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PARAMETRIC REPRESENTATION OF
THE SHIELDING FACTOR CURVES
Y. GUR and S. YIFTAH
is rat 3 Atomic Energy Go mm isnon PARAHE'IRIC REPRESENTATION OF THE SHIEIDING FAC '.'OR CISVhb
^i- SAL and S- YiiLah
ed in pare by GlK, K«rnl jeschungsi'-entram, K.irlsruhe, Gurm;my
Israel Atomic Energy Commission January 1974 LCS9TENTS
Page
INTRODUCTION 1
THE CONCEPT OF A SELF-SHIELDED MULT1GROUP CONSTANTS SET 2
TEMPERATURE INTERPOLATION 4
BACKGROUND CROSS SECTION INTERPOLATION 6
PARAMETRIC REPRESENTATION OF TEMPERATURE DEPENDENT SELF-
SHIELDING FACTORS 11
Hyperbolic Tangent Representation 12
Tangent Representation 13
CALCULATIONS 14
Accuracy 15
REFERENCES 17
APPENDIX 18 PARAMETRIC REPRESENTATION OF THE SHIELDING FACTOR CURVES
Y. Gur and S. Yiftah
ABSTRACT
Two new methods for a parametric represen tation of the temperature dependent self-shielding factor curve are given. The concept of the self- shielding factor is described in detail and current conventional methods of interpolation between two tabulated values of the shielding factor curve are reviewed. Two methods for the parametric represen tation of the curve are suggested. Of the two, one is found to fit the data very well. A complete list of parameters for the temperature dependent self-shielding factor curves, using the better method, is given for U-235, U-238, Pu-239, Pu-240, Pu-241, and Pu-242.
INTRODUCTION
With the publication of the Bondarenko cross sections1" in 1964, the shielding factor method for the generation of multigroup constants (?) received wide recognition. Since then, the methods have been extended and use of the shielding factor approach has steadily increased primarily due to its speed and ease of application. According to the concept of the self-shielded raultigroup cross section set (described in tiie next section) a typical set can be divided into two parts: infinitely diluted cross sections and scattering matrix elements, which are constants, and self-shielding factors (ssf) which are curves given in tabular form- Since the ssf are tabulated curves of two variables, temperature and background cross section, the user must interpolate i between given values. There is as yet no single or accepted solution to the problem of interpolation, which is reviewed in succeeding sections. Parametric representation is a natural means of denoting a curve. Two methods for parametric representation of the ssf curvee are given, both of which use three temperature dependent parameters. Two sets of these parameters (a total of six parameters) completely define the temperature dependent self-shielding factor curve per energy group.
Details of computation and use of these parameters are given for both methods- Of the two methods, one is much more effective than the other in fitting the analytic curve to the data. Calculations performed in connection with the better representation and its accuracy are discusse. in the last section.
In the Appendix, a complete list of parameters of the temperature dependent, ssf curve, represented by the better method, is given for U-235, U-23S, Pu-239, Pu-240, Pu-241 and Pu~2->2,
A table, showing the accuracy of the fit obtained using the parameters given in the Appendix, is available, upon request, from the authors,
THE CONCEPT OF A SELF-SHIELDED MDLTIGROUP CONSTANTS SET
Only a brief outline of the shielding factor method will be given here as a complete and detailed exposition can be found in Rafs. (1) and (4). First, shielding factors and infitnitely diluted cross sections are generated for all isotopes of interest. The shielding factor is defined by the equation
f - ?\ (1) where: o effective resonance self-shielded cross section of x,g type x in group g
j av(E)4>(E)dE — = -J& (2) x,g I "B
lg - 3 -
E. , E, == lower and higher energy boundaries of group g 4>(E) «• weighting flux, defined by
E
a=4 I N- o~ - (5) other isotopes where: N. = atom density of the i-th isotope o . = effective total cross section of the i-th isotope, in group g.
For each isotope, shielding factors and infinitely diluted ::OFS sections are computed for each energy group and reaction type. The sei shielding factors are computed for selected temperatures and background cross sections. Usually, three temperatures and up to eight background cross sections are considered.
