112449 0 0163561 0 0204165 0 0095513 0 0046556 0 0019304 0 0008028 0 0003285 0 0001342 0 0000556 0 0000280 0 2169E 01 0 2126E 01 0 2116E 01 0 2056E 01 FOR N P 00 FOR 00 FOR N HE3 00 FOR ND 00 FOR 00 for n n 65cu 19 20 01111 0 9000 0 0000 00 26 1 00000 1 00000 1 00000 1 00000 0 4306029 0 2000085 0 0741151 0 0199395 0 0135000 0 0425118 0 0268081 0 0137639 0 0193177 0 0104380 0 0162710 0 0201069 0 0092726 0 0044589 0 0018423 0 0007628 0 0003107 0 0001266 0 0000525 0 0000267 0 4249518 0 1980161 0 0702780 0 01882
25. 1121 13122 21312 32131 33312 3133 ANGLES IN LS FOR FITTING DDCS OF NEUTRON 30 60 90 120 150 BIN SIZE IN GAMMA PRODUCTION 0 10 M T CK EF 62 9295898 500 0 32 0 1 0 ENERGY BOUND BETWEEN AND MULTI STEP REACTION MODEL 17 6 5 BINDING ENERGIES 0 13 0 0 7 9160919 7 1995635 6 2011445 17 444110 11 816096 16 155116 10 854230 6 1246310 5 7765668 6 8411410 11 275454 7 4915142 8 8941669 LEVEL DENSITY PARAMETERS 0 10 7 165 7 161 7 455 7 754 8 195 7 336 7 857 6 731 7 199 8 804 6 182 PAIR CORRECTION VALUES 0 10 0 18 1 3 2 5 0 25 1 2 2 5 1 05 0 15 1 22 0 28 1 32 PARAMETERS OF GIANT RESONANSE MODEL CSE EE GG 0 10 0 075 0 075 0 034 0 026 0 026 0 034 0 034 0 075 0 026 0 026 0 075 0 0 0 0 0 050 0 040 0 040 0 050 0 050 0 0 0 040 0 040 0 0 16 70 16 70 16 30 16 37 16 37 16 30 16 30 16 70 16 37 16 37 16 70 16 70 16 70 16 30 16 37 16 37 16 30 16 30 16 70 16 37 16 37 16 70 0 0 0 0 18 51 18 90 18 90 18 51 18 51 0 0 18 90 18 90 0 0 6 89 6 89 2 44 2 56 2 56 2 44 244 6 89 2 56 2 56 6 89 PARAMETER OF DIRRECT GAMMA DGAM 0 25 DISCRETE LEVEL NUMBER FOR ALL RESIDUAL NUCLEI No 1 11 18 0 0 0 0 0 8 9 0 9 FOR N G 64 CU 0 0 0 1593 0 2783 0 3439 0 3622 0 5746 0 6088 0 6630 0 7391 0 7462 0 8783 10 20 20 10 30 40 20 10 20 30 00 1151 FOR N N 63 CU 0 0 0 6697 0 9621 1 3270 1 4120 1 5470 1 8612 2 0112 2 0622 2 081
26. 1994 Vol 2 p676 American Nuclear Society 1994 60
27. 2007 0 00 00 0 00 000 0000 0 FOR N P 63 Ni 0 0 00 19 0 FOR N A Co 60 0 FOR N He Co 61 0 FOR N D Ni 62 0 FOR N T Ni 61 0 FOR N 2N 62 CU 3 2 1100 3 10 99 6 2100 7 10 8 8 20 90 8 30 08 FOR N NA 59 Co 3 2 11 00 3 11 00 6 10 93 6 30 07 8 2034 8 70 11 FOR N 2P 62 Co 0 FOR N 3N 61 CU 4 2 11 00 3 10 99 5 2012 5 30 03 7 1062 7 30 14 8 40 22 9 10 67 9 2 0 01 2 0 47 4 0 01 1 0 93 1 0 76 1 0 08 2 0 01 1 0 65 4 0 22 2 0 25 OPTICAL MODEL PARAMETERS 0 7457460 0 580 0 900 0 2568850 0 360 0 8800 0 2568850 0 360 1 0000 0 7457460 0 650 0 7200 1 1855790 1 250 1 2000 1 4129900 1 250 1 4000 20 0 7200 0 8800 1 0000 0 7200 1 2000 1 4000 2 1 00 3 0 01 0 0 00 2 0 07 20 23 3 0 47 1 0 94 2 0 16 5 0 02 3 0 08 N o 20 96 40 04 00 00 20 21 40 01 70 41 30 06 30 14 10 36 00 00 0 5000 0 410 0 800 0 500 0 800 0 500 0 5000 1 0000 1 0500 1 6400 1 4300 1 0000 30 04 1 0 01 0 0 00 4 0 79 1 0 55 8 0 04 10 85 50 05 30 42 0 0 00 1 4129900 1 250 1 0000 1 0000 1 0000 1 6400 1 1855790 1 250 1 2000 1 2000 0 7500 1 0000 1 0000000 1 2500 1 3000 1 3000 1 3000 1 3000 0 845861 2 700 0 0000 0 0000 0 0000 1 3500 0 2384280 0 2200 0 0000 0 0000 0 0000 0 0000 0 0000000 0 0000 0 0000 0 0000 0 0000 0 0000 55 563385 55 38500 151 90 151 90 91 130 45 00 0 457278 0 32
28. 24 0 0138332 0 0431027 0 0242241 0 0132231 0 0188408 0 0093874 0 0160966 0 0196675 0 0089323 0 0042217 0 0017375 0 0007153 0 0002897 0 0001175 0 0000487 0 0000252 0 4235179 0 1974981 0 0693169 0 0185524 0 0139286 0 0432347 0 0235960 0 0130850 0 0187152 0 0091341 0 0160463 0 0195564 0 0088540 0 0041676 0 0017138 0 0007046 0 0002849 0 0001155 0 0000479 0 0000249 0 4151993 0 1944040 0 0638418 0 0170790 0 0145536 0 0438827 0 0201276 0 0122988 0 0179715 0 0077347 0 0157299 0 0189160 0 0084443 0 0038888 0 0015928 0 0006501 0 0002609 0 0001053 0 0000437 0 0000232 notation 19 incident neutron energies and Lmax 20 0 1 1 11000 notation the first incident energy 1 00000 0 2768671 0 0430051 0 0071451 0 0021647 0 0001294 0 0000057 0 0000005 0 0000007 0 0000009 0 0000011 0 0000013 0 0000016 0 0000018 0 0000022 0 0000024 0 0000028 0 0000031 0 0000036 0 0000040 0 0000045 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 0 0000E 00 1 0000 0 6254E 02 0 0000E 00 0 00000 0 00000 0 00000 0 00000 0 00000 0 00000 0 00000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000 0 0000000
29. 4 2 0926 2 2079 2 3366 2 3380 2 4048 2 4972 2 5064 2 5120 15 05 25 25 15 3 5 1 5 05 2 5 3 5 05 25 15 35 15 45 405 13 1 1 1 1 1 1 FOR 63 Ni FOR N A 60 Co FOR N He 61 Co FOR N D 62 Ni FOR N T 61 Ni 18 FOR N 2N 62 CU 0 0 0 0408 0 2435 0 2878 0 3902 0 4261 0 5483 0 6375 1 0 2 0 20 2 0 40 30 10 10 8 1 FOR 59 Co 0 0 1 0993 1 1905 1 2916 1 4343 1 4595 1 4817 1 7447 2 0618 3 5 15 45 15 05 55 25 35 35 9 1 FOR N 2P 62 Co FOR N 3N 61 CU 0 0 0 4751 0 9701 1 3106 1 3942 1 6605 1 7326 1 9042 1 9327 1 5 0 5 25 35 25 15 35 25 15 9 1 BRANCHING RATIO 0 10 FORNAT 6 213 F5 2 NO 1 FOR N G 64 CU 5 2 1100 3 1100 4 1096 4 2004 5 1002 5 6 2006 6 5094 7 1082 7 2008 7 3004 7 8 1032 8 2027 8 3035 8 4006 9 1007 9 9 3010 9 40 03 9 50 1710 30 70 10 502110 10 5711 20 03 4040 0 00 00 0 00 00 0 FOR N N 63 CU 10 2 1100 3 11 00 4 1084 4 3016 5 1072 5 5 3022 6 10 6 6 2002 6 3022 7 1055 7 8 1048 8 2022 8 3026 8 50 02 8 60 02 9 9 20 48 9 60 36 10 10 810 302410 4026 10 10 70 0211 10 08 11 304911 403811 50 05 12 12 40 5713 10 65 13 20 0313 302013 50 07 13 14 11 0015 10 07 15 20 0415 303015 4024 15 15 60 0415 70 04 15 80 0415 90 0415100 04 16 2 0 98 4 0 06 2 0 63 7 0 09 0 0 00 2 0 06 3 0 45 1 0 16 6 0 10 3 0 43 7 0 05 50 15 1 0 82 16 20 1416 30 02 16 50 0217 402717 70 40 171 0 33 18 10 9318
