Confidential JEF Report 2 JEF/DOC 41.2 IKE 6-147 -
JEF-1 SCATTERING LAW DATA
September 1984
J. Keinert M. Mattes IKE Stuttgart
ABsrRAcr
This report describes the scattering-law data adopted for the Joint Evaluated File UEF) for light water, heavy water, graphite and polyethylene. Tests that have been carried out on these data are outlined and comparisons of derived quantities with experimental data are presented in graphical form.
Report prepared at the NEA Data Bank by M. Mattes and E. Sartori - 2 -
Contents
Page I INTRODUCTION 6
II GENERAL DATA DESCRIPTION 7
III MODERATORS 8
1. Water H20, MAT=4001 0
1.1 Physics of the Neutron-Proton Scattering, Phonon 0 frequency Spectra and Related Parameters 1.2 Data Stored in the JEF File 9 1.3 Differential Neutron Scattering Data 10 1.4 Comparison with Integral Data 10 1.5 Comparison of Computed and Measured Neutron Flux 10 Spectra
2. Heavy Water D,O, MAT=4002 28 L 2.1 Physics of the Neutron-Deuterium Scattering, Phonon 28 Frequency Spectra and Related Parameters 2.2 Data Stored in the JEF File 29 2.3 Comparison of Calculated and Measured Scattering-Law 30 Data 2.4 Comparison with Integral Data 30 2.5 Comparison of Computed and Measured Neutron Flux 30 Spectra
3. Graphite, MAT=“4003 37
3.1 Physics of the Neutron Scattering in Graphite, Phonon 37 Frequency Spectrum, Related Parameters, and Specific Heat 3.2 Data Stored in the JEF File 38 3.3 Comparison of Calculated and Measured Scattering-Law 38 Data 3.4 Comparison with Integral Data 39 3.5 Comparison of Computed and Measured Neutron Flux 39 Spectra
4. Polyethylene (CH21 , MAT=4004 45
4.1 Physics of the Neutron-Proton Scattering, Phonon Fre- 45 quency Spectrum, Related Parameters and Specific Heat 4.2 Data Stored in the JEF File 45 4.3 Differential Neutron Scattering Data 46 4.4 Comparison with Integral Data of Polyethelene and 46 Paraffin 4.5 Comparison of Computed and Measured Neutron Flux 47 Spectra in Polyethylene and Paraffin
IV REFERENCES 60
APPENDICES 64
ACKNOWLEDGEMENT 69 - 3 -
LIST OF FIGURES Page
Fig. 1 Cluster Structures of Water (Eucken 1946) 11
Fig, 2 Translational Masses of Water, l-l20 11
Fig. 3 Phonon Frequency Spectra for the Hindered Rotations of Hydrogen 12 Bound in Liquid Water
Fig. 4 'Effective Scattering Temperature of Hydrogen Bound in Water 12
Fig. 5 Double Differential Neutron Scattering Cross Section for Water 13 at 300 K at E = 0.154 eV and 40 degrees
Fig. 6 Double Differential Neutron Scattering Cross Section for Water 13 at 300 K at E = 0.154 eV and 60 degrees
Fig. 7 Double Differential Neutron Scattering Cross Section for Water 14 at 300 K at E = 0.231 eV and 40 degrees
Fig. 8 Double Differential Neutron Scattering Cross Section for Water 14 at 300 K at E = 0.231 eV and 60 degrees
Fig. 9 Double Differential Neutron Scattering Cross Section for Water 15 at 300 K at E = 0.154 eV and 90 degrees
Fig. 10 Double Differential Neutron Scattering Cross Section for Water 15 at 300 K at E = 0.231 eV and 90 degrees
Fig. 11 Differential Neutron Scattering Cross Section of Water at 16 T = 293.6 K at E = 0.044 eV
Fig. 12 Differential Neutron Scattering Cross Section of Water at 16 T = 293.6 K at E = 0.105 eV
Fig. 13 Differential Neutron Scattering Cross Section of Water at 17 T = 293.6 K at E = 0.2 eV
Fig. 14 Differential Neutron Scattering Cross Section of Water at 17 T= 293.6 K at E = 0.5 eV
Fig. 15 Total Neutron Cross Section of H20 at Room Temperature 18
Fig. 16 Total Neutron Cross Section of H20 at T = 450 K 18
Fig. 17 Average Cosine of the Neutron Scattering Angle for H20 at 19 Room Temperature
Fig. 18 Average Cosine of the Neutron Scattering Angle for H20 at 19 T = 200 c
Fig. 19 Neutron Diffusion Coefficient in H20 at Room Temperature 20
Fig. 20 Neutron Diffusion Coefficient in H20 at T = 200 C (473 K) 20
Fig. 21 Neutron Diffusion Coefficient 6(T) in Water, H20 21
Fig. 22 Neutron Diffusion Length I(T) in Water, H20 21 - 4 -
Page
Fig. 23 Average Diffusion Constant E(T) in Light Water 22
Fig. 24 Infinite Medium Neutron Spectra in Pure Water at T = 23 C 23
Fig. 25 Infinite Medium Neutron Spectra in Borated Water at Room 23 Temperature
Fig. 26 Infinite Medium Neutron Spectra in Borated Water at T = 150 C 24
Fig. 27 Infinite Medium Neutron Spectra in Borated Water at T = 316 C 24
Fig. 20 Infinite Medium Neutron Spectra in Gadolinium Poisoned Water 25 at Room Temperature
Fig. 29 Infinite Medium Neutron Spectra in Cadmium Poisoned H20 25
Fig. 30 Perpendicular Surface Leakage Spectrum in Cadmium Poisoned H20 26
Fig. 31 Infinite Medium Neutron Spectrum in Samarium Poisoned H20 26
Fig. 32 Infinite Medium Neutron Spectrum in a Plutonium Nitrate 27 Solution (193.4 g Pu/l at 5 wtX Pu-240)
Fig. 33 Infinite Medium Neutron Spectrum in a Plutonium Nitrate 27 Solution' (197.9 g Pu/l at 23 wtX Pu-240)
Fig. 34 Temperature Dependence of the Phonon Frequency Spectra for 31 the Hindered Rotations of Deuterium Bound in Heavy Water D20
Fig. 35 Phonon Frequency Spectra of Deuterium Bound in Heavy Water 32
Fig. 36 Effective Scattering Temperature of Deuterium Bound in D20 32
Fig. 37 Scattering Law Data for Heavy Water at T = 30@ K 33 for/j = -1, -5, and -9.
Fig. 3B Scattering Law Data for Heavy Water at T = 300 K for/j = -2, 33 -6, and -10
Fig. 39 Total Neutron Cross Sections for Heavy Water at Room Temperature 34
Fig. 40 Average Cosine of the Neutron Scattering Angle for Heavy 34 Water at Room Temperature
Fig. 41 Neutron Diffusion Coefficient in D20 as a Function of Energy 35
Fig. 42 Neutron Diffusion Coefficient in Heavy Water D20 as a Function 35 of Temperature
Fig. 43 Neutron Spectrum in Borated D20 at Room Temperature (2.1 36 b/D-atom)
Fig. 44 Neutron Spectrum in D20 + Cd - Nitrate at Room Temperature 36 (2.4 b/D-atom)
Fig. 45 Comparison of Phonon Frequency Spectra in Graphite 40
Fig. 46 Specific Heat of Graphite 40 - 5 -
*
Fig. 47 Effective Scattering Temperature of Graphite 41
Fig. 48 Scattering Law Data for Graphite at T = 300 K for Different f3 42
Fig. 49 Scattering Law Data for Graphite at T = 635 K (/3= 1.0) 42
Fig. 50 Total Neutron Cross Section for Graphite at Room Temperature 43
Fig. 51 Neutron Diffusion LengthT(T) in Graphite 43
Fig. 52 Neutron Spectrum in Samarium Poisoned Graphite at 300 K 44
Fig. 53 Neutron Spectrum in Samarium Poisoned Graphite at 600 K 44
Fig. 54 Phonon Spectrum of Hydrogen Bound in Polyethylene 48
Fig. 55 Structure and Dynamics of Polyethylene 48
Fig. 56 Specific Heat of Polyethylene 49
Fig. 57 Double Differential Neutron Cross Section for Polyethylene 50 at Room Temperature at E = 0.328 eV and 60 Degrees
Fig. 58 Double Differential Neutron Cross Section for Polyethylene 50 at Room Temperature at E = 0.328 eV and 90 Degrees
Fig. 59 Double.Differential Neutron Cross Section for Polyethylene 51 at Room Temperature at E = 0.65 eV and 60 Degrees
Fig. 60 Double Differential Neutron Cross Section for Polyethylene 51 at Room Temperature at E = 0.65 eV and 90 Degrees
Fig. 61 Double Differential Neutron Cross Section for Polyethylene 52 at Room Temperature at E = 1.02 eV for Different Angles
Fig. 62 Differential Neutron Scattering Cross Section of Polyethylene 53 at Room Temperature at E = 0.044 eV
Fig. 63 Differential Neutron Scattering Cross Section of Polyethylene 54
at Room Temperature at E q 0.1823 eV
Fig. 64 Differential Neutron Scattering Cross Section of Polyethylene 55 at Room Temperature at E = 0.408 eV
Fig. 65 Total Neutron Cross Section of Polyethylene at Room Temperature 56
Fig. 66 Average Cosine of the Neutron Scattering Angle in Polyethylene 57 at Room Temperature
Fig. 67 Infinite Medium Neutron Spectrum in Borated Polyethylene at 58 Room Temperature (QA = 5*74 b/H-atom)
Fig. 68 Infinite Medium Neutron Spectrum in Borated Polyethylene at 58 Room Temperature (bA = 10.6 b/H-atom)
Fig. 69 Infinite Medium Neutron Spectrum in UF4 + Paraffin at Room 59 Temperature - 6 -
I. INTRODUCTION
The scattering law data that are still widely utilised are those re- leased with the version III of ENDF/B. Their use has shown that they are of acceptable quality. New evaluations of the phonon fr.equency spectra have, however, been carried out since then and comparison with experiment has shown that these give better results especially for light water. In addition the number of points at which the scattering law data were tabu- lated in ENDF/B has not always been found to be adequate.
The new scattering law data have therefore been calculated on a finer mesh of o( and /3 values. Extensive comparisons with experimental data have also been carried out.
These improved data for the thermal neutron scattering behaviour are adopted for inclusion in the Joint Evaluated File JEF. - 7 -
II. GENERAL DATA DESCRIPTION
The scattering law S(o(,p) describes the binding of the scattering atoms in a moderator material.