The generated tables are used for the calculation of mixture (4) dependent effective cross sections as follows : - It _
Obtain, for heavy elements
0a . . -• U(X - N.... o. ,)/N. (6)
or, for light and structured elements:
o • * U££) - N. 5. CJ .J/N. c <7) o,g,i t,g, i si t,g,i li
a . = background cross section for the i-th isotope in energy group g I = total macroscopic cross section of the mixture in group g- C. = average lethargy gain per collision for the i-th isotope.
C^t,g " I Hi Sl "t.g.l
For the first iteration the effective total microscopic cross section is replaced by the infinitely diluted cotal microscopic cross section. In most cases * , Eq (6) is used for all elements.
After o . has been determined, for group g and isotope i , the shielding factors are obtained from the tables. To date, as shielding factors are given in tables only for certain temperatures and background cross sections, interpolation muse be used in intermediate cases.
TEtlPERATURE INTERPOLATION Below are two simple schemes which may serve for interpolation of shielding factors , i> in T , as well as for extrapolation, provided the temper <•• cure is not toe far from the range of tabulation.
a) fCc0,T) * a(o ) In T + b(o )
b) ln(f (c ,T>) = a(o ) In T + b (o ) Given f(o ,T.) and f (o ,T_) , f(a ,T) is expressed an followb 1V1 0 1 o 2 o scheme "a":
and for scheme "b":
L(T) f(VT) = f£ao,TI)-[f(ao,T2Vf(00.T1))
LCT) = ln(T/T VlnOyT^)
It was established that both methods can be used for the temperature interpolation as follows, f (a .,T.) was calculated for all types of x,gx 0,1' 2 reactions and all fissile and fertile isotopes. All groups in the 25 Bondarenko energy group structure, and seven background cross sections (0 . = HPi-2\ where i=l,...,7) for three temperatures (300, 900 and o ,1 15001:) were considered. The input data was taken from Ref. (4).f(c .,300)
and f(a .,1500) were considered as f(a .,Tn) and f(o . ,T0) from which A 0,1 o,i 1 o,i 2 f (a ,1=900) was calculatedfby Eq. (8) and Eq. (9). A The relative deviation of f (a .,T-900) from f(a .,900) was o,x o,i ^ calculated. It was found that in general the deviation of f and the maximum deviation calculated by the first method are somewhat larger than those calculated by the second method. In Table 1 the maximum deviation for each f of each isotope is x given. The basic data of Pu-240 in ENDF/B-III shows that Pu-240 has a wide resonance whose center is in group 23 and whose wing contri butes most of the cross section in group 24. This explains the anomalously large deviations in the behavior of the shielding factors found in these two groups.
fce designated f to be the value obtained by interpolation to distinguish it from f obtained directly from tables in Ref. 4. - 6 -
TABLE 1 Maximum relative deviation of Interpolated shielding factors from directly calculated shielding factors at 900°K
Maximum relative deviation (percent) of
Isotope total elastic f !f fission . capture method method method method a b a b a b a b
U-235 2 2 0-2 0.2 2.5 2 3.2 2.6 U-238 2.2 1.5 1.55 1.2 -- 3.6 3.6 Pu-239 1.6 1.4 0.4 0.4 3 2.6 3.3 2.6 Pu-240* 2.25 2 1.5 1.5 4.7 3.2 4.4 3.9 Pu-241 1.2 1 1 1 1.45 1.35 2.7 2.4 Pu-242 2.A 2.1 1.1 1 1 - - 3.8 3.2
* In groups 23 and 24 of Pu-240 Che maximum relative deviation is in the order of 10-16%. The second method is setter in these cases also.
BACKGROUND CROSS SECTION INTERPOLATION f 3—8) Various authors suggest different o interpolation schemes, (7) ° Segev gives a dense grid of o , which differs from element to element (e.g. a = 10, 50, 100, 300, 600, 1000 for Pu-239; a = 100, 300, 600, o o 1000, 3000, 6000 for Pu-240) so that any interpolation would be satis factory. (4) Gur, Yiftah and Segev give tables of shielding factors, f(o ), with a recommended interpolation scheme of log (f(a )), linear in
log (oo).