30. 51066 0 0192106 0 0087612 0 0040738 0 0006770 0 0002702 0 0001085 0 0000449 0 4170552 0 1924539 0 0664851 0 0176233 0 0150973 0 0191909 0 0087491 0 0040653 0 0006754 0 0002695 0 0001082 0 0000448 0 4149379 0 1914496 0 0650769 0 0172355 0 0427137 0 0201333 0 0108295 0 0172811 0 0150222 0 0190310 0 0086532 0 0039975 0 0006624 0 0002639 0 0001058 0 0000438 0 0102917 0 0018034 0 0000255 0 0126283 0 0088923 0 0016686 0 0000237 0 0126430 0 0425668 0 0210188 0 0110821 0 0174295 0 0088513 0 0016649 0 0000236 0 0127682 0 0085164 0 0016357 0 0000232 0 4135808 0 1908043 0 0641802 0 0169929 0 0128523 0 0428014 0 0195739 0 0106701 0 0171858 0 0149738 0 0189285 0 0085934 0 0039556 0 0006544 0 0002604 0 0001044 0 0000432 0 0083038 0 0016178 0 0000230 29 OTH DAT FILE INPUT FOR THE ELEMENT No 1 FOR LEVELS OF GAMMA PRODUCTION CROSS SECTION BETWEEN DISCRETE LEVELS N G 0 N N 0 N P 0 N A 0 N HE 0 N D 0 0 N 2N 0 N NP 0 N NA 0 N 2P 0 N 3N 0 FOR ISOMERIC LEVELS NUMBER OF IV 0 10 FOR 11 RESIDUAL NUCLEI 0 00000 00000 IF THE DPA DATA ARE NEEDED SET KDPA 1 OTHERWISE KDPA 0 0 INPUT THE THRESHOULD ENERGY Ed OF PKA IN UNIT OF MeV 0 000060 INPUT FOR THE ELEMENT No 2 INPUT FOR THE ELEMENT No 3 INPUT FOR THE ELEMENT No 4 30 Appendix B UNF Code for Fast Neutron Reaction Data Calculations Abstract
31. CNIC 01616 CNDC 0032 USER MANUAL OF UNF CODE ZHANG Jingshang China Nuclear Data Centre China Nuclear Information Centre China Nuclear Industry Audio amp Visual Publishing House Contents Ertrodut TOM cok e u yupasqa obe rat ade ean c RIA 1 I Spherical Optical Potential 3 2 Parameters Of UNF Code 6 SNL a T 7 A Input Biles e qa Saver Edi 7 5S Output Files iuo tete ua bos n e bU VER aa insti Vies 13 6 Guide for Running UNF Code 14 Appendix 17 n Cu sample input files of 17 n Cu sample input files of DIR DAT 25 sample input files of OTH DAT 30 Appendix B UNF Code for Fast Neutron Reaction Data Calculations 31 Reference n 5 8 Introduction The UNF code 2001 version written in FORTRAN 90 is developed for calculating fast neutron reaction data of structure materials with incident energies from about 1 keV up to 20 MeV There are 87 subroutines and 15 functions in UNF code The code consists of the spherical optical model the unified Hauser Feshbach and exciton model The angular momentum dependent exciton model is established to describe the emis
32. and Emission Spectra LA 0947 Los Alamos Scientific Laboratory Nov 1977 2 YOUNG P G ARTHUR E D Chadwick M B Comprehensive Nuclear Model Calculations Theory and Use of the GHASH Code LA UR 96 3739 1996 3 FU C Y Approximation of Precompound Effect Hauser Feshbach Codes for Calculating Double Differential n xn Cross Sections Nucl Sci Eng 1998 100 61 4 ZHANG J S A Unified Hauser Feshbach and Exciton Model for Calculating Double Differential Cross Sections of Neutron Induced Reactions Below 20 MeV Nucl Sci Eng 1993 114 55 5 Feshbach H Kerman A Koonin S The Statistical Theory of Multi Step Compound and 58 10 11 12 13 14 15 16 17 Direct Reactions Ann Phys N Y 1980 125 429 ZHANG J S HAN Y L FAN X L Theoretical Analysis of the Neutron Double Differential Cross Section of n O at 14 1 MeV Commun Theor Phys Beijing China 2001 35 579 ZHANG J S HAN Y L CAO L G Model Calculation of n C Reactions from 4 8 to 20 MeV Nucl Sci Eng 1999 133 218 IWAMOTO A HARADA K Mechanism Cluster Emission in Nucleon Induced Pre equilibrium Reactions Phys Rev C 1982 26 1812 ZHANG J S Improvement of Computation on Neutron Induced Helium Gas Production Proc Int Conf Nuclear Data for Science and Technology Gatlinburg Tennesses May 9 13 1994 Vol 2 p932 American Nuclear Society 1994 see also J Z ZHANG and S J ZHOU Improvement pf Pickup Mechanism for Composite
33. d have the same one Thus only 11 sets of the discrete level schemes are needed in the input parameters including level energy spin and parity As the same reason the data of the pair corrections and the level density parameters are also needed as the same as the afore mentioned 11 sets input parameters The conversion array KGD 0 13 is used for denoting the 11 sets parameters with the order number 0 10 the conversion arrays are listed in the Table 2 The phenomenological optical potential includes the following parts a Real part yo exp R r a b Imaginary part of surface absorption RJ 1 c Imaginary part of volume absorption U 1 exp r R a r d Spin orbit potential y Ve expl ar exp r R a e Coulomb potential Z Z i 0 7720448 3 1 if r amp R R R MES Z Z 1 440975 if r gt R r where Z stand for the mass and charge numbers of target nucleus s and Z are the spin and charge number of particle b and is the energy of particle b in the center of mass system The total optical potential reads VO VOMO WO V The energy dependence of potential depths are given by V e V V e Vie V A 2Z AtV Z 4 W Wy W W A 2Z A U e max 0 U U U e kinds of radius are given R r A v so In particular the diff