In EP\‘DF/B notation cl’), the thermal incoherent- scattering cross section is related to S Cinc(E4Et ,,M,T, = bb/(-2kT) E’ e-&(c+T) F where E - initial neutron energy energy of the scattered neutron ;: scattering cosine in the laboratory system bound incoherent scattering cross section of the nuclide 6b - k - Boltzmann’s constant T - temperature in Kelvin dimensionless energy transfer = (El-E)/kT squared dimensionless momentum transfer = (Ef+E-2f*e)/(AkT) A - ratio of the scatterer mass to the neutron mass The bound scattering cross section is related to the free atom scat- tering cross section as follows: Olb= (A+~)~/A~ * cfree For binding in liquids and solids, S(U ,/3, T) for several moderator materials has been computed with the GASKET code (2). The data has been produced in ENDF/B-V File 7 format. The scattering law is given as tables of S versus U for various values of p and different temperatures. Any desired value of S for the given temperatures can be obtained by interpo- lation in o( arid/3. Interpolation in temperature of S(oC,/J) is not recom- mended. For intermediate temperatures the interpolation should be carried out on the cross sections and not on the S(a,p> values. If the required ti or fi is outside the range of the table in File 7, the scattering law may be computed using the short collision time approximation for neutron downscattering (p 1 P T a+p2 S(d,/3,T,Teff) = (4XuTeff/T) - 7 e 2 e- Weff Neutron upscattering can be computed by forcing detailed balance (Sk4 $I) = Sk%,-(J)). T ff is the effective temperature of the scatterer; its values are usually larger than the corresponding Maxwellian tempera- ture. T is related to the phonon frequency spectrum 9(w) of the scat- terer aseFofl lows T eff = +/2k ~~(W)Y~coth~hw,2kr)dw , ho = E-E’ s 0 Another parameter related to q(W) is the Debye-Wailer integral. 0 w= lfi B(W)/W*coth(~w/2kT)do s It is used”in calculating coherent or incoherent elastic scattering cross sections. - 8 - III. MODERATORS 1. WATER H20, MAT=4001 1.1 Physics of the Neutron-Proton Scattering, Frequency Spectra and Related Parameters The thermal neutron-proton scattering dynamics for Hydrogen bound in water, H20, is characterised by the excitation of the fundamental dynami- cal modes of the H20 molecules. For the three modes of motion, the fol- lowing assumptions are made: (a) Free translational motion of H2Cl molecules clusters. The number of molecules in the water clusters is temperature-dependent (3) as shown in Fig. 1. The temperature dependent translational masses were derived and are displayed in Fig. 2 and Table 1. This is an improvement compared to ENDF/B (MAT=1002) (4,5) where a single H 0 molecule of mass 18 is used as a translational unit. A better a if reement with experiment is achieved for the double-differential scattering cross sections in the quasi-elastic scattering range as shown, in Figs. 5 and 6 for exam- ple. Table 1: Effective temperature-dependent translational masses(amu) of the H20 molecular clusters T/K 293.6 323.6 373.6 423.6 473.6 523.6 573.6 623.6 Mt 46 39 31 27 25 23 22 21 (b) The frequency band of hindered rotations (torsional harmonic oscilla- tions of the H20 molecule) is assumed to be temperature dependent. By interpolating the two frequency spectra at T = 295K and 550K (Fig. 3) based on the results of Haywood, Page (6) spectra for other tem- peratures were derived. (c) The internal vibrations of the H20 molecule are treated as discrete harmonic oscillations according to Nelkin (7), assuming W ~205 meV for the bending vibration. The symmetric and asymmetric sa retching vibrations are combined at W = 480 meV. The corresponding oscil- lator masses are assumed as ~ ‘2nd 6 (see Table 2). - 9 - Table 2: Effective masses (amu) related to the H20 dynamical modes JEF-l/IKE translations 18 46-21 rotations 2.25 2.09-2.21 oscillations w1,3 3 3 cQ2 6 6 The effective scattering temperature of hydrogen bound in water is given in Table 3 and shown in Fig. 4. Table 3: Integral parameters derived from the frequency spectra of H in Hz0 Debye-Wailer Temperature T integral eff (k) (l/eV) (K) 293.6 20.68 1398.6 323.6 21.78 1405.1 373.6 23.68 1417.9 423.6 25.66 1433.3 473.6 27.69 1450.9 523.6 29.75 1470.1 573.6 31.82 1491.0 623.6 33.91 1513.2 Thermal neutron scattering in water is dominated by the hydrogen nucleus because of its large free atom scattering cross section and the double atomic density. The hydrogen scatter is essentially incoherent because the coherent scattering cross section is very si,iall and there is little relative order in the liquid phase. 1.2 Data stored in the JEF File The quantities stored for light water (MATz4001) are described in the information file MF=l, MT=451 given in Appendix 2. These are: S(d, /j,T) (MF=7,MT=4) for H in H20 at the following 8 temperatures: 293.6 323.6 373.6 423.6 473.6 523.6 573.6 623.6 K i.e. 20 50 1oc: 150 200 250 3OG 350 c - 10 - The data are represented in the temperature-dependent ENDF/B data format (see Appendix F of (1)) at 100 values of o( and lS@ values of /3. The energy limit Emax up to which S(b,lj,T) can be used is 1.8554 eV. The effective scattering temperatures that are required for the short collision time approximation for higher energy transfers are given in the form of a table in MF=l, MT=451. The total free atom scattering cross section of Hydrogen is 20.449 b as in ENDF/B-V MAT=13@1. For the neutron scattering by Oxygen, the values for free gas appro- ximation are also stored in file 7. The molecular absorption cross section is given in MF=3, MT=lOZ. 1.3 Differential Neutron Scattering Data Comparisons of experimental and derived data from S(o(,/$T) for double differential and differential neutron scattering cross sections for diffe- rent incident energies and angles are shown in Figs. S through 14. An improvement in the double differential data when compared to ENDF/B can be observed. 1.4 Comoarison with Intearal Data The total cross section for water computed from ENDF/B and IKE/JEF-1 .data are compared against experimental data in Fig. 15 for room tempera- ture. At lower ‘energies a better agreement with experiment is observed. Fig. 16 shows the comparison at 450 K. P The average cosine of the scattering angle and the neutron diffusion coefficient D(E) for H20 obtained by processing the JEF data are compared against experimental data at room temperature and at T=ZOO C in Figs. 17 through 20. A set of 126 group cross sections derived from the JEF/IKE data was used to calculate the temperature dependence of the diffusion coefficient b, the neutron diffusion length T and the average diffusion constant D (their definition is given in the Appendix 1). The obtained results ar8 compared against experiments in Figs. 21, 22, and 23. A good agreement is observed. 1.5 Comparison of Computed and Measured Neutron Flux Spectra This section shows graphical comparisons of computed and measured neutron flux spectra at different temperatures and different poison con- centrations. A 126 thermal-group cross-section library has been used for this purpose (42). Figs. 24 through 33 show the good agreement that has been obtained with experimental data. - 11 - IKE STUTTGRI I I I I I I I h 1 wH2(1 2wH20 Fig. 1 Cluster Structures of Water (Eucken 1946) 3.000 EUCKEN ( 19Lc61 2.250 2.000 1.750 1.500 1.250 I I I I I I I 0 300.0 350.0 400.0 450.0 500.0 550.0 600.0 6 TEMPERATURE CKJ Fig. 2 Translational Masses of Water, HZ0 - 12 - IKE SiUTTGAR 7.000 I I I I I I I JEF-1 / T = 295K z3.000 a 1.000 0 0 .0250 .osoo .0750 1250 . 1500 . 1750 .2000 Fig. 3 Phonon Frequency Spectra for the Hindered Rotations of Hydrogen Bound in Liquid Water 5.000 IKE STUTTGRI I I I I I I I u.500 -- ENDF/B u.000 3.500 2.500 2.000 1.500 I I 0 300.0 I I I I I 350.0 uoo. 0 u50.0 500.0 550.0 600.0 6! .O TEMPERATURE CKJ Fig. 4 Effective Scattering Temperature of Hydrogen Bound in Water - 13 - SO0.l IKE STUTTGA RT I I I I INITIRL NEUTRON ENERGY = 0.154 EV SCATTERING FlNGLE = UO DEG. w---m ENDI=/@ 296 K Q RP I-326-67 I19671 /8/ . ...*. JEF-1 300K E 100.0 s E c” c a 50.0 =: 0 Fig. 5 Double Differential Neutron Scattering Cross Section for Water at 300 K at E = 0.154 eV and 40 degrees IKE STUfTCAf ?T ‘r I I I I INITIRL NEIJTRCIN ENERGY = 0.151 EV SCRTTERING ANGLE = 60 OEG; JEF-1 293.6K L E-D F/o 296 Y RP I-326-67 (19671 l8/ 1 ...... JEF-1 300K I ID 1200 ~~ ~- -Isnn .f ENERGYE (EV)' Fig. 6 Double Differential Neutron Scattering Cross Section for Water at 300 K - 14 - IKE 6fUTftAR 140.0 I . I I , I I I’ INITIAL NEUTRON ENERGY - 0.231 EV SCATTERING ANGLE - 40 DEC. 120.0 EAlDF4.7 JEF-1 100.0 60.0 60.0 40.0 20.0 ENERGY E lEV1 Fig. 7 Double Differential Neutron Scattering Cross Section for Water at 300 K 60.01 I-- 6O.Ot 40.00 30.01) 20.00 10.00 ENERGY E l EV I Fig. 8 Double Differential Neutron Scattering Cross Section for Water at 300 K SCATTERING CS IBARN/STER./EV/MOLECULEl SCATTERJ NG CS IBARNI/STER. YEV/MIY;ECULEI 0 0 z . l I: k I: -i I *. I I . . I :. u; . I - 16 - IKE STUTTGRRT I I I I I I I I INITIAL NEUTRUN ENERGY = O.Ouu EV LEtMEL (19651 /4/ --w-w ENDF/B I I I I I I I I 20.0 YO.0 00.0 60.0 100.0 120.0 luo.o 160.0 II BO.b SCATTERING FlNCLE (DECREE) Fig. 11 Differential Neutron Scattering Cross Section of Water at T = 293.6 K, 0 20.0 uo. 0 60.0 60.0 100.0 120.0 lUO.0 160.0 180.0 SCRTTERING RNGLE (DEGREE1 Fig. 12 Differential Neutron Scattering Cross Section of Water at T = 293.6 K - 17 - IKE STUTTGART is.00 I I I I I I I I I INITIAL NEUTRON ENERGY = D,2 EV . 