Hardie and Little recommend, and use in 1DX, an interpolation scheme of f(a ) linear in log (a ), and suggest f(10 )=1 to be used for cross section in the shielding factor cables. (9) Hutchins and Price suggest the following scheme for use in ENDRUN-I. If f has been calculated for specific values of y - log r then the interpolated value of f at y = y + 6 is found by expanding a Taylor series around the closest value. The Taylor series expansion of f at y about y is df
f = f (y + <5) = f J(y ) + -^ 6 + x,n x ^n x n My J 2 Uy , n Evaluation of these derivatives will depend on the location of y with regard to y . and y , the minimum and maximum values of v in a ram max given ENDRUN calculation. Interpolation results in one of the following 5 cases, where A = y . - y (constant for all values of n ); n+l n
(1) For y <. ymin;
fx(y) - 1.0
(3) For ym + A;
f + £ (y . ) f (y) - v(ym,„ + A) I - x mm A x min
161 l4l1 2 A where 6, = y . + A - y. 1 Jmin J
(4) For y
(y) - (y ; t x Sx max 2 A where 5- 7 + A 2 min case f (y) is ssee t at 1.0. or f {y ) > 1 and f (y) •> f (y ), in which x x 'max xw x 'max
case f (y) is set at f (y maxJ -
J + A < y <- y (5) For ymi n ' *" •'max' locate n such that y < y < y Then n — n y - y„ £ (y) . *3tkl± f x,n+l
U i + £*(Vl>
+ £ ( x W 2 4 for: and
VW J1
15«1 + £x 'n+l- (10) (6) The same method is used in ENDRUN-IIr and TDOWN Kidman„C8 "'> suggests the following interpolation schemes: For a given temperature, let o be the current background cross section which lies between the values, a , and a „ of the f-factor table, with fn ol o2 1 and f- f-factors. The current f factor is computed from the expression: [(u j = A tanh(ii(in J + CJ 1 + D where: A = (11 - 95 C)/J a G _ J A - (il - Gj -1 .05/J ii G .3 H = the greater J£ i.O or 1.0001-:. cr 1.0001-l\ ii = H + Ltti - G)/15] ii t7 _ 1 and f - 1 and ; : ^ : (j^ . ,: ) •, ( : ^ ,t ) = largest ard smallest:, respectiw Ly, tar-u 1.-.; c J ba_kgr ound :ioss section and its L-factcr . G = 5ma 11c i oi 1 or f s J. D = H - A _1 x B = '„tanh [ t£?-DJ/Aj - tanh~ [ (i , -D) /AJ J / ln(j /c,,) C = -;tanh"1[Cf -D)/Aj; / B - in J i o For z outside the range oi tabulated values, one extrawlates o using t ".j two closest table values, assuming f is linear in ln(- ). o If J -0, its value f is reset to 0.1 and its associated f-factuc OS is adjusted so that the above interpolation scheme will give an asymptotic approach to the original data point Ir. this work group 14 f-factors for U-238 at 300JK are plotted and shown to be better approximated by his suggested method than by interpolating f(o > linear in ln(o ). Kidman does not claim to have checked his o o procedure in all other groups, temperatures and isotopes. This method is used by Kidman ec al in a later paper This four-parameter method is not yet a parametric representation of the shielding factors, as the values of the parameters are computed from the values of the two nearest (o ,f) tabulated values. In his (8) ° conclusions Kidman suggests "a possible future refinement to the ET0X-1DX method: ET0X could be altered to furnish curve parameters rather than tables of f-factors. Such a method might be more rigorous, faster, and simpler than the current method. Complete f-factor curves would be readily available for the purposes of trouble shooting and better understanding problems. The Idea seems worthy of further consider ation". - 10 - Independently,we tried to obtain a truly parametric representation of the shielding factor curves, and arrived at a three-parameter repre sentation (instead oi taut, as suggested by Kidman), but before our method is described let us review the onLy other parametric represen tation of shielding factor curves, kncwn to us Vlachevsky defines 30 "P" iunc-ions whish are based upon combinations o: the ^hree-parametric "R" function: RU,j,c)(xj _ { (cx^/fl + (cx)1].