34. ds E E E E Q B17 where stands for the incident neutron energy in laboratory system LS If the recoil nucleus is assumed static in the center of mass system CMS after sequential particle emission in this way neither the accurate shape of outgoing particle spectra nor the energy balance could be obtained This paper will give the formulation of the energy balance of the secondary particle emissions which is employed in the UNF code In UNF code only the sequential particle emissions are taken into account The particle emissions have three cases 1 from continuum states to continuum states 2 from continuum states to discrete levels 3 from discrete levels to discrete levels of which the formulation has been given in Ref 7 Beside the laboratory system LS and the center of mass system CMS the recoil nucleus system RNS is also needed which is a moving system along with the recoil residual nucleus The physical quantities are labeled by subscripts Lc r respectively for the three motion systems At low incident energies 20 38 MeV the pre equilibrium mechanism is taken into account only for the first particle emissions while the isotropic distribution is employed for the second emission particles in RNS In this case the double differential cross sections of the secondary particle emissions in CMS can be easily obtained The physical quantities used in this paper are defined as following M 5 6
35. e Hauser Feshbach model is used If EL LE gt EHF the pre equilibrium reaction model is performed Card 3 BIND 0 13 real Binding energies of the last emitted particle of the reaction channels 0 13 Notation BIND 0 0 for gamma emission ALD 0 10 real Level density parameters of the 11 residual nuclei Gilbert Cammeron formula is employed in UNF code DELT 0 10 real Pair correction values of 11 residual nuclei Card 4 Two peak giant resonance parameter used for Gamma emissions CSGA 0 10 1 2 absorption cross sections of photo nuclear reactions for 11 residual nuclei in b EG 0 10 1 2 Energies of two peak giant dipole resonance for 11 residual nuclei in MeV GG 0 10 1 2 Widths of giant dipole resonance peaks in MeV The input sequence is CSGA L1 CSGA L2 EG L1 EG L2 GG L1 GG L2 I 0 10 Card 5 DGM real The parameter of the direct gamma emission Card 6 Data of the discrete levels NDL 0 10 integer Number of discrete levels of residual nuclei EDL 0 10 K real K 1 NDL I Level energies in unit of MeV SDL 0 10 K real K 1 NDL I Spins of levels IPD 0 10 K integer K 1 Parities of levels 1 or 1 The input sequence is NDL I 1 0 10 J 0 10 for n y n n np n a n d n t 2 n no n 2p and n 3n reaction channels K 1 SDL J K K 1 NDL J IPD K K 1 NDL J Notation the order number of the ground state is 1 the
36. e ez EL 33 The double differential cross section and the energy region of the recoil residual nucleus after the second particle emission can be obtained by replacing with and in Eq B28 respectively On the other hand one can prove the energy balance is held in an analytical way By means of the velocity v where _ is the motion velocity of the center of the mass the energy carried by the first emitted particle from compound nucleus to the continuum states can be given by mm 24m m E de E E E f e B34 m m M n m Mf M n UTE By using the following formula the energy carried for the second emitted particle m in LS can be given by gt y ea 35 The energy carried by the second emitted particle in LS is given by 43 From Eq B28 the third term in Eq B36 has the explicit form M mE f es JE js ILE T m s dE See de do M Nia a de 1 TS fa 7 B37 m Substituting Eq B37 into Eq B36 and by exchanging the integration order as the same as in Eq B32 the third term in Eq B36 becomes 1 M I LE do de fde e TE B38 4M E de Cem M Carrying out the integration over with the integration limits as the same as that in Eq B32 this part becomes into m pe E B 1 1
37. e optical potential parameters then set KOPP 1 otherwise set KOPP 0 3 KDDCS It is used to control the double differential cross section calculations When user only want to calculate the data of the reaction cross sections then set KDDCS 0 while user needs the data of the double differential cross sections then set KDDCS 1 4 KGYD It is used to control the y production calculation When users not need them then set KGYD 0 otherwise set KGYD 1 5 KENDF It is used to control the ENDF B 6 format output In general the physical results are output in the file UNF OUT When users need the ENDF B 6 format outputting then set KENDF 1 for the files 3 4 6 12 13 14 15 outputting and set KENDF 2 for only the files 3 4 5 otherwise set KENDF 0 without ENDF B 6 format outputting 4 Input Files Three input files are set up in UNF code 41 File UNF DAT A For the common used parameters The sequence of the input data is illustrated as below Card 1 The 5 flags are input with the sequence as same as that mentioned 7 Card 2 Card 3 Card 4 Card 5 Card 6 Card 7 Card 8 above which are KTEST KOPP KDDCS KGYD KENDF The status of target KSO Integer KSO 1 for ground state 50 gt 1 for isomeric state the number is the level order number here the ground state 15 1 NAB Integer is the number of isotopes NAB 1 only for one isotope while NAB gt 1 for natural nucleus So far lt 10 is