0 GR - 4659 (196rll MO/ ti -m--s x 12.00 ENDF/B \ *B 3.00 I I I I I I I I Oo 20.0 YO.0 60.0 80.0 100.0 120.0 lUO.0 160.0 160.0 SCATTERING ANGLE (DECREE) Fig. 13 Differential Neutron Scattering Cross Section of Water at T = 293.6 K 15.00 c INITIRL NEUTRON ENERGY = 0.5 EV . 0 GA - 4659 (19641 ho/ ------d 12.00 ENDF/B 2 \ JEF-1 0 O- I I I I I 1 I I 0 20.0 YO. II 60.0 BO. 0 100.0 120.0 IYO. 0 160.0 180.0 SCATTERING ANGLE [DEGREE) Fig. 14 Differential Neutron Scattering Cross Section of Water at T = 293.6 K - 18 - IKE STUTTCRR If 310. I I III I I 1 I lllll 1 I I11l111 I I I Ill111 I I 1 b \ JEF-1 / IKE \ \ c----B Gfb877U/ENOF/B /5/ 3006 6 , A HEINLOTH [I9611 /1+/ tso* 1 gzrlo. E c I $0. 5; 100. SO. lllll I I I I ,l,ll t I 1 klllll I 1 I I11111 I I 1 10-3 2 5 10-z 2 10” 2 5 100 2 Y.00 ENERGT’CE”, Fig. 15 Total Neutron Cross Section of Hz0 at Room Temperature ; IKE STUTfGRfi 33-l / IKE 250.0 0 DRITSA,KOSTIK~S (19671 /‘3/ 200.0 n f z I u ,150.o 4 I.3 In 100.0 50.0 a Fig. 16. Total Neutron Cross Section of Ii20 at T = 450 K - 19 - IKE STIJTftAr: . moo I I I111111 I I I 111111 I I I ItI,,, IKE /THERM-126tI ------.sooo - GA-877U/ENDF/B /5/ 0 BEYSTER I19651 /-fu/ A BEYSTER 11966) 1951 D RElNStH I19611 /16/ .uooo - e LEtttlEL (19651 / 9/ -. 1000’ 1 I Illi I I I111111 I I I111111 10-3 2 5 10-2 2 IO” 2 5 100 1.80 ENERGY &EU Fig. 17 Average Cosine of the Neutron Scattering Angle for H20 at Room Temperature .6OOC IKE STUTTGAR7 Ill,, I I I I ,,,I, I I I I Ill,, IKE . soot LEHHEL (19651 191 . YOOO E m I .3000 w r’ .2600 . 1000 I LIL ’ ’ “I I I I I lllll I I I I Illll 6 8 10-2 2 v ENh?GT6EtoE”3-1 2 u 6 6 IO0 Fig. 18 Average Cosine of the Neutron Scattering Angle for H20 at T = 200 C - 20 - IKE STUTTGRF 1 I III 1 I I I IIIII I I I I Illll 0 LEHMEL (19651 /9/ I I I Illi. I I I IIIIII 0 1 I III I I 6 8 10-2 2 U EiERGT8 10-l 2 1 6 8 loo 1 .so ECEV7 Fig. 19 Neutron Diffusion Coefficient in Hz0 at Room Temperature .sooo z. UOOO l-l c . w 0 I-* 3000 z W z ii ii. 2000 u z 2 IL k. 1000 0 IKE ? LEMMEL (19651 191 I I II.1 I I I I I ,,I, I I I I III,, 0 _I -6 8 10-L 2 1 Ei4ERGY8 10-I 2 ( ,u 6 8 100 1. so ECEV3 Fig. 20 Neutron Diffusion Coefficient in HZ0 at T = 200.C (473 K) - 21 - IKE STUTTGRR -3500 I I I I I I I 0 BOWEN, SCBTT (19691 /lir/ 0 ANTCINDV [ 19601 /2X/ v KUECHLE [ 1960) 1291 =.3000 A 010, SCHCIPPER [19581 /a/ =: IKE c 0. l--.2500 z w u 2 LL E u.2000 z 0 s k ;.1500 I I I I I I I .I000 250.0 300.0 350.0 uoo.0 1150.0 500.0 550.0 600.0 6' I. 0 TEMPERQTURE CH3 Fig. 21 Neutron Diffusion Coefficient E(T) in Water, Hz0 IKE STUTTGRR 7.0001 I I I 1 I I I 6.500 u BOWEN.SCOTT I19691 a NfXSFIR. MURPHY (1969) v BESRNT.GRRNT (19651 8.000 ! 0 LEMMEL (19651 l-l 0 LOPEZ, BEYSTER (1962) ~5.500 @ REIER. OEJUREN (19621 1 x CSIKFlI (19611 i= r;s.ooo + ANTClNCJV 119601 x /ZYI r KUECHLE (1960) c w RCJCKEY,SKOLNIK cl9601 / 2x7 gu. 500 w 0 010. SCHOPPER t19581 I&/ -I I I K E gu.000 t u-l 3 ~3.500 0 - t 3.000 t I I I I I I I 300.0 350.0 uoo. 0 u50.0 500.0 550.0 600.0 6 TEMPERRTURE CK3 Fig. 22 Neutron Diffusion Length r(T) in Water, ~~0 - 22 - lSOO/ IKE STUTTGRI I 1 , I I I 1 0 1200 - KUECHLE [ 19601 1241 I‘..’ m f-l FlNTONOV ( 1960) I23 I Y v BOWEN,SCBTT 11969) /fir/ RI 1100 - X 0 REIER.DEJUREN Cl9611 /ZI/ :: 0 LEMIEL [ 19651 Ij/ z: 1000 - IKE e z E 900 - P Y t / f5 “, 600 - zz 0 cl7 3 700 - k z 600 - W s LIL so0 - Y a 900 - Fig. 23 Average Diffusion Constant K(T) in Light Water - 23 - . 10-z 0 6 Y .332 b/H-ATOM /THERM-126M 10” 6 6 RBBRTE ET AL. 119761 Y 5 10-2 2 5 &RtT-1 CE:3 5 100 2 U.DD Fig. 24 Infinite Medium Neutron Spectra in Pure Water at T = 23 C IKE STUTTGART 2 I I I I SIGRO=5.2b/H-ATOM YOUNG,HUFFMAN (19611 /30/ I 111,111 I I , I11111 I. I I IlII~~ I I 10-3 2 5 10-Z 2 -1 2 5 100 2 4.00 ENEEGY Ck Fig. 25 Infinite Medium Neutron I Spectra in Borated Water at Room Tem- perature 2 - $ -1z 8 z -6 - Z’- n. 2 - 1($-G SIGAO=5.2b/H-ATOM IKE 0 YOUNG,HUFFHAN 119611 1301 2 . 1 I ,I,1111 I I I, I,,,, , I I , , , I I I I , 10-S 2 5 10-Z 2 ENE”RGY &I 1 2 S 100 2 4.00 Fig. 26 Infinite Medium Neutron Spectra in Borat,ed Water at T = 150 C 50 ‘8’ 6 4 q-1 6 U q-2 SIGAO=5.2 b/H-ATOM 6 IKE/ THERM-126 Yf3UNG,HUFFMAN I19611 2 r I I I,,,,,, 1 I I I I,,,, I I I I I I , , I I I 10-S 2 5 10-2 2 ENE"RGY 10-l 2 5 100 2 u.00 CEV7 Fig. 27 Infinite Medium Neutron Spectra in Borated Water at T = 316 C - 25 - I 1 !i u - 2 - ~‘IgO z .c -6 - Ju - -E2 F q-2 21 6 b/H-ATOM Y IKE /THERIG126M 2 0 YOUNG.HlJFFWAN I196Yl /30/ k Fig. 28 Infinite Medium Neutron Spectra in Gadolinium Poisoned Water at , Room Temperature THERH-126 0 EXPER I IlENT& I I Il1llI I I I I11111 I I I IllIll 1 I , s lo-* 2 5 10” 2 S 100 2 4.00 ‘NrDeV f r\/ I Fig. 29 Infinite Medium Neutron Spectra in Cadmium Poisoned l-i20 - 26 - 103 S I I I , , , , , I I I ,,I,,, 2 ’ I , I I ,‘,,, I 11 13-a 2 S 13-2 2 -’ 2 S 133 2 S EN&Y ‘PEV I Fig. 30 v Perpendicular Surface Leakage Spectrum in Cadmium Poisoned Hz0 10’210-a 1 I 1 I,,‘,, I , I-I,,,,, I 1 I I I,,,, 1 I 2 S 13’2 El&Y 2 S 130 2 4.03 2 Xl Fig. 31 Infinite Medium Neutron Spectrum in Samarium Poisoned Hz0 - 27 - Fig. 32 Infinite Medium Neutron Spectrum in a Plutonium Nitrate Solution (193.4 g Pu/l at 5 wtL Pu-240) TMERtI-126 LXPER I tENTL3/,’ Fig. 33 Infinite medium Neutron Spectrum in a Plutonium Nitrate Solution (197.9 g Pu/l at 23 wt% Pu-240) - 20 - 2. HEAVY WATER D20, MAT=4002 2.1. Physics of the Neutron Deuterium Scattering, Phonon Frequency Spectra and Related Parameters The molecular structure of D 0 is similar to the one of H 0 and therefore the neutron-deuterium s 2 attering dynamics in some aspe ;5ts is comparable to the one contained in the model for light water. The fre- quencies of the internal modes of vibration however are approximately smaller by a factor l/flbecause of the mass ratio. The following fundamental dynamical modes of motion are considered in (32) : - free translational motion of the single D20 molecule. No temperature dependent translational masses are used. This simplification was also used in producing the ENDF/B scattering law data for D20, MAT = 1004 (4,5). - the hindered rotations of the Deuterium atoms are represented by tem- perature dependent broad band frequencies, derived from the results of Haywood, Page (33) by inter- and extrapolation. In Fig. 34, the phonon spectra for the lowest and highest considered temperatures are shown. - the internal vibrations of the Deuterium atoms are represented by discrete harmonic oscillations. The bending vibration frequency is W,= 0.145 eV and the symmetric and asymmetric stretching vibrations ;;~se’,oca;.s,e”,n;t6ul, 3 = 0.338 eV. The corresponding oscillation . The same effective masses as in ENDF/B have been used (Table 4). Fig. 35 displays the phonon spectra used for JEF-l/IKE and ENDF/B. Table 4: Effective masses (amu) of the D20 dynamical unit IKE/JEF-1 MAT.=4002 translations 20.0 20.0 rotations 2.222 2.222 oscillations ?,3 3.0 3.0 U2 6.C! 6.0 * The effective scattering temperature of Deuterium bound in heavy water is given in Table 5 and shown in Fig. 36. - 29 - Table 5: Integral parameters derived from the frequency spectra of D in D20 Debye-Waller Temperature T integral eff (K) (l/eV> (K) 293.6 40.32 1015.6C 323.6 42.BE 1026.71 373.6 47.11 1046.74 423.6 51.24 1068.50 473.6 55.24 1091.84 523.6 59.10 1116.63 573.6 62.69 1143.10 673.6 69.15 1200.08 Unlike the neutron scattering on Hydrogen bound in H20, the scat- tering on D bound in D20 is largely coherent. Inter- and intramolecular interference scattering would therefore have to be considered at low ener- gies. For higher energies, however, important cancellation effects in the scattering occur. For practical applications in the field of neutron thermalisation, the neutron scattering in D 0 can be predicted accurately with the incohe- rent approximation. In fat Q large neutron energy transfer is predominant and the quasi-elastic scattering may be neglected. 