^ x = B; o Seven forms are given b> FORK = A -t u-A) G. k-1,2,. ,,7 and seven G. are given which are rational functions of x of up to sixth degree polynomials in the "P" functions, and the remaining 24 forms (31 forms in all; are defined by FORM, -= A + U-A) P k k A and B aie given tjr ea:h ssi curve, With 9 decimal places. A function of temperature, X(T), is defined, and with it the temperature interpolation is carried out. The interpolation formulae are built up sc that the maximum relative error is less than 5%, yet there is one case with an error of 10.8% and a number of cases with errors of 5%-l0%- Some irregular shielding factor curves are given specially designed parametric forms that fit Bondarenko's x data- No description is given as to how the parameters were obtained and how to fit them to recent data such as ENDF/B-III based shielding factors, etc. The method does not seem to be faster and simpler than currently used methods, and, therefore, we did not check it, It should be mentioned that this is a three- parameter representation with A, B and k ("FORM" number parameter) given for each curve. PARAMETRIC REPRESENTATION OF TEMPERATURE DEPENDENT SELF-SHIELDI NT FACTORS Inspection of any shielding factor curve* of fixed temperature, plotted on semi-log paper (Fig. 1), suggests a resemblance to the well- known tangent curve as well as the arctanh curve. therefore, aii attempt to find parameters that fit either of these curves to the tabulated data, was made as described below. 100000 10000 1000 t ,o 100 Fig. 1 A typical self-shielding factor curve (U-235 fissipn, group 22, 300°K) Hyperbolic Tangent Representation In the following, temperature dependence is omitted as we are co fit parameters to a curve of a fixed temperature. Write 1OE(C ) = A arctanh {jut (o )+n) + D o o arctanhCx) is defined in the range -1 < x < 1. Therefore, when £{o ) = 1 the argument should be +1 and when f(a ) » f(0) the argument should be -1 Thus: m + n = 1 mf(0) + n = -1 and m = 2/(1 - f(0)) n = 1 - 2/(1 - f(0)> 1 - f(0) and obtain 2 2 log(o ) = A arctanh ^ f(o ) + 1 - — + D (10) o C o CI This definition of C is convenient since when C=0, f(0)=l, so tha by C=0, a shielding factor equal to 1 is represented. With any two points (a ,, f(a .)) and (o „, f(o -)) A and D o,J_ o»J- o, Z "»*- may be found with the help of Eq. (10). Having A and D write: r f logCa )-D > f (ffQ) = 1 + J t^nh ^2 ij Cn) As A, C and D are temperature dependent, a set of six parameters CACTL) , A(T2), CO^), C(T2) > D(T1), DCO) completely defines f(o o ,T) as follows, Denote C(T ) / log(a )-D(T ) ^ £COo.Ti) . x + _±_ [tanh aj_L- _ xj C(T ) , log(o )-D(TJ f(oo,I2) - 1+-J— [tanh ^-y— - 1( logCT/T ) LCT) = logCr^) then, by Eq. (9) fCa ,T) = f(a ,T.) [f(o ,T,) / f(o ,T,)J L(T) O O 1 Q I O 1 Tangent Representation As in the previous section write: log (a ) = A tan(mfCo ) + n) + D tan(x) is defined in the range - T- < x < y . Therefore when f ( we wish the argument to be -~ and when f (a ) = f(0) we wish it I o be - y , thus m + n = TT/2 m f(0)+n = -rr/2 m = Tr/(l-f CO)) n " I i1 • i=f(o) iog(ff ) - A tan l-f(O) 2 l-f(0)j C = 1 - £(0> and obtain: log Co ) = A tan Any 2 points (o , f(o )) define A and D . Having A and D logCo )-D fCo ) - 1 + C - arctan - 14 - A, C and D are temperature dependent. The set of six parameters Ady, A(T2), CC^), C(T2), Ddj) and D(T2) define f(oo>T). 