38. er and charge number accordingly The transmission coefficients of p and in the reaction channels n np and n na are taken from and n o channels respectively Therefore 9 sets of the transmission coefficients are needed to be calculated Some conversion arrays are used in the UNF code to mark the data The conversion array KOP 0 13 denotes the corresponding number 1 9 of the transmission coefficients for each reaction channel 0 13 The type of the emitted particle from every reaction channel is denoted by the conversion array 0 13 and conversion array KTYP2 0 13 for the first and second emitted particles respectively The reaction channel number 0 11 are marked by the conversion array KCH 0 13 See Table 2 Table2 14 conversion arrays No Channels KOP KTYPI KTYP2 KGD KCH 0 m y 0 0 0 0 1 n n 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 5 nd 5 5 5 5 5 6 n t 6 6 6 6 6 7 n 2n 1 1 1 7 7 8 2 1 2 5 8 9 nna 3 1 3 8 9 10 npn 7 2 1 5 8 11 n 2p 8 2 2 9 10 12 n an 9 3 1 8 9 13 n 3n 1 1 1 10 11 The construction of the discrete levels of the residual nuclei for the 14 reaction channels has only 11 sets of independent nuclei of which the n np and n pn reaction channels have the identical residual nuclei as same as that of the n d reaction channel while that of the reaction channels nno an
39. f the theoretical model used in UNF code has some improvements Mainly in three aspects as afore mentioned Previously limited by computer condition the UNF code system included three codes 1 UNF code used for single element NUNF used for natural nucleus SUNF code for fission production nucleus Now these three codes are unified into one code Meanwhile 57 for the purpose of varied utilization more functions were added in this code Thus the 2001 version of UNF code was issued Information on the energies of charged particles produced in the nuclear reactions is needed in several applications For example the kerma factor is of specific interest regarding the heat produced in reactors as well as regarding the calculation of radiation damage in structure materials Being the accurate kinematics used in the UNF code the energy angular spectra of outgoing charged particles as well as recoil nuclei can be obtained with the accurate kinematics so the single particle approximation is not needed in the calculations of kerma factor and radiation damage Now the manual of the UNF code is available for users The format of the input parameter files and the output files as well as the functions of flag used in UNF code are introduced in detail and the examples of the format of input parameters files are given Reference 1 YOUNG P ARTHUR E D GNASH A Pre Equilibrium Statistical Nuclear Model Code for Calculation of Cross Section
40. ides the particle a and the particle hole b and d the residual part of the compound nucleus is called observer which has the spin S The angular momentum coupling triangle relations A J J S A J Ja J J J must be held to keep the angular momentum conservation in the pre equilibrium process The final result of the angular momentum factor of y7 is obtained by 1 MEG R R F HAM uy P FRU GAGS B12 1 0 0 DRG G J j B13 3 GOJA 1007 DR GIR G Jo Ja Io E und T C D i 14 For the case of y a particle annihilates a particle hole pair the derivation procedure is as the same as that of y In this case only the weight 8 is used instead of 5 in Eq B12 Being consistent with the independent exciton model the angular momentum factors satisfy the normalization condition 36 J DR Jx 1 0 B15 where R J is the spin distribution factor of angular momentum in n exciton state 1 J RJ expl B16 d Jn 20 20 where 0 24nA refers to the spin cut off factor of the n exciton state for the nucleus with the mass number A is independent of energy Table occupation probabilities of n 3 P n 3 and the absorption cross section of Fe at E 12 MeV j Q 3
41. iffusivities of sur abs ima potentials AVV Array 1 6 Diffusivities of volume absor imag potentials ASO Array 1 6 Diffusivities of L S coupling potentials XR Array 1 6 Radius parameters of real potentials XS Array 1 6 Radiuses of sur abs ima potentials XV Array 1 6 Radiuses of volume absor imag potentials XS0 Array 1 6 Radiuses of L S coupling potentials XC Array 1 6 Coulomb potentials Radius parameters UO Array 1 6 Constant terms of volume absorption imaginary potentials UI Array 1 6 Energy linear term factors of volume absorption imaginary potentials U2 Array 1 6 Energy square term factors of volume absorption imaginary potentials VO Array 1 6 Constant factors in real potential for x particle of nx reactions with x n p d t V1 Array 1 6 Energy linear term factors in real potentials V2 Array 1 6 Energy square term factors in real potentials V3 Array 1 6 Charge symmetry term factors in real potentials V4 Array 1 6 Charge linear term factors in real potentials VSO Array 1 6 Constant factors of L S coupling potentials WO Array 1 6 Constant terms of surface absorption imaginary potentials W1 Array 1 6 Energy linear term factors of surface absorption imaginary potentials W2 Array 1 6 Charge symmetry term factors of surface absorption imaginary potentials A2S AS proton AS 2 A2S N Z A only for proton A2V AVV proton AVV 2 A2V N Z A only for pro