2.2 Data Stored in the JEF File The quantities stored for heavy water (MATz4002) are described in the information file MF=l, MT=451 given in Appendix 3. These are: S(c+T) (MF=7, 11T=4) for D in D20 at the following 8 temperatures: 293.6 323.6 373.6 423.6 473.6 523.6 573.6 673.6 K i.e. 20 50 100 150 200 250 300 400 c The data are represented in the temperature-dependent ENDF/B data format (see Appendix F of (1)) at 100 values of d and 150 values of(3 . The energy limit Emax up to which S(o(,/3,T) can be used is 1.8554 eV. The effective scattering temperatures that are required for the short collision time approximation for higher energy transfers are given in the form of a table in MF=l, MT=451. The total free atom cross section of Deuterium is 3.395 b as in ENDF/B-V MATz1302. For the neutron scattering by Oxygen, the values for free gas appro- ximation are also stored in file 7. The molecular absorption cross section is given in MF=3, MT=lOZ. - 30 - 2.3 Comparison of Calculated and Measured Scattering Law Data Comparisons of experimental and theoretical S(o(,lj) data for different values of /3 as a function of ti are shown in Figs. 37 and 38 together with the corresponding ENDF/B data. _ .- 2.4 Comparison with Integral Data The total cross section, the average cosine of the scattering angle and the neutron diffusion coefficient for heavy water obtained by proces- sing the 3EF data, are compared against experimental data in Fig. 39 through 42. 2.5 Comparison of Computed and Measured Neutron Flux Spectra A 126 group cross-section library (42) was used for calculating neu- tron flux spectra at room temperature for two different poisons. These resul ts are compared with experimental data in Figs. 43 and 44. - 31 - IKE -STUTTGART 120.0 I I I I I I 1 I T = 293.6K ----- T = 673.6K 100.0 E : c( 2 80.0 E iii . \ 5 60.0 \ \ \ \ E cl w g 40.0 a z 20.0 I! .0200 .01100 .0600 .0800 1000 .I200 .lUOO .1600 .1800 OMEGFI ;EVI Fig. 34 Temperature Dependence of the Phonon Frequency Spectra for the Hindered Rotations of Deuteriym Bound in Heavy Water D2D - 32 - knr JIUIIUH~ 12.00 r I I I / JEF-1 / IKE ----- 10.00 ENDF/B E E G 8 . 00 22 a a5 6.00 5 E m z 4.00 z !z CL 2.00 0 U . IUU .200 * 400 .500 FREQUENCY OMEGi$I Fig. 35 Phonon Frequency Spectra of Deuterium Bound in Heavy Water ?* IKE STUTTGFiRT r1.006 I- I I I I I I I 1 1 3.sbo I- 3.000 2.500 t \ g2.000 m I c 1.500 1 1.000 I ,500 I ! JEF-1 / IKE ----- ENDF/B 1 I I I , I I 1 I , 2go.o 300.0 1100.0 350.0 450.0 500.0 550.0 600.0 650.0 700.0 TEMPERATURE T (Kl Fig. 36 Effective Scattering Temperature of Deuterium Bound in D20 100 f s 2 ;r 10-l ! L (05 . (: ?I 2 a la 1 o-?z 1o-q’ I I I I IIIII x I I I II111 I Illllclj 10-l 100 101 102 ALPHFI RLPHA Fig. 37 Scattering Law Data for Heavy Water at T = 300 K Fig. 38 Scattering Law Data for Heavy Water at T = 300 K - 34 - IKE STUTTGRF 30.00 8 .., , , Ilil ! 5.00 f H E A H - 126 /42/ ENDFIB BNL-325 I19581 /35/ 2 5 10-l ENERGY E IEVI Fig. 39 Total Neutron Cross Sections for Heavy Water at Room Temperature . 3000 0 BEYSTER (19681 /35/ 0 KORNBICHLER (19651 /37/ .2500 THERM-126 ----em_ ENOF/B .2000 z m 1 .lSOO Y IT . 1000 .0500 0 10-j 2 -5 10-z 2 ENERG; E [EVI10-l 2 s 100 2 3.00 Fig. 40 Average Cosine of the Neutron Scattering Angle for Heavy Water at Room Temperature 1.500 THERM-126 (T=20Cl ----- THERM-126 (T=lBOC) ~#_..---/----' KCIRNBICHLER (19651 /3?/ --.-.-*- ii KCIRNBICHLER (19651 ,.-- _/ / .’ g.200 0 0 . IL IL W z .900 E 2; -600 I I III I I I I IIIII I I I I IIll, 10-2 10-l LOO I * 50 ENERGY E(EVI Fig. 41 Neutron Diffusion Coefficient in D,O L z T H !E R M - 126 0 OFIUGHTRY,WQLTNER[19651/36/ 0 BROWN.HENNELLY(l9621 /39/ SPRINGER(19651 /40/ ii BRUMRNNL19621 /Ql/ f 0 0 . LL IA. ii ,I.000 zi I 1 I I I I .O 300.0 350.0 uoo.0 u50.0 500.0 550.0 600.0 TEMPERRTURE T[KI Fig. 42 Neutron Diffusion Coefficient in Heavy Water 020 cd2 - E u q-1: -6 1 u - T LL x2 - w . 0 GA - 5319 Cl9641 /30/ THERM - 126 /‘f2/ I I I,,,,,, 1jJ-+10-3 I I 1 I I I I I 1 I I I I II,,, I 1 - . 2 s 10-2 2 ENEF?GT E&3 1 2 5 100 2 u.bo Fig. 43 Neutron Spectrum in Berated D20 at,Room Temperature (2.1 b/D-atom) 101 5 - 2 - 100 E 5 r 2 - 10-l E i l- 5 F 2 I 10-z 5 2 ri 0 GR - 5319 T H E R M - 3.00 ’ I I I,,,,,, I I , II,, I I I m;,,:, I 1 10-S 2 5 10-2 2 ENE& E’;E”l-! 2 5 IO0 2 4.00 Fig. 44 Neutron Spectrum in D20 + Cd - Nitrate at Room Temperature (2.4 b/D-atom) It.-.ty I--.- .._. ____.-.-.- - 37 - 3. GRAPHITE, MAT=4003 3.1 Physics of the Neutron Scatterinq in Graphite, Phonon Frequency Spec- trum, Related Parameters and Specific Heat - A central-force lattice-dynamics model for the graphite unit cell (43,44) was used for deriving the frequency spectrum of Carbon bound in graphite. This model contains four force constants: - the nearest neighbour central force which binds two hexagonal planes together ; - a bond-bending force in a hexagonal plane; - the bond-stretching force between the nearest neighbours in the plane ; - the restoring force against bending of the hexagonal plane. The force constants are precisely fitted to the high and low tempera- ture specific heat, and to the compressibility of reactor grade graphite. This model is the same as the one used in deriving the ENDF/B data for MAT=1065 (5,45). The theoretical phonon frequency spectrum is shown in Fig. 45 together with the phonon spectra derived by -Butland (47) and Haywood (4Bj from experimental data. .’ Assuming that the vibrational states of the nuclei at a given tem- perature may be described by a set of harmonic oscillators obeying Bose- Einstein-statistics, and assuming that the phonon frequency spectrum 0 is temperature invariant, it may be shown that the specific heat at i! on- stant volume, Cv, is generally given by: R is the gas constant, Cv applies to one mole, m and y(W)dw= 1. I The specifk heat of graphite as derived from different phonon spec- tra are shown in Fig. 46. A good agreement with the results of Butland and experimental data is observed. The effective scattering temperatures and the Debye-Waller integrals for graphite derived from the phonon frequency spectrum are given in Table 6 and shown in Fig. 47. - 3e - Table 6: Integral parameters derived from the frequency spectrum of graphite Oebye-Waller Temperature T integral eff (l/eV) (K) . I 293.6 26.G6 712.61 4CC 32.70 754.66 500 39.20 806.65 600 45.88 868.37 7OG 52.66 937.62 800 59.53 1012.64 1OOC 73.41 1174.94 1200 87.42 1348.12 16OC 115.66 1712.90 zooc 144.04 2090.99 3occ 215.26 3061.02 3.2 Data Stored in the JEF File The different quantities stored for graphite, MAT=4003, are described in the information file (MF=l, MT=451) given in Appendix 4. These are: S(#,lj,T) (MF=7,MT=4) for Carbon bound in graphite at the following temperatures: 293.6 400 500 600 7clo 800 1OOiJ 1200 1600 2000 3000 K The data are represented in the temperature-dependent ENDF/B data format (see Appendix F of (1)) at 100 values of o( and 150 values of /3 . The energy limit Emax up to which S(c(,p,T) can be used is 1.8554 eV. The effective scattering temperatures that are required for the short collision time approximation for higher energy transfers are given in the form of a table in MF=l, MT=451. The total free atom scattering cross section of Carbon is 4.74 b. The coherent elastic cross sections are not given in this file. They should be computed by the method given in HEXSCAT (60) as coded in the THERMR module of NJUY (61). The Debye-Waller integrals required for this purpose are provided for different temperatures in tabular form in MF=l, MT=451. The numerical values of the phonon spectrum are also given. 3.3 Comparison of Calculated and Measured Scattering Law Data The JEF/IKE scattering law data for two temperatures are compared against experimental data in Figs. 48 and 49. - 39 - 3.4 Comparison with Integral Data The total neutron cross sections for graphite as computed by NJOY (61) using the S(o(,fJ) data of JEF-1 are compared against experimental data in Fig. 50. A set of 126 group cross sections derived from the JEF/IKE data was used to calculate the temperature dependence of the neutron diffusion length 75. The obtained results together with experimental results are shown in Fig. 51. 3.5 Comparison of Computed and Measured Neutron Flux Spectra The same 126 group cross section library was used for calculating neutron flux spectra at two temperatures for Samarium poisoned graphite. The Figs. 52 and 53 show a good agreement with experimental data. - 40 - 15.0: IKE STUTTGAR T I i I , I I ENDFIB -Be-- HAYWOCD ( 1968 1 . . . . . BUTLAND I 1973 1 12.02 Fig. 45 Comparison of Phonon Frequency Spectra in Graphite 1 .oot I- IKE STUTTGAR I I I .aocI - (y ,600 I - m \ t .400 .200 0 DE SORSO ( 1353 ‘/f’ 0 SPENCER ( 134X/s; -- JEF-1 / IKE - - - F-IAYUODD i 1365 1 ----a BUTLAND i 1973 I 0 L I 0 400 800 12co 16iliJ TEMPERATURE TI K 1 Fig. 46 Specific Heat of Graphite . ..---“I. --- - - 41 - 3.500 ----e HAYWOOD (!9681 3.000 -e-w- BUTLAND ( 19731 2.500 ~2.000 CY Is I 1.500 I-- 1 .ooo .50b / - I OL I I I I t 0 500 ' loco 1500 2000 2500 3000 TEMPERATURE T(K) Fig. 47 Effective Scattering Temperature of Graphite - 42 - IKE SiUTTCART ! -!E 1 1, I,,,!’ 1 1 I t: . .- 0 000 0 0 0 A AA ^;Ph -%O% I- +-I -3- 0. 