1 logC^J-DCTj^) x- EC^.T^ = 1 + CCip arctan - — -^ j Ai ^ A , log(o )-DCT ) f(VV - 1+ CCT2) (i ar.tan ^ - § and use Eq. tl2) to obtain £(a ,T). CALCULATIONS NOTE - IN ALL OUR CALCULATIONS - log(X) is log1QCX>. WHEN USING OUR DATA log,Q GO MUST BE USED. ENDF/B-III based data from Kef. 4 have been used. We looked far values of A and D that would best fit the shielding factor curves in the following manner: All possible pairs of tabulated (a ,f(.0 )) were considered. With each pair A and D for TAN or TANH representation were computed. The highest and the lowest values so obtained for A and D defined the range of A and D. 20 points in the range of A and 11 points in the range of D were considered and curves using these points as parameters were calculated for c "=10i- 2 i-1,.,.7. For each A,D pair o the sura of the squares of deviations of the calculated points from the input data points for the same a was computed. The A,D pair yielding the minimum sum was chosen to represent the shielding factor curve, and, was printed, together with C The exact value, the calculated value t-f the chosen pair and the deviation were printed out to check the accuracy of the fit. At first we chose some typical ssf curves, and fitted them with both TAN and TANK. The TAN fitting was fair to good while the TANH fitting was excellent. Therefore, the TANH fitting was chosen as the representation for which a complete Bet of parameters will be calculated. - 15 - Parametric representation of ENDF/B-II1 based shielding fartor Lurvi-&Vi' (l) for Tj»300°K and T2=1500°K, groups 10 to 25 in the ABN structure, was calculated for U-235, U-238, Pu-239, Pu-240, Pu-241 and Pu-2-W. Accuracy The raw data contains f(o ) for o =10 , i=l,...,7. Self- o o shielding factors for the same o values were calculated from the o parametric representation and compared with the raw data. In each case the deviations were computed and printed. (A print out of the deviation tables is available^upon request, from the authors.) It was found that, in general, deviations higher than IX are not consnon and deviations higher than 2% are rare Excluding the special cases reported in Table 2, there are no deviations greater than 5%. Specifically: tf-235: There are no deviations > 2% U-238: There are only a few points (see Table 2) with deviations > 5% Pu-239: There are no deviations > 2.6% Pu-240: Excluding groups 23, 24 (see Table 2) there are no deviations * 3-5% Pu-241: There are only two deviations (3.8% and 4.2%) > 2.5% Pu-242: There are only two deviations (4,2% and 4.4%) > 3.5% Table 2 contains the entice list of points where f calculated from parametric representation deviates from the exact f by more than 5%. As can be seen all the points for U-238 fall within groups 19 and 20 and those for Pu-240 within groups 23 and 24. This can be explained as follows: Group 19 of U-238 contains IT- resonances none of which is fully included in the group = Group 20 of U-238 contains -? resonance (the rest of which belongs to group 19). Group 23 of Pu-240 contains most of the lowest resonance of the isotope. - 16 - Group 24 of Pu-240 contains the lower wing of the lowest resonance of this isotope. It is not surprising that In groups having so few resonances, the behavior of the shielding factor curve is somewhat irregular. Parametric representation of these four groups is fair, as seen in Table 2. TABLE 2 Deviations above 5% of the parametric