42. ision of energy balance in general is much less than one percent due to the accurate kinematics 50 B3 4 Double Differential Cross Section of Composite Particle Emissions The pickup mechanism should be involved in the composite particle emission to give the pre formation probability of composite particle in compound nucleus At first the Iwamoto Harada model has been employed in UNF code But the calculated result indicated that this model overestimated the pre formation probabilities of the composite particles The study turns out that the integration over momentum space in the phase space integration has the superfluous part which is the forbidden area restricted by excitation energy So the E dependent improved Iwamoto Harada pickup mechanism was developed to reduce the pre formation probabilities and used in UNF code The double differential cross sections of single nucleon can be calculated by generalized master equation to get the angular momentum dependent lifetime 2 with the Legendre expansion form as gt 0 64 The double differential cross section of particle b 15 represented 2 T ah m Amea B65 where d component of n exciton state in the spectrum b In the case of composite particle emission the outgoing nucleon may pickup some nucleons below and above the Fermi surface to form a composite particle to be emitted According to the studies on picku
43. iven to make sure that the input data file are or not correct 7 Only in the case of NOE gt 0 for one incident energy point calculation the 5 set of double differential cross sections will be output in PLO OUT file for fitting the measured data Notations In the input files UNF DAT and DIR DAT there are some one line annotations to indicate the data contents UNF code reads them as a character So the users must pay attention to do not leaving any space lines ahead these characters when writing at the input data Otherwise all of the reading must be out of order An interface PRE UNF based on has been established to set up the UNF DAT and OTH DAT files mentioned above automatically If gt 1 the NAB elements for each element with the charged number of Z can be set up simultaneously for both UNF DAT file and OTH DAT file so the user needs to pay attention to whether any isomeric level is involved in a element 16 Appendix A UNF DAT FILE KTEST KOPP KDDCS KGYD KENDF 0 0 1 1 1 THE STATUS OF TARGET 1 GROUND STATE gt 1 ISOMERIC STATE 1 THE NUMVER OF ISOTOPES 2 THE CHARGE NUMBER OF THE NUECLEUS 29 MASS NUMBERS OF EACH ISOTOPES 63 65 ABUNDANCE OF EACH ISOTOPES 0 6917 0 3083 MATERIAL NUMBER 3290 NUMBER OF INCIDENT ENERGIES NOE EL D I 1 MEL AND MET D J 1 MEL 29 0 0 001 0 01 0 05 01 05 0 75 10 15 20 25 3 0 35 40 45 50 6 0 70 7 5 8 amp 0 9 0 100 12 0 140 145 150 16 0 17 5 18 0 20 0 3
44. l elastic scattering non elastic scattering and all reaction channels in which the discrete level emissions and continuum emissions are included 2 Angular distributions of elastic scattering both in CMS and LS 3 The energy spectra of the particle emitted in all reaction channels 4 Double differential cross sections of all kinds of particle emissions neutron proton alpha particle deuteron triton and He as well as the recoil nuclei 5 Partial kerma factors of every reaction channels and the total kerma factor 6 Gamma production data gamma spectra gamma production cross sections and multiplicity including the gamma production cross sections from level to level 7 Total double differential cross sections of all kinds outgoing particles from all reaction channels 8 Cross sections of isomeric states if the level is a isomeric state of residual nucleus 9 dpa cross sections used in radiation damage UNF code can also handle the calculations for a single element or for natural nucleus and the target can be in ground state or in isomeric state Besides the output file the outputting in ENDF B 6 format is also included files3 4 6 12 13 14 15 or files 3 4 5 which controlled by a flag 54 Meanwhile some self checking functions are designed for checking the errors in the input parameter data if it exist B5 Calculated Examples and Discussion Some calculated results have been shown