0. . i f 6 - \, 4 - *:Fig. 48 Scattering Law Data for Graphite at 1 = 300 K for Different p IKE STUTTGART 1 I I I Jff-1 / IKE 0 Gk-3542 (4962 1 /52/ .400 .600 .800 I .ooo ALPHA Fig. 49 Scattering Law Data for Graphite at T = 635 K 9.000 8.000 7.000 6.000 z E a-J. 000 u c Au. 000 s a cn 3.000 2.000 JEF-1 / IKE 0 B N L - 325 (19581 135/ 0 NEILL ET AL. Cl9651 1561 1.000 a PFlLEVSKY (195Ul /5.? / v EGELSTAFF t 19571 /sa 1 0 5 10-3 2 5 10-2 2 5 10-l 2 5 100 2 4.00 ENERGY CEV3 Fig. 50 Total Neutron Cross Section for Graphite at Room Temperature IKE STUTTGRR THERH-126 Q HILLS (19551 1591 0 LLOYD I19561 /s31 e3 SHCHEBOLEV (19731/s+, I I I I 1 I __-I 3 300 uoo 500 600 700 800 800 DO TEIIPERRTURE EK3 Fig. 51 Neutron Diffusion Length l(T) in Graphite IKE STUTTCAR7 2 I I Il1llll I 1 I llllll I 1 1111111 1 I SIGRO=O.lSB/C-FITtIM 2 - 0 YOUNG, HUFFHFlN ( 196U) 1301 10-3 . I I I111111 I I I111111 I I I111111 I I 10-3 2 S 10-2 2 -I 2 5 100 2 4.00 ENEiGY Ck Fig. 52 Neutron Spectrum in Samarium Poisoned Graphite at 300 K IKE STUTTGART I , 1 I r:,,,, I I , , , , 1 ( , I I , I , , , , I I I . E2 - - lo-‘: G;s - z CL2 - -2 rsi0 5 5319 (196Ul 13 THERM-126 2 - Fig. 53 Neutron Spectrum in Samarium Poigoned Graphite at 600 K _." _l---l__l.~ ".ll,-ll-___--.~.. ^---~---- - ~- 45 - 4. POLYETHYLENE (CH2)-, MAT=4004 4.1 Physics of the Neutron-Proton Scattering, Phonon Frequency Spectrum, Related Parameters and Soecific Heat The phonon frequency spectrum of hydrogen bound in polyethylene has been derived by Sprevak, Koppel (71) on the basis of a model of non- interacting infinite chains of CH2 radicals originally developed by Lin, Koenig (70). The lattice dynamics of polyethylene shows that nine branches of the dispersion relation are present, the frequencies in each branch being a function of the phase difference of the vibration of cor- responding atoms in neighbouring CH2 units. For some normal modes of vibration the ratio of the amplitude of the hydrogen atom vibrations to the amplitude of the carbon atom vibrations depends strongly on the phase difference. Sprevak, Koppel (71) calculated the phonon frequency spectrum of hydrogen bound in polyethylene exactly, using the computed frequencies and amplitude vectors. The weighted frequency spectrum used for computing the neutron scattering was first derived in histogram form; then two modifica- tions were made: - the low frequency part for&J< 20 meV was replaced by a Debye spectrum having the same area; - to avoid numerical difficulties, the histogram was replaced by Gaussian functions of area equal to the area under each step and centered at the center of each interval in the histogram. The phonon frequency spectrum of hydrogen bound in polyethylene is represented in Fig. 54. The dynamical modes of vibration of the CH2 unit are shown in Fig. 55. The frequency spectrum model is the same as the one used in deriving the ENDF/B data for MAT=1114 (5,45). The effective scattering temperatures and the Debye-Waller integrals for hydrogen bound in polyethylene are given in Table 7. Table 7: Integral parameters derived from the frequency spectrum of H in (CH2)n Debye-Wailer T Temperature eff integral (K) (K) (l/eV> 293.6 34.73 1203.87 350 40.29 1214.98 The specific heat of polyethylene as derived from the phonon spectrum is shown in Fig. 56. 4.2 Data Stored in the JEF File The quantities stored for polyethylene (MATz4004) are described in the information file MF=l, MT=451 given in Appendix 5. - 46 - These are: S(c(,p,T) (MF=7,MT=4) for H in (CH2)n at the two temperatures: 293.6, 350 K The data are represented in the temperature-dependent ENDF/B data format (see appendix F of (1)) at 100 values of cx and 150 values of/j . The energy limit Emax up to which S(a ,/3,T) is treated exactly is 1.8554 eV. The effective scattering temperatures that are required for the short collision time approximation for energy transfers beyond Emax are given in the form of a table in MF=l, MT=451. The same total free atom neutron scattering cross section for hydro- gen is used as in ENDF/B-V MATz1301, namely 20.449 b. The values required for the free gas approximation of the neutron scattering by carbon are also stored in file 7. The incoherent elastic scattering cross sections are not given ex- plicitly in the file for polyethylene. This contribution to the total scattering should be computed by the THERMR module of NJOY (61). The Debye-Wailer integrals required for this purpose are provided for the two temperatures in tabular form in MF=l, MT=451. The molecular absorption cross section for polyethylene is given in MF=3, MT=102, and has the value of 0.6675 b at 0.0253 eV. 4.3 Differential Neutron Scattering Data Comparisons with experiment of double differential and differential neutron scattering cross sections derived from S(a,/3,T) for various inci- dent neutron energies and scattering angles are shown in Figs. 57 through 64. 4.4 Comparison with Integral Data of Polyethylene and Paraffin The total neutron cross section for polyethylene is compared against experimental data in Fig. 65 for room temperature. The average cosine of the neutron scattering angle in polyethylene is represented in Fig. 66 where, in addition, a comparison with ENDF/B data (5) is shown. A set of 126-group cross-sections (42) generated from JEF/IKE data with NJOY was used to calculate the neutron diffusion parameters at room temperature. The results for polyethylene are compared against experi- ments in Table 8. For practical purposes, the data derived for polyethylene can also be used for paraffin. Experimental results for paraffin with two different densities are shown in Table 9 together with the computed values. - 47 - Table 8: Neutron Diffusion Parameters of Polyethylene at Room Temperature D (cm) L cm> Reference 0.103 2.12 Calculation (55) 0.103f0.004 2.12+0.04 Measurement (67) t I I 1 Table 9: Neutron Diffusion Parameters of Paraffin at Room Temperature D (cm) L (cm> Density (g/cm31 Reference 0.109f0.004 2.19+0.07 Measurement (68) 0.87 0.1087 2.237 Calculation (55) -I----- 0.108f0.002 2.13+0.04 Measurement (69) 0.89 0.1062 2.187 Calculation (5 5) 1 4 4.5 Comparison of Computed and Measured Neutron Flux Spectra in Polyethy- lene and Paraffin Graphical comparisons of computed and measured neutron flux spectra in polyethylene are shown for two poison concentrations in Fig. 67 and 68. A 126-group neutron cross-section library (42) has been used to compute these two energy spectra. In addition the neutron spectrum in a mixture of uranium tetrafluo- ride and paraffin was calculated using the polyethylene scattering kernel data. The results are compared against experimental data and presented in Fig. 69. The good agreement shows that the polyethylene data are well suited to describe the neutron thermalisation in paraffin. 25.00 20.00 15.00 a 5.00 00 .080 .160 .3110 .360 0 CARBONatom ' Fig. 54 Phonon Spectrum of Hydrogen Bound in Polyethylene 0 HYDROGENatoms Fig. 55 Structure and Dynamics of Polyethylene -_~.----_-IKE STUTTGRR I. lllJCl I ------1 . C.-l II- I-J 0 600 if . u-l 0 WUNOERL I CH (19621h IKE _.--.-L--~----.--.----I~~-1-- . 11002on.o 250.0 3uo.o 350.0 &.o TEMPERFlTUHE T (Kl Fig. 56 Specific Heat of Polyethylene - 50 - 30.00 1 IKE STUTTCAI RT T 1 , 1 1 1 1 - INITIFlL NEUTRON ENERGY = 0.328 EV SCRTTERING ANGLE = 60 DEG. 25.00 IKE t BISCHtlFF.ET FIL. (19661 /?3/ ERRLIER RPI DATA ll T 0’ L20.00 - f & \ z . . t5!5.00 - t- *n G u cl-l p*o.oo - c3 cn 0 1 ldO0 I I I A00 1 0 .osoo . . lSO0 .2000 .2500 . -3500 .uooo .usoo ENERGY ECEV3 Fig. 57 Double Differential Neutron Cross Section for Polyethylene at Room Temperature at E = 0.328 eV and 6C Degrees 15. DO IKE STUTTCRRT I I I I I I I I INITIRL NEUTRON ENERGY t 0.32B EV 2 If SCATTERING ANGLE = 90 DEG. CI: IKE BISCHOFF ET RL. 11966) /?3/ ERRLIER RPI DFlTA FNERCY ECEVI Fig. 58 Double Differential Neutron Cross Section for Polyethylene at Room Temperature at E = @.32F eV and 9C Degrees - 51 - IKE STUTTCRRT 12.00 1 I I I 1 I 1 I INITIAL NEUTRON ENERGY = 0.650 EV SCATTERING RNGLE = 60 DEG. IKE 0 BISCHOFF-Ei RL. Cl9661 /73/ A ERRLIER RPI ORTR Fig. 59 Double Differential Neutron Cross Section for Polyethylene at Room Temperature at E = 0.65 eV and 60 Degrees IKE STUTTGRRT ,6.000 [ 1 I I I I I I 1 INITIAL NEUTRON ENERGl - 0.650 EV SCATTERING RNGLE = 90 DEG. /?J/ *O, A .a000 ENERGY EtEV3 Fig. 6C Double Differential Neutron Cross Section for Polyethylene at Room Temperature at E = 0.65 eV and 9C Degrees - 52 - POLYETHYLENE E,= 1.02 eV IKE BISCWJFF ET RL. 119661 /f3/ E E r (3 4 i C 4 2 0 4 2 ENERGY EfEV3 Fig. 61 Double Differential Neutron Cross Section for Polyethylene at Room Temperature at E = 1.C2 eV for Different Angles _- _.-.___u__--.~-iu.-.~-“~Y~ - 53 - 12.00 - 10.00 - n w ti u w ii r \ $ 6.00. I w iIt 2 u 2.00 - INiTIRL NEUTRON ENERGY = O.OuI CV I K E Q HOFHEYR (19651 /65/ 0' I , I '1-1 0 20.0 YO.0 60.0 60.0 100.0 1tzo.o 140.0 160.0 1ec.o SCRTTERING ANGLE [DEGREE3 Fig. 62 Differential Neutron Scattering Cross Section of Polyethylene at Room Temperature at E = C.C44 eV . IKE STtiTTGRR T 15.00 I I I I I I I I INITIAL NEUTRON ENERGY = 0.1823 EV . ;E;S;ER ET AL (19681 1601 $2.00 \ . 