45. ls by user Then input NGM pair integer of the level order numbers in this residual nucleus For each integer pair kl k2 implies the y ray is emitted from k1 level to k2 level so k1 gt k2 If the user does not want to observe this term then set a 0 in this residual nuclei Card 2 If the user wants to calculate the reaction cross sections of the isomeric level within the 11 kind of residual nuclei 0 10 then set the isomeric level number in this residual nucleus otherwise only set 0 in it Card 3 If set KDPA 1 the dpa cross sections will be calculated otherwise set KDPA 0 Card 4 Input the threshold energy E of PKA in unit of MeV This file only used for NAB 1 for one element calculation But in the case of gt 1 the NAB elements data for OTH DAT are needed since different element may have different status of isomeric level 5 Output Files Five files are opened in UNF code for outputting 1 File UNF OUT This file is used for the output of calculated quantities 2 File PLO OUT This file is used for the DDCS outputting of all kinds outgoing particles as well as the angular energy spectra of 5 angles for 13 outgoing neutron in laboratory system when NOE gt 0 3 File B6 OUT This file is used for outputting the file in ENDF B 6 format if KENDF 1 or 2 4 File KMA OUT This file is used for outputting kerma factors 5 File DPA OUT This file is used for outputting the
46. nsidered properly Following the approach of FKK model the angular momentum factor can be constructed But in FKK model only spin zero nucleon was used In this paper the spin 1 2 nucleon is used to provide the angular momentum factor The 6 type residual two body interaction is used for the particle hole excitation which can be expanded in the form as follows FY Bs rr mm Applying the basic formula the reduced matrix elements are defined by 34 Uma m Cis Vr i di and unn LM jm 7 Where is Clebsch Gordon coefficient The tenser product of T satisfies the equation as Up gt 6 B8 Thus the reduced matrix element is obtained by Us impr xut js m Je JU Aug cu IDE Us lis jm jam pm joM qm jama 4 j hj 1 jj 4 Qj jj Ur xvj B9 p qr where j J2j l and is the 9 j coefficient Using T U 1 alr xu and Jadid rm 7 2 2 uo WCG Jap B10 p po we have JIJI Uu ug JJ CD 8 35 p In our case T Y and where stands for spherical 2 2 40 B11 harmonics function The derivation procedure can be found in Ref 6 in detail For the nucleon with spin 1 2 the antisymmetrization needs to be taken into account In the case of A a particle 7 creates a particle hole Bes
47. odel while if the pre equilibrium effect 15 omitted 1 is reduced to the Hauser Feshbach model In the case of low incident energies lt 20 MeV only n 3 is taken into account for the pre equilibrium mechanism Therefore the formula of the energy spectrum in practical calculation reads 32 22 3 We BENE on ge cel 22 3 H where 3 1 3 is occupation probability of equilibrium state in channel and W E is the emission rate in the Hauser Feshbach model in which the width fluctuation correction 15 included Based on the unified Hauser Feshbach and exciton model the emissions of the first particle emissions from compound nucleus can be described with pre equilibrium mechanism and equilibrium mechanism as well as direct reaction process In this model the angular momentum depended exciton model is used for conserving angular momentum in the pre equilibrium emission processes At low incident energies lt 20 MeV the secondary particle emissions are described by multi step Hauser Feshbach model To do so in this way the angular momentum conservation and the parity conservation can be carried through the whole reaction processes up to n 3n reaction channel The second point 15 the energy balance for each reaction channel since it 15 quite important in the application of the nuclear engineering To meet the needs of energy balance the recoil effects
48. of the condition M 1 lt lt 1 for the Legendre polynomial of P x the integration limits of a and b in Eq B28 are given by 2 a max RA 5 E 2 b min en B In terms of the velocity composition relation of v and v the energy B29 region of the second particle emission is obtained by 2 r B30 m M M max 2 A r m c ox 7 Y T E if lt E cb gh Ed den 2 cg 31 2 E M 25 0 othewise 1 When is normalized the f is also normalized By means of exchanging the integration order the integration limits of are j for every values of and By using Eq B28 1 oae f E dE 1 B32 d x It is easy to see from Eq B30 that the scope of the outgoing energy spectrum is broadened when the recoil effect is taken into account The lighter of the nucleus the stronger of recoil effect and the broad effect even more 42 obviously When the value of is given and amp lt SE the integration area of is given by the existing condition of the integration amp a lt b as follows max m gt a NE ai h gt E mx 4max E ac We ae fe Jy if es lt E c IS othewise M min B in MM
49. p mechanism at low energies lt 20 MeV the dominant configuration is pickup the nucleons below Fermi surface The angular distribution factor in Eq B65 of b particle with emitted energy 51 and direction 2 at n exciton state is introduced by 1 A 4 A n Q x S p 2 D V t n Q B66 with p gt p and p lt p 2 Ap where T n lifetime of the outgoing single nucleon marked by 1 Pp Fermi momentum momentum of outgoing composite particle b with mass number A D momentum distribution of the compound nucleus N normalization factor The 6 function in Eq B66 implies momentum conservation Obviously if emitted particle b is a nucleon then Eq B66 will return to the case of single nucleon emission The Fermi gas model is employed to give the momentum distribution of the nucleon below the Fermi surface D p dp O p p dp B67 The procedure to carry out the integration analytically over angle and momentum of Eq B66 can be found in Refs 13 and 14 which is reduced into the following form 1 n 09 68 Am x The factor in Eq B68 is defined by G 2 69 G amp where PE 4 ag G amp x ji Z P ER y B70 max lxy 4 1j xy x 1 E excitation energy 52 Fermi energy x dimensionless momentum of particle 1 P dimen
50. rvation should be taken into account properly These three types of emission mechanisms have been taken into account in both GNASH code and TNG code But GNASH code does consider the angular momentum conservation in the pre equilibrium part of the calculations The TNG code is based on a unified model in which the lifetime of particle hole states are independent of spin which imply that the angular momentum conservation in the pre equilibrium process is not included So locating a proper approach to describe the pre equilibrium emissions from compound nucleus to the discrete levels is required which needs to develop an angular momentum dependent exciton model It is introduced in Sec B1 Combining with the Hauser Feshbach model this kind of reaction mechanism can be described based on the unified Hauser Feshbach and exciton model In this model the formula of the energy spectrum reads as follows do yos XP n s m En de s W n E where o stands for the absorption cross section refers to the occupation probability of n exciton state in the channel which can be obtained by solving the j dependent exciton master equation to conserve the angular momentum in the pre equilibrium reaction processes W n E is the emission rates of particle b at exciton state n with outgoing energy Obviously if we do not consider the parity and angular momentum effects 1 is reduced to the exciton m
51. sionless momentum of particle b P ES 2 2 y XE t x 2 cos 0 The final result of Z in Eq B70 is obtained as follows 1 b d Z y 4 55 4 b He B71 6 10 1208 y E E G y b y In Eq B68 the partial wave coefficients of single nucleon emission are calculated by the linear momentum dependent exciton state density This approach is a consistent way to obtain the angular distribution of mode outgoing nucleons In this method the leading particle is not assumed instead a statistical population of all states compatible with energy and momentum conservation is proposed The effects of the Fermi motion of the nucleons as well as the Pauli blocking by the sea of nucleons are included In particular the angular distribution from the first pre equilibrium state in a nucleon induced reaction is identical to that obtained with the Kicuchi Kawai scattering 16 11 kernel 1 There is no any additional free parameter in this method which should be pointed out emphatically 53 B4 Functions of UNF Code The UNF code 2001 version was developed for calculating fast neutron reaction data of structural materials with incident energies from a few kilo electron volts to 20 MeV This code can handle a decay sequence up to n 3n reaction channel including 14 reaction channels The physical quantities calculated by UNF code contain the follows 1 Cross sections of tota
52. sions from compound nucleus to the discrete levels of the residual nuclei in pre equilibrium processes while the equilibrium processes are described by the Hauser Feshbach model with width fluctuation correction The emissions to the discrete level in the multi particle emissions for all opened channels are included The double differential cross sections of neutron and proton are calculated by the linear momentum dependent exciton state density Since the improved pickup mechanism has been employed based on the Iwamoto Harada model the double differential cross sections of alpha particle deuteron and triton can be calculated by using a new method based on the Fermi gas model The recoil effects in multi particle emissions from continuum state to discrete level as well as from continuum to continuum state are taken into account strictly so the energy balance is held accurately in every reaction channels If the calculated direct inelastic scattering data and the calculated direct reaction data of the outgoing charged particles are available from other codes one can input them so that the calculated results will included the effects of the direct reaction processes To keep the energy balance the recoil effects are taken into account for all of the reaction processes The gamma production data are also calculated The calculated neutron reaction data can be output in the ENDF B 6 format All formulation used in UNF code can be found in the