5 =; 2 9.00 E m I I I I I I I I 20.0 uo. 0 60.0 60.0 100.0 120.0 1110.0 160.0 160.0 SCATTERING ANGLE (DEGREE) Fig. 63 Differential Neutron Scattering Cross Section of Polyethylene . at Room Temperature at E = 0.1823 eV - 55 - lu~oo, \, , , , , , f”’ STUJTGRF IT INiT:RL NEUTRL3ti ENERGY = C.UOB l V -IKE 12.00 - 0 WHITTEMORE (19661 /66/ \ s,lO.OO - 3 ” w d T: \ P a 6.00 - f c u u tn d: g 4.00 - ln 2.00 - -0 20.0 UO.0 60.0 0 100. .o 120.0 lUO.0 160.0 160.0 SCATTER RNGLE COEGREEJ Fig. 64 Differential Neutron Scattering Cross Section of Polyethylene at Room Temperature at E = 0.408 eV IKE 57UTTGRR ’ “rrr-1--r I K E /THERM-I26 RRHSTRUNG I19651 /63/ I I I I IIIII I I 1 I Illll I I I I III1 3 '* ., 10-J 2 II 6 6 10-c 2 E&I 6 6 10-l 2 4 6 6 100 ENERGY Fig. 65 Total Neutron Cross Section of Polyethylene at Room Temperature - 57 - IKE STUTTGRR' .sooa I- I I Ill1111 I 1 I I11111 I I III i IKE ------. YSOCl- ENDF/B/GR-B77U 0 BEYSTER ET FIL. (19681 /iv/ . YOOCl- .35oc l- .3oot )- z ?.250( I- W z .;5s: ‘7 . IS01 o- .lOOl o- .050 0 0 i IO- 3 2 5 104 10-I 2 S 100 ENERGT E&3 Fig. 66 Average Cosine of the Neutron Scattering Angle in Polyethylene at Room Temperature - 58 - IKE STUTTCQRT ‘I” 6 uU 2 lcp Z6 t. 4 z 3 2 E u 10-Z “i w u I “;2 w y-3 6 SIGMA0 = 5.711 B/H-FITOH u I K E /THERM-126 2 0 YIYUNG ET FIL. C196Ql 1621 Fig. 67 Infinite Medium Neutron Spectrum in Berated Polyethylene at Room Temperature (CF’ = 5.74 b/H-atom) IKE STUTTCFIRT I ,,m!“.* I I I ,,I”’ I I , I I I!!’ E z 1g-’ : -6’ r : SIGMQO = 10.4 B/H-RTOH I K E /THERM-126 0 YOUNG. HUFFHRN 11964) 1301 I I I I .i;;i / I I1 Ill,, 10-3’ I I I I I I I I I 4 1 10-3 2 5 10-Z 2 EN&T. &3 1 2 5 100 2 4.00 Fig. 68 Infinite Medium Neutron Spectrum in Berated Polyethylene at Room Temperature (vA = 10.6 b/H-atom) u - 2 - ‘g’ ,: =: 6 . . Lu - Z 3 2 - ai it 100 :. UR - 6 -. w -u - :2 - lz y- -i r 6 u I K E /THERM-l26 2 0 YOUNG. HUFFMAN (19611) 1301 I I I I I1 t1lll I I I I Illll I I I I11111 I 10-210-3 2 5 10-2 2 ENEiGY E&3 1 2 5 I00 2 4.00 Fig. 69 Infinite Medium Neutron Spectrum in UF4 + Paraffin at Room Temperature - 60 - IV. REFERENCES (1) ENDF-102. Data Formats and Procedures for the Evaluated Nuclear Data File, ENDF/B-V; edited by R. Kinsey, Oct. 1979, revised by B.A. Magurno, Nov. 1983 (BNL-NCS-50496). . -- (2) Koppel, J.U., Triplett, J.R., Naliboff, Y.D.: GASKET, a Unified Code for Thermal Neutron Scattering, GA-7417 (1966). (3) Eucken, A: Zur Kenntnis der Konstitution des Wassers, Nachr. Akad. Wiss., Gattingen, Math. Phys. Kl. 2, 38 (1946). (4) ENDF/B Scattering Law Data: Tape 320, National Nuclear Data Center, Brookhaven National Laboratory, UPTON, N.Y. (5) Koppel, J.U., Houston, D.H.: Reference Manual for ENDF Thermal Neu- tron Scattering Data, GA-8774 (1968). (6) Page, D.I., Haywood, B.C.: The HARWELL Scattering Law Programme: Frequency Distributions of Moderators, AERE-R 5778 (1968). (7) Nelkin, M.: Scattering of Slow Neutrons by Water, Phys. Rev. 119, 741 (1960). (8) Bischoff, F. et al.: Low-Energy Neutron Inelastic Scattering, RPI- 328-87 (1967). (9) Lemmel, H.D.: Bestimmung der Diffusionskonstanten D(E,T) und D+v (T) thermischer Neutronen in H20, Phenylen, Zr H und D20 durch Mes- , sung der Streuwinkelverteilungen 4X B*dtVdfl."%il I : H20, Nukleo- nik 7, 265 (1965). (10) Beyster, J.R. et al: Integral Neutron Thermalisation, GA-4659 (1964). (11) Heinloth, K.: Scattering of Subthermal Neutrons of H20, CH202 and C6H6, Z. Physik 163, 218 (1961). (12) Russell, J.L., Neill, J.M., Brown, J.R.: Total Cross Section Mea- surements of H20, GA-7581 (1966). (13) Dritsa, M., Kostikas, A.: Total Cross-Section of Water at Room Tem- perature and 200 C, EANDC (OR)-63L (1967). (14) Beyster, J.R. et al.: Pulsed Neutron Research, IAEA, Vienna, Vol. I, 407 (1965). (15) Beyster, J.R. : Neutron Scattering from Light Water, NSE 31, ‘254 (1968). (16) Reinsch, C.: Messung des differentiellen Wirkungsquerschnitts und des mittleren logarithmischen Energieverlustes bei der Streuung langsamer Neutronen an Wasser und Eis, Z. Physik 163, 424 (1961). (17) Bowen, R.A., Scott, M.C.: Neutron Diffusion Measurements in Water from 18 to 280 C, Brit. J. Appl. Phys. Series 2, 2, 401 (1969). (18) Nassar, S.F., Murphy, G.: Pulsed Neutron Diffusion Parameters in Spherical Water Systems, NSE 35, 70 (1969). - 61 - (19) Besant, C.B., Grant, P.J.: The Diffusion Length of Thermal Neutrons in Water between 18 and 255 C, Proc. Roy. Sot. 289A, 342 (1965). (20) Lopez, W.M., Beyster, J.R.: Measurement of Neutron Diffusion Para- meters in Water by the Pulsed Neutron Method, NSE 12, 190 (1962). (21) Reier, M., De J&en, J,A.: Diffusion Length Measurement of Thermal Neutrons in Water, BNL-719, 977 (1962). (22) Csikai, J., Daroczy, A., Dede, K.: Measurement of the Diffsion Length of Thermal Neutrons in Water from 16 to 89 C and in Diphenyl (DOWNTHERM A) at 185 C, J. Nucl. Energy 15, 204 (1961). (23) Antonov, A.V. et al.: Study of the Diffusion and Thermalization of Neutrons in Water and Ice within a Range of Temperatures using the Impulse Method, Proc. Symp. Inelastic Scattering of Neutrons in Solids and Liquids, Vienna, 377 (1960). (24) Kiichle, M.: Measurements of the Temperature Dependence of Thermal Neutron Diffusion Parameters in Water and Downtherm A, NSE 8, 88 (1960). (25) Rockey, K.S., Skolnik, W.: Measurement on the Diffusion Length of Thermal Neutrons in Water from 25 to 296 C, NSE 8, 62 (1960). (26) Dio, W.H., Schopper, E.: Temperature Dependence of the Diffusion Coefficient and the Diffusion Length of Thermal Neutrons in Water, Nucl. Phys. 6, 175 (1958). (27) Reier, M., De Juren, J.A.: Diffusion Length of Thermal Neutrons in Water from 23 C to 244 C, J. Nucl. Energy A14, 186 (1961). (28) Keinert, 3.: THERM-126, A Thermal Neutron Cross Section Library Including Scattering Matrices, IKE 6-105/l (1978). (29) Abbate, M.J., Lolich, J.V., Parkinson, T.F.: Neutron Thermalization in Light Water-Measurement and Calculation of Spectra, NSE 60, 471 (1976). (30) Young, C.J., Huffman, D.: Experimental and Theoretical Neutron Spec- tra, GA-5319 (1964). (31) ENEA, OECD: Neutron Spectra, EACRP-L-62 and Supplements (1968, 1972). (32) Keinert, J.: Reevaluation of the Neutron Scattering Dynamics in Heavy Water, Generation of Multigroup Cross Sections for THERM-126, IKE 6-138 (1982). (33) Haywood, B.C., Page, D.I.: Scattering Laws for Heavy Water at 540 OK and Light Water at 550 OK. Neutron Thermalization and Reactor Spec- tra, IAEA, Vol. 1, 361 (1968). (34) Whittemore, W.L.: Inelastic Thermal-neutron Scattering by Liquid D2O* NSE 33, 195 (1968). (35) Hughes, D.J., Schwartz, R.B.: Neutron Cross Sections. BNL-325 (1958). (36) Beyster, J.R., Antun”ez, H.M. et al.: Integral Neutron Thermalisation. GA-6824 (1968). - 62 - (37) Kornbichler, S.: Bestimmung der Diffusionskonstanten D(E ,T) und K(T) thermischer Neutronen in H20, Phenylen, ZrH .92 und @20 durch Messung der Streuwinkelverteilungen. Nukleonik 7, h 81 (1965). (38) Daughtry, J.W., Waltner, A.W.: The Diffusion Parameters of Heavy Water, Proc. Symp. Pulsed Neutron Research, Karlsruhe, Vol. 1, 65 (1965). (39) Brown, H.D., Hennelly, E.J.: Neutron Thermalisation Studies at Savannah River, BNL-719, 3, 879 (1962). (40) Springer, T. et al.: On the Determination of the Diffusion Constants of H20, Phenyls, ZrHl and D 0 by Neutron Single Scattering Ex- periments, Proc. Third?%nf. Peaseful Uses of Atomic Energy, 2, 351 (1965). (41) Baumann, N.P.: Determination of Diffusion Coefficients for Thermal Neutrons in D20 at 20, 100, 165 and 220°C, NSE 14, 179 (1962). (42) THERM-126, A Thermal Group Cross Section Library in Use at IKE, Stuttgart. (43) Young, J.A., Koppel, J.U.: Phonon Spectrum of Graphite, J. Chem. Phys. 42, 357 (1965). (44) Young, J.A., Wikner, N.R., Parks, D.E.: Neutron Thermalisation in Graphite II, Nukleonik 7, 295 (1965). (45) ENDF/B Scattering Law Data, Tape 322, NNDC/BNL, Upton, N.Y. (46) Keinert, J.: Analyse der Neutronenstreudynamik in Graphit, IKE 6-TN-5 (1979). (47) Butland, A.T.C.: The Generation of Improved Thermal Neutron Scatter- ing Models for Graphite, AEEW-R-882 (1973). (48) Page, D.I., Haywood, B.C.: The Harwell Scattering Law Programme: Frequency Distributions of Moderators, AERE-R-5778 (1968). (49) De Sorbo, W., Tyler, W.W.: The Specific Heat of Graphite from 13 to 300 K, J. Chem. Phys. 21, 1660 (1953). (50) Spencer, H.M.: Empirical Heat Capacity Equation of Gases and Gra- phite, J. Ind. Eng. Chem. 40, 2152 (1948). (51) Glgser, W.: A Review of Scattering Law Studies for Moderators, KFK-602 (1976). (52) Beyster, J.R. et al.: Integral Neutron Thermalization, GA-3542 (1962) (53) Lloyd, R.C., Clayton, E.D., Richey, C.R.: Variation of Graphite Diffusion Length with Temperature, NSE 4, 690 (1958). (54) Shchebolev, V.T.: Determination of the Integral Parameters of the Interaction of Neutrons with Carbon, At. Energy (USSR) 34 (4), 291- 293 (1973). - 63 - (55) Keinert, J.: Neutronenstreudynamik von Polytithylen, Erzeugung von Wirkungsquerschnitten fijr THERM-126, IKE 6-136 (1981). (56) Neill, J.M., et al.: Graphite Interface Studies, GA-6753 (1965). (57) Palevsky, H.: (1954), unpublished. (58) Egelstaff, P.A.: J. Nucl. Eng. 5, 2d3 (1957). (59) Mills, J.E.C.: AERE-RP-R-1618 (1955). (60) Naliboff, Y.D., Koppel, J.N.: HEXSCAT Coherent Elastic Scattering of Neutrons by Hexagonal Lattices, GA-6026 (1964). (61) MacFarlane, R.E., Muir, D.W., Boicourt, R.M.: The NJOY Nuclear Data Processing System, Vol. I and II, LA-9303M (1982). (62) Young, J.C., Trimble, G.D., Naliboff, Y.D., Houston, D.H., Beyster, J.R.: Neutron-spectrum Measurements in H20,CH2 and C6H6, NSE 18, 376 (1964). (63) Armstrong, S.B.: The Energy-dependent Total Neutron Cross-section of Polyethylene, NSE 23, 192 (1965). (64) Beyster, J.R., Borgonovi, G.M., Carriveau, G.W.: Angular Scattering Neutron Thermalization and Reactor Spec- !