53. spectrum the more energy carried by the emitted particle while the energies carried by the residual nucleus and de excitation emissions are reduced But in pure equilibrium emission process either isotropic approximation or the Hauser Feshbach theory the partial wave with 1 of the Legendre expansion is zero only the energy distributions for all of kinds of the 46 emitted particles are influenced by the shapes of the first emitted particle B2 2 Double Differential Cross Sections from Continuum State to Discrete Levels When the residual nucleus is in discrete level states the double differential cross section has different expression since is single value In this case 1 6 e amp 47 de 4 gt 4 952 where is the function of and has the value as r M M B Ev E E B M 48 1 1 The Legendre coefficient in Eq B38 becomes into the form a f E A E dert P cosO dE B49 with 2 E du ELS cosO B50 2 E gt 1 For a value of maximum energy of second emitted particle should correspond to direction of second emitted particle with my same direction of the first outgoing particle E EET B51 47 There is a maximum value in Eq B51 which is given by pcs A 52 ie sea m m with E E B B E
54. the first particle emission the double differential cross section of the second particle emission can be obtained by d dE de 40 dE dQ dQ gt 21 where the double differential cross section of the residual nucleus of M has form 2141 poner E P 22 dE 1 dO pr 10598 The isotropic distribution of the second particle emission in RNS reads 40 do _ 1 do de dQ 4r de B23 In terms of the orthogonal property of the Legendre polynomial the Legendre coefficient of the second emitted particle is obtained by 1 do do je E 1440 P cos0 dE dQ B24 ACCS 140 Er Denoting as the angle between 2 and then the integration over m can be replaced by dcosO and the relation P cos0 B25 Lm 2L l1 7 Then carrying out the integration over dcosO dO we have TW E f e 2 P cosO dE dcosO B26 i En En From the energy relation between RNS and CMS m m 2 E B27 2 2 M M M M 2 then Eq B26 becomes into the and substituting cosO in Eq B26 by m following form 2 b de M M do B28 a borne M m zc feu 41 For the given values of 6 and E by means
55. ton In the case of natural nucleus the more isotopes NAB gt 1 are needed to be calculated the input parameters of the second isotope should be given in the same format as the first isotope Then the ENDF B 6 outputting 15 given for the natural nucleus 4 2 File DIR DAT This file is used for inputting the data of direct inelastic scattering and direct reactions the input sequence is I 1 direct inelastic scattering I 2 direct reaction of n p I 3 direct reaction of n o I 4 direct reaction of I 5 direct reaction of n d I 6 direct reaction of n t In 1 term the input order is that the first line is the channel explanatory note the second line gives the values of NPE the number of incident energies so far NPE lt 40 is limited in UNF code and LDM the maximum value of the angular momentum in Legendre expansion form LDMx20 is limited in UNF code the third line gives integers with 1 or 0 while 1 or 0 means the direct process is taken or is not taken into account for the level In each incident energy input the cross section CSDIR K and the Legendre coefficients FL 0 LDM K of the level with the integer 1 in the array NDL 12 43 File OTH DAT Card 1 If the user wants to observe the production data between levels then set this file as follows For each kind of residual nuclei 0 10 at first input a integer NGM which implies the number of the observed y ray production between leve
56. usion widths of imaginary potential for proton take form A 2Z a A 2Z a T a A Thus altogether there are 12 parameters for potential depth 5 parameters for radiuses and 4 or 6 for proton for diffusion widths in the phenomenological optical potential 2 Parameters of UNF Code There are three parameters in UNF code to control the storage size NEL integer is the permitted maximum number of incident energy points NLV integer is the permitted maximum number of the discrete levels including the ground state of the compound nucleus and the residual nuclei of the reaction channel No 1 6 The permitted maximum number is fixed 20 for the residual nuclei of the reaction channels No 7 11 NGS integer is the permitted maximum bin number of the production spectra So far the values of the three parameters in UNF code are set NEL 250 NLV 40 and NGS 300 respectively If the users want to increase the size then change the value accordingly and compile the code again 3 Flags In UNF code several flags were set for different calculation purpose so that the users should understand the functions of these flags in advance 1 KTEST if users want to study some medium results for physical analysis then set KTEST 1 when doing the calculation of multi incident energy points users would be better to set KTEST 0 otherwise the output size may be too large 2 KOPP if users want to output th

USER MANUAL OF UNF CODE - International Atomic Energy Agency

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