~a~HldEAZ:HSdci!? ~~&?Pb68). (65) Hofmeyr, C.: Bestimmung der Diffusionskonstanten D(E ,T) und E(T) thermischer Neutronen in H20, Phenylen, ZrH und D 8 durch Messung der Streuwinkelverteilungen 4X/p d6’/d& h?? Benzo I, Diphenyl, o-, m-und p-Terphenyl, Nukleonik 7, 286 (1965). (66) Whittemore, W.L.: Scattering of Neutrons by Polyethylene, NSE 24, 394 (1966). (67) SjBstrand, N.G., Mednis, J., Nilsson, T.: Arkiv Fysik 15, 471 (1959). (68) KUchle, M.: Messung der Temperaturabhsngigkeit der Neutronendiffusion in Wasser und Diphyl mit der lmpulsmethode, Nukleonik 2, 131 (1960). (69) Dio, W.H.: Uber Untersuchungen der Diffusion thermischer Neutronen in Wasser und Paraffin mit einer gepulsten Quelle, Nukleonik 1,13 (1958) (70) Lin, T.P., Kbnig, J.L.: A Method for the Complete Vibrational Analy- sis of the Isolated Polyethylene Chain, J. Molec. Spectr. 9, 228 (1962). (71) Sprevak, D., Koppel, J.U.: Neutron Scattering by Polyethylene, Nukleonik 12, 87 (1967). (72) Wunderlich, B.: Motion in Polyethylene. I. Temperature and Crystal- linity Dependence of the Specific Heat, J. Chem. Phys. 37, 1203 (1962). (73) Bischoff, F. et al.: Low Energy Neutron Inelastic Scattering, RPI-328 (1966). - 64 - Appendix 1 Definition of the Maxwellian Averaged Thermal Neutron Diffusion Coeffi- cient 3(T), Diffusion Length T(T)., and the Diffusion Constant Do(T) for the Temperature T of the Medium. In the multigroup representation b is defined by: b = l& where str =zA + ’ E cl-1 E !I! 4! exp(-E/kTn) dE c 9 = 1, cl= g I (kT,,)* E 9 where T n is the neutron temperature. The thermal neutron diffusion length is related to the thermal neu- tron diffusion coefficient by: r(T) = JB(T)/~(TY The neutron diffusion “constant”, D (T), of a homogeneous medium and the diffusion coefficient, r(T), are relayed by Do(T) = 2 where v (T ) is the most probable neutron velocity for a Maxwellian spec- trum at’thg neutron temperature Tn. The neutron temperature T is slightly higher than the temperature T of the medium. The constant c%hat proportionally relates these two quan- titites (T,=cT) has approximately the following values: Moderator C light water 1.056 heavy water 1.001 graphite 1.015 polyethylene 1.056 ,. . . _--_---..- - 65 - Appendix 2 SCATTERING LAW DATA AND C/S FOR H(H20) FROM IKE STUTTGART 10 0 0 l.OOOOO+2 1.78606+ 1 0 0 0 14001 1451 1 o.ooooo+ 0 o.ooooo+ 0 0 0 0 04001 1451 2 0.00000, 0 o.ooooo+ 0 0 0 73 34001 1451 3 H(H20) IKE EVAL-AUG71 J.KEINERT 4001 1451 JEF/DOC-41 IKE 6-147 DIST-SEPB3 REV1 JUNE2 4001 1451 ‘: 4001 1451 6 REEVALUATION OF THE SCATTERING DYNAMIC MODEL GIVEN IN /2,3/ AT 4001 1451 7 IKE. THE FREGIJENCY SPECTRUM OF HYDROGEN BOUND IN WATER (H20) WAS 4001 Ias1.TF - El IMPROVED AS FOLLOWS 4001 1451 9 4001 1451 10 - TEMPERATURE DEPENDENCE FOR THE TRANSLATIONAL MASS OF H20 4001 1451 11 BASED ON THE RESULTS OF EUCKEN /5/ 12 - .-- 13 - TEMPERATURE DEPENDENCE FOR THE HINDERED ROTATIONAL BAND 4001 1451 14 DERIVED FROM HAYWOOD,PAGE /4/ 4001 1451 15 4001 1451 THE TWO DISCRETE VIBRATIONAL MODES FOR THE INTRAMOLECULAR 4001 1451 :; OSCILLATIONS REMAINED UNCHANGED.. 4001 1451 18 4001 1451 19 l **** 4001 1451 20 DATA TRANSLATED INTO ENDF/B-V FORMAT BY MMATTES (IKE) AUG.1983 4001 1451 21 4001 1451 22 IN ADDITION DATA NECESSARY FOR THE CALCULATION OF THERMAL NEUTRON4001 1451 CROSS SECTIONS FOR H20 (LIGHT WATER) ARE STORE0 IN MF=~ AND wF=7 4001 1451 (FREE GAS APPROXIMATION FOR OXYGEN). THE GIVEN AWR VALUE 4001 1451 CORRESPONDS TO THE MOLECULAR MASS OF 18.0154. THE SIGMA-SFREE 4001 1451 26 VALUES ARE 20.449 BARN FOR HYDROGEN AS IN ENDF/B-V HAT=1301 4001 1451 27 AND 3.761 BARN FOR OXYGEN /6/. 4001 1451 28 4001 1451 29 *it++* 4001 1451 30 4001 1451 31 W = 3 MT = 102 4001 1451 32 SIGMAAT 0.0253 EV = 0.6642 BARN FOR THE HZO-MOLECULE 4001 1451 33 4001 1451 34 w ~7 MT=4 4001 1451 35 4001 1451 36 THE THERMAL SCATTERING LAW DATA ARE COMPUTED FOR ONE HYDROGEN 4001 1451 37 ATOM IN THE H20 MOLECULE IN INCOHERENT APPROXIMATION FOR 4001 1451 38 8 TEMPERATURES WITH THE GASKET CODE /l/. A MAXIMUMNEUTRON ENERGY4001 1451 39 TRANSFER OF 1.8554 EV WAS USED. 4001 1451 40 HIGHER ENERGY TRANSFERS CAN BE COHPUTED WITH THE SHORT COLLISION 4001 1451 41 TIME APPROXIMATION USING THE CORRESPONDING EFFECTIVE SCATTERING 4001 1451 42 TEMPERATURE TEFF. 4001 1451 43 4001 1451 44 DEBYE-WALLER EFFECTIVE 4001 1451 45 TEMPERATURE INTEGRAL SCATTERING 4001 1451 46 K l/EV TEMPERATURE 4001 1451 47 K 4001 1451 48 ------em 4001 1451 49 293.6 20.68 1398.6 4001 1451 50 323.6 21.78 1405.1 4001 1451 51 373.6 23.68 1417.9 4001 1451 52 423.6 25.66 1433.3 4001 1451 53 473.6 27.69 1450.9 4001 1451 523.6 29.75 1470.1 4001 1451 52 573.6 31.82 1491.0 4001 1451 56 623.6 33.91 1513.2 4001 1451 57 I-----_------~ 4001 1451 4001 1451 ;“3 l HH+m*H+wP --+++I-**~-* 4001 1451 60 l INTERMEDIATE TEMPERATURES SHOULD BE OBTAINED BY INTERPOLAT N l BETWEEN THE RESULTING CROSS SECTIONS AND NOT BY INTERPOLAT i NE = %881 #I %h * S(ALPHA,BETA). l 4001 1451 63 l ))*~~H***~~I)*HI-+++MIHHI+++H*m+, +*H+WbWW+H*+*~ +**+* 4001 1451 64 4001 1451 65 REFERENCES 4001 1451 66 4001 1451 67 /l/ J.U.KOPPEL,J.R.TRIPLETT,Y.D.NALIBOFF, GA-7417 (1966) 4001 1451 68 J.U.KOPPEL,D.H.HOUSTON, GA-6774 (1968) 4001 1451 69 :3 J.KEINERT, IKE 6-105/l (1978) 4001 1451 70 /4/ D.I.PAGE,B.C.HAYWOOD, AERE-R 5778 (lY6B) 4001 1451 71 /5/ A.EUCKEN, NACHR.AKAD.WISS. GOETTINGEN,MATH.PHYS.KL 2,3B 4001 1451 72 (1946) 4001 1451 73 /6/ S.F.MUGHAGHAB,M.DIVADEENAM,N.E.HOLDEN: NEUTRON CROSS 4001 1451 74 SECTIONS, VOL.l,PART A, ACADEMICPRESS (1981) 4001 1451 75 4001 1451 76 1 451 79 04001 1451 77 3 102 04001 1451 78 7 4 2430: 04001 1451 79 0.0 0.0 0 0 0 04001 1 0 80 0.0 81 0.0 . 0 0 0 04001 0 0 - 66 - Appendix 3 SCATTERING LAW DATA AND CS FOR D(oD2D) FROM ;KE STUTTGA; 20 0 0 1.01000+ 2 1.985x+ 1 14002 1451 1 o.cmooo+ 0 o.ooooo+ 0 0 0 0 04002 1451 2 o.ooooo+ 0 o.ooooo+ 0 0 0 70 34002 1451 3 D(D20) IKE EVAL-JUL71 J.KEINERT 4002 1451 4 JEF/DOC-41 IKE 6-147 DIST-JAN84 REV1AUG81 4002 1451 5 4002 1451 6 SCATTERINC LAW DATA FOR D IN D20 STORED IN MF= 7 ARE BASED ON THE4002 1451 7 REEVALUATION OF THE SCATTERING DYNAMICMODEL AT IKE /1,2/. 4002 1451 THE FRE@JENCY SPECTRUM OF DEUTERIUM BOUND IN HEAVY WATER (020) 4002 1451 - -es WAS MODIFIED AS FOLLOWS 4002 1451 10 4002 1451 11 - UPPER OSCILLATOR FREQUENCY INCREASED TO 0.338 EV, BEING 4002 1451 12 CONSISTENT WITH THE VALUE FOR H IN H20 4002 1451 13 4002 1451 14 - RENORMALIZATION OF THE TEMPERATURE DEPENDENT BAND OF HINDERED4002 1451 15 ROTATIONS OERIVED FROM THE RESULTS OF HAYWOOD,PAGE /3/. 4002 1451 16 4002 1451 17 - TRANSLATIONAL NASS UNIT = 20.0 (TEMPERATURE INDEPENDENT) 4002 1451 4002 1451 :; l **** 4002 1451 20 DATA TRANSLATED INTO ENDF/B-V FORMAT BY MMATTES (IKE) NOV.1983 4002 1451 21 4002 1451 22 IN ADDITION DATA NECESSARY FOR THE CALCULATION OF THERMAL NEUTRON4002 1451 23 CROSS SECTIONS FOR D20 (HEAVY WATER) ARE STORED IN W=3 AND H-7 4002 1451 (FREE GAS APPROXIMATION FOR OXYGEN). THE GIVEN AWR VALUE 4002 1451 z: CORRESPONDS TO THE MOLECULAR MASS OF 20.02761. THE SIGMA-SFREE 4002 1451 26 VALUES ARE 3.395 BARN FOR DEUTERIUH AS IN ENDF/B-V MAT=1302 4002 1451 27 AND 3.761 BARN FOR OXYGEN /5/. 4002 1451 28 4002 1451 29 l **** 4002 1451 4002 1451 ;: PC = 3 MT = 102 4002 1451 32 SIGMAAT 0.0253EV~O.OO1312 BARN FOR THE DZO-MOLECULE 4002 1451 33 4002 1451 34 K=7 MT = 4 4002 1451 35 4002 1451 THE THERMAL SCATTERING LAW DATA ARE COMPUTED FOR ONE DEUTERIUH 4002 1451 ;4 ATOM IN THE D20 MOLECULE IN INCOHERENT APPROXIMATION FOR 4002 1451 38 B TEMPERATURES WITH THE GASKET CODE /4/. A MAXIMUMNEUTRON ENERGY4002 1451 39 TRANSFER OF 1.8554 EV WAS USED. 4002 1451 40 HIGHER ENERGY TRANSFERS CAN BE COMPUTED WITH THE SHORT COLLISION 4002 1451 41 TIME APPROXIMATION USING THE CORRESPONDING EFFECTIVE SCATTERING 4002 1451 42 TEMPERATURE TEFF. 4002 1451 43 4002 1451 44 DEBYE-WALLER EFFECTIVE 4002 1451 45 TEMPERATURE INTEGRAL SCATTERING 4002 1451 46 K l/EV TEMPERATURE K 4002 1451 47 c------_____l__l______- 4002 1451 48 293.6 40.32 1015.60 4002 1451 49 323.6 42.88 1026.71 4002 1451 50 373.6 47.11 1046.74 4002 1451 51 423.6 51.24 1068.50 4002 1451 52 473.6 55.24 1091.84 4002 1451 53 523.6 59.10 1116.63 4002 1451 54 573.6 62.69 1143.10 4002 1451 55 673.6 69.15 1200.08 4002 1451 56 ------______II______4002 1451 57 4002 1451 * $802 1451 z l INTERMEDIATE TEMPERATURES SHOULD BE OBTAINEO BY INTERPOLATING l 4002 1451 60 l BETWEEN THE RESULTING CROSS SECTIONS AND NOT BY INTERPOLATING * 4002 1451 61 l S(ALPHA,BETA). + 4002 1451 62 -w* 4002 1451 63 4002 1451 64 . REFERENCES 4002 1451 65 4002 1451 66 /l/ J.KEINERT, IKE 6-138 (1982) 4002 1451 67 /2/ J.KEINERT, IKE 6-89 (1975) (IN GERMAN) 4002 1451 68 /3/ B.C.HAYWOOD,D.I.PAGE,IAEA CONF. ANN ARBOR VOL.1,361 (1968)4002 1451 69 /4/ J.U.KOPPEL,J.R.TRIPLETT,Y.D.NALIBOFF,GA-7417 (1966) 4002 1451 70 /5/ S.F.HUGHAGHAB,H.DIVADEENAM,N.E.HOLDEN: NEUTRON CROSS 4002 1451 71 SECTIONS, VOL.l,PART A, ACADEMIC PRESS (1981) 4002 1451 4002 1451 775 451 76 0 4002 1451 74 : 102 4 0 4002 1451 7 4 24302 0 4002 1451 32 4002 1 0 77 4002 0 0 78 Appendix 4 - 67 - SCATTERING LAW DATA FOR GRAPHITE FROM IKE STUTTGART 300 0 2,41DOO+2 1.19080+ 1 0 0 0 14003 1451 1 o.Doooo+ 0 o.ooooo+ 0 O.OOOOO+ 0 O.OODOO+ 0 x 0 7; Oooo324003 1451 3 GRAPHITE IKE EVAL-SEP72 J.KEINERT 4003 1451 4 JEF/DDC-41 IKE 6-147 DIST-JAN84 REV0 4003 1451 5 4003 1451 6 DATA TRANSLATED INTO Et@F/B-V FORMAT BY H.MATTES (IKE) JAN.1984 4003 1451 7 4003 1451 8 M=7,'MT=4 THERMAL WEIJTRON SCATTERING LAW DATA s(ALPHA,BETA) 4003 1451 9 SIGMA-SFREE = 4.74 BARN /l/ MO3 1451 10 4003 1451 11 THE FREWENCY SPECTRUM OF CARBON BOUN) IN GRAPHITE WAS DERIVED 4003 1451 12 FROM A CENTRAL FORCE LATTICE DYNAMICAL MODEL CALCULATION OF THE 4003 1451 13 GRAPHITE UNIT CELL /4,5/. THE NUMERICAL VALUES ARE LISTED BELOW 4003 1451 14 AS PAIRS ff MEGA AND RHO(OMEGA) (TAB1 RECORD): 4003 1451 15 0.0 0.0 0 0 1 404003 1451 16 40 2 4003 1451 17 0. 0. 5.48470-03 3.46610-01 1.09690-02 1.4135O+DO4003 1451 18 1.64540-02 3.03320+00 2.19390-02 3.25900+00 2.74240-02 3.3847O+DO40031451 19 3.29080-02 3.48270+00 3.83930-02 3.76400+00 4.38780-02 4.05030+004003 1451 20 4.93630-02 4.84700+00 5.48470-02 7.35740+00 6.03320-02 5.88220+004003 1451 21 6.58170-02 4.63260+00 7.13020-02 4.48290+00 7.67860-02 5.80640+004003 1451 22 8.22710-02 4.63800+00 8.77560-02 4.28500+00 9.32410-02 3.92080+004003 1451 23 9.87250-02 4.91350+00 1.04210-01 5.53840+00 1.09690-01 7.51080+004003 1451 24 1.15180-01 5.31650+00 1.20660-01 3.40530+00 1.26150-01 5.20380+004003 1451 25 1.31630-01 5.32760+00 1.37120-01 7.17250+00 1.42600-01 3.31810+004003 1451 26 1.48090-01 4.50130+00 1.53570-01 5.04660+00 1.59060-01 4.20890+004DO3 1451 27 1.64540-01 2.91990+00 1.70030-01 4.65110+00 1.75510-01 1.31320+014003 1451 28 1.81000-01 7.25020+00 1.86480-01 6.56620+00 1.91970-01 5.47180+004003 1451 29 1.97450-01 5.06140+00 2.02940-01 5.19810+00 2.08420-01 4.57090-014003 1451 30 2.08430-01 0. 4003 1451 31 4003 1451 32 WITH THIS FREIJIJENCYDISTRIBUTION THE THERMAL SCATTERING LAW DATA 4003 1451 33 HAVE BEEN GENERATED IN INCOHERENTAPPROXIMATION WITH THE GASKET 4003 1451 34 CODE /6/ FOR 11 TEMPERATURES FROM ROOM TEMPERATURE UP TO 3DDOK. 4003 1451 35 A MAXIHlM NUTRDN ENERGY TRANSFER OF 1.8554 EV WAS USED. GREATER 4003 1451 36 ENERGY TRANSFERS CAN BE COMPUTED WITH THE SHORT COLLISION 4003 1451 37 TIM APPROXIMATION USING THE CORRESPONDING EFFECTIVE 4003 1451 38 SCATTERING TEMPERATURE TEFF. 4003 1451 39 4003 1451 40 DEBYE-WALLER EFFECTIVE 4003 1451 41 , TEMPERATURE INTEGRAL SCATTERING 4003 1451 ,K ‘l/EV TEMPERATURE K 4003 1451 :: ------______I___-- 4003 1451 44 293.6 26.06 712.61 4003 1451 45 400 32.70 754.66 4003 1451 46 500 39.20 806.65 4003 1451 47 600 45.88 868.37 4003 1451 48 700 52.66 937.62 4003 1451 49 800 59.53 1012.64 4003 1451 50 1000 73.41 1174.94 4003 1451 51 1200 87.42 1348.12 4003 1451 52 1600 115.66 1712.90 4003 1451 53 2000 144.04 2090.99 4003 1451 54 3000 215.26 3061.02 4003 1451 55 ------4003 1451 56 4003 1451 57 4003 1451 58 FOR GRAPHITE THE THERMAL. SCATTERING CROSS SECTIONS GENERATED FROM4003 1451 59 S(ALPHA BETA) MUST BE SUPPLEMENTED BY THE COHERENT ELASTIC CROSS 4003 1451 2; SECTIONS USING THE METHCO OF HEXSCAT /2/. THIS IS DONE E.G. IN 4003 1451 THE THERMR MODULE OF THE NJOY NUCLEAR DATA PROCESSING SYSTEM /3/.4003 1451 62 4003 1451 63 l INTERMEDIATE TEMPERATURES SHOULD BE OBTAINED BY INTERPOLATING l 4003 1451 65 l BETWEEN THE RESULTING CROSS SECTIONS AND NOT BY INTERPOLATING l 4003 1451 66 l S(ALPHA,BETA). l 4003 1451 67 l +++++*+tH++**-*W --•-+* --•HH*++++ l 4003 1451 68 4003 1451 69 REFERENCES 4003 1451 70 4003 1451 71 /l/ S.F.MUGHAfjGHA8,M.DIVADEENAM,N.E.HOLDEN: NEUTRON CROSS 4003 1451 72 SECTIONS,VOL. 1, PART A, ACADEMIC PRESS (1981) 4003 1451 73 /2/ Y.D.NALIBOFF,J.U.KOPPEL: GA-6026 (1964) 4003 1451 74 /3/ R.E.MACFARLANE,O.W.MUIR,R.M.l3OICOURT: LA-9303-M 4003 1451 75 (ENDF-324) (1982) 4003 1451 76 /4/ J.A.YOUNG,N.F.WIKNER,D.E.PARKS, NUKLEONIK 7,295 (1965) 4003 1451 77 /5/ J.U.KOPPEL,D.H.HOUSTON, GA-8774 (1968) 4003 1451 78 /6/ J.U.KOPPEL,J.R.TRIPLETT,Y.D.NALIBOFF, GA-7417 (1966) 4003 1451 79 4003 1451 80 1 451 82 04003 1451 81 7 4 32406 04003 1451 82 0.0 0.0 0 0 04003 1 0 83 0.0 0.0 0 x 0 04003 0 0 84 - 60 - Appendix 5 SCATTERING LAW DATA AND C/S FOR H(CH2) FROM IKE STUTTGART 40 0 0 2.05000+ 2 1.39063+ 1 0 0 0 14004 1451 o.ooooo+ 0 o.ooooo+ 0 0 0 0 04004 1451 2 o.ooooo+ 0 o.ooooo+ 0 0 0 66 34004 1451 3 H(CH2) IKE EVAL-MAY71 J.KEINERT 4004 1451 4 JEF/DOC-41 IKE 6-147 DIST-APR84 REV1 SEPII 4004 1451 5 4004 1451 6 THE PHONDN FREOUENCY SPECTRUM OF HYDROGEN BOUND IN POLYETHYLENE 4004 1451 7 WAS DERIVED BY SPREVAK.KDPPEL /I/ IN CALCULATIFJG THE DISPERSION 4004 1451 8 RELATIONS FOR THE INFINITE CHAIN DF CH2 RAGICALS AS WELL AS THE 4004 1451 9 POLARIZATION VECTOR FOR EACH NDRMAL FREQUENCY USING THE SET OF 4004 1451 10 FORCE CDNSTANTS DETERMINED BY LIN.KOENIG /2/. THE WEIGHTED 4004 t451 11 FREGUENCY SPECTRUM WAS THEN CALCULATED USING THE COMPUTED 4004 1451 $2 DISPERSION RELATIONS AND THE COMPUTED AMPLITUDE VECTORS. 4004 1451 13 4004 1451 14 * * l * l 4004 145; 15 OATA TRANSLATED INTO ENDF/B-V FORMAT BY M.MATTES (IKE) APR.1984 4004 1451 16 4004 1451 17 IN ADDITION DATA NECESSARY FOR THE CALCULATION DF THERMAL NEUTRON4004 1451 18 CROSS SECTIONS FOR CH2 (POLYETHYLENE) ARE STORED IN MF-3 AND MF=74004 1451 19 (FREE GAS APPROXIMATION FOR CARBON). THE GIVEN AWR VALUE 4004 1451 20 CORRESPONDS TO THE MOLECULAR MASS OF 14.0268. THE SIGMA-SFREE 4004 1451 21 VALUES ARE 20.449 BARN FOR HYDROGEN AS IN ENDF/B-V MAT=1301 4004 1451 22 AND 4.74 BARN FOR CARBON /3/. 4004 1451 23 4004 1451 24 * t * t t 4004 $451 25 4004 1151 26 MF = 3 MT = 102 4004 1451 27 SIGMA AT 0.0253 EV = 0.6675 BARN FOR THE CH2-MOLECULE 4004 145 1 28 4004 1451 29 MF = 7 MT = 4 4004 1451 30 4004 1451 31 THE THERMAL SCATTERING LAW DATA ARE COMPUTED FOR ONE HYDROGEN 4004 1451 32 ATOM IN THE CH2 MOLECULE IN INCOHERENT APPROXIMATIDN FOR 4004 1451 33 2 TEMPERATURES WITH THE GASKET CODE /4/. A MAXIMUM NEUTRON ENERGY4004 1451 34 TRANSFER OF 1.8554 EV WAS USED. 4004 1451 35 HIGHER ENERGY TRANSFERS CAN BE COMPUTED WITH THE SHORT COLLISION 4004 1451 36 TIME APPROXIMATION USING THE CORRESPONDING EFFECTIVE SCATTERING 4004 1451 37 TEMPERATURE TEFF. 4004 1451 38 4do4 1451 39 DEBYE-WALLER EFFECTIVE 4004 1451 40 TEMPERATURE INTEGRAL SCATTERING 4004 1451 41 K l/EV TEMPERATURE 4004 1451 42 K 4004 1451 43 ------4004 1451 44 293.6 34.73 1203.9 4004 1451 45 350.0 40.29 1215.0 4004 1451 46 ------4004 1451 47 4004 1451 48 FOR POLYETHYLENE THE INCDHERENT ELASTIC SCATTERING CROSS SECTION 4004 1451 49 SHOULD BE CALCULATED SEPARATELY AND ADDED TO THE INCOHERENT 4004 1451 50 CROSS SECTION GENERATED FROM S(ALPHA.BETA). THIS CAN BE DONE 4004 1451 51 E.G.BY THE THERMR MODULE OF NJDY /5/. 4004 145 1 52 4004 1451 53 ******+**************.*.**************************************** 4004 145 1 54 INTERMEDIATE TEMPERATURES SHOULD BE OBTAINED BY INTERPOLATING * 4004 1451 55 BETWEEN THE RESULTING CROSS SECTIDNS AND NOT BY INTERPOLATING * 4004 1451 56 S(ALPHA.BETA). * 4004 1451 57 **************************************************************** 4004 1451 58 4004 1451 59 REFERENCES 4004 1451 60 4004 1451 61 /I/ D.SPREVAK.J.U.KOPPEL. NUKLEONIK 12.87 (1969) 4004 1451 62 /2/ T.P.LIN.J.L.KOENIG. J.MOLEC.SPECTRA 9.228 (1962) 4004 1451 63 /3/ S.F.MUGHABGHAB,M.DIVADEENAM,N.E.HDLDEN: NEUTRON CROSS 4004 145 1 64 SECTIONS, VOL.I,PART A. ACADEMIC PRESS (1981) 4004 1451 65 /4/ J.U.KOPPEL.J.R.TRIPLETT.Y.D.NALIBOFF, GA-7417 (1966) 4004 1451 66 /5/ R.E.MACFARLANE,D.W.MUIR,R.M.BCICOURT: LA-9303-M 4004 1451 67 (ENDF-324) (1982) 4004 1451 68 4004 1451 69 1 451 72 04004 1451 70 3 102 4 04004 1451 71 7 4 8106 04004 1451 72 40041 0 73 40040 0 74 - 69 - ACKNOWLEDGEMENT The data discussed in this report were generated with ,the support of ‘IKE Stuttgart and BMFT/GID/FIZ. The authors wish to acknowledge this con- tribution, and the permission of the sponsors to release these data for incorporation in the Joint Evaluated File.