representation from the ray data Reaction a Error Isotope group o T, °K type % U-238 total 19 10* 300 5.39 105 300 5.63 10* 1500 6.41 capture 10" 300 5.22 105 300 5.19 elastic 20 10* 1500 5.7 Pu-240 total 23 100 300 -12.2 1000 300 5.75 10* 300 5.9 10* 1500 -7.8 105 1500 -16.7 elastic 105 1500 -15 ioo 300 -5.7 fission 100 300 -12.8 1000 300 -5.28 10* 300 6.2 105 1500 • -11 capture io3 300 8 10* 300 9.3 105 1500 -9.2 total 24 10* 300 9.5 fission 100 300 5.6 10* 300 9.25 capture 100 300 5.44 1000 300 -9.11 i - 17 - REFERENCES BONDARENKO, I.I , ABAGVAN, L. k , BAZAZYAKT, K.O. and SI K01.AEV , M.S.. ''Group Constants for Nuclear Reactor Calculation", Consultant Bureau, New York (1964) YIFTAH, S., SEGEV, M. , LEMANSKA, M. and CANES., M. , "Modern Fast Reactor Cross Section Systems", IA-1144 (1967) KIDMAN, R.E., SCIENTER, R.E., HARDIE, R.W. and LITTLE, «.'••:. , Jr., Nucl. Set- Eng. 48_, 189 U972) GUR, Y., YIFTAH, S. and SECEV, M., "Self-Shielded Group Constants for Fast Reactor Calculations", LA-1291 (1973) HARDIE, R.W. and LITTLE, K.U. ,Jr., "1DX, A One Dimensional Diffusion Code for Generating Effective Nuclear Cross Section", BNWL 954 (1959) COWAN, C.L., HUTCHINS, B.A. and TURNER, J.E., "TDOWN: A Code to Generate Composition and Spatially Dependent Cross Sections" GEAP- 13740 (1971) SEGEV, M., "Cross Section Sets for Fast Reactor Calculations", D.Sc. Thesis, in Hebrew C1967) KIDMAN, R.B., "Cross Section Structure Factor Interpolation Schemes" HEDL-TME-71-40 (1971) HUTCHINS, B.A. and PRICE, L.N., "ENDRUN-1: A Computer Code to Generate a Generalized Ilultigroup Data File from ENDF/B", GEAP - 13592 (April 1970) HUTCHINS, B.A., COWAN, C.L., KELLEY, M.D. and TURNEK, J.E., "ENDRUN-II: A Computer Code to Generate a Generalized Multigroup 1 ata File from ENDF/B", GEAP - 13704 (1971) VLACHOVSKY, K., "Approximation of Resonance Self-Shieiding Coefficients" ZJE-124 (1972) - 18 - APPENDIX Parameters representing the shielding factor curves of U-235, U-238, Pu-239, Pu-240, Pu-241 and Pu-242 are given in the tables below. How to use the parameters: Given the temperature, T, (kelvin), and the background cross section, o , (barns), get £(a ,T) with Eq. (12) as follows: o o Let: - , , C<«X» L..L l0S(g°} " D(300) ,1 fL - 1 + — ^tanh j^ Ij log( ) Da500) f , , CC1500) L , °o - £ l + tanh 2 - —2 [ —lasm LCT) = logCT/300)('log(5) £(o I) - f - o> x f, log(X) - log Q(X) - 19 - UKANIu'-' 235 E'JOi /3-I I I SHIKLUlHb HACTUKi tUR TOTAL X-^cCT ! IN 300- KtLVIN A C n jtsnjp 0,. 100E 01 0..OOO E 00 0.,000 F 00 1 ° 0.. 100E 01 0..4U0E --02 0.,100 E 01 1! 0..103 b 01 0..ai2E --02 0..860 t 00 1? 0..925 E 00 0..262E --01 0..U5 E 01 13 0.,ti45 E 00 0.. 7d3E--01 0..127 E 01 14 0.. 70SE 00 0.• 5->?E--01 0..132 E 01 15 0.,8?1 E 00 0.,2«S E 00 0., 154E 01 1ft 0.. M73i- 00 0..507 E 00 0..18 7 = 01 1"* 0.,'idbt 00 0..475 £ 00 0..lb9 E 01 1° 0..S34 E ou 0.,b35 E 00 0..215 E 01 11 0.. 102E 01 0..633 E 00 c..2*>1 E 01 20 0..993 E 00 0.,656 E 00 0.,246 E 01 21 0..H-)H E 00 0..354 E 00 0..179 E 01 ?2 0.. WV5E 00 0..404 E no 0..174 E 01 23 0.,dU E 00 0.,626 E 00 0., 20HE 01 24 0.,100 t 01 0., 157E 00 0.,269 E 01 25 1500. KELVIN A C 0 GTHUP 0..100 E 01 0,.OOO E 00 O.OOOE 00 in 0.. 13 re 00 0,. 100E-0- 2 0. 1>>0E 01 11 0..137 E 00 0..200E --02 0.100C 01 12 0.. 103E ol 0..ai2£ --02 O.HftOE 00 13 0..S80 E 00 0,.332E --01 0.1OOE 01 14 0..794 E 00 0,.231E --01 0 . 1 2 1 E0 1 15 0,.U6.3 E 00 0,. 171E 00 0.130E 01 16 0..bBf E 00 0,.405 E 00 0.166E 01 17 0.,900 E 00 0..415 E 00 0.177E 01 l« 0..927 E 00 0.,4,54 E 00 0.199E 01 19 0..95T E 00 0,• 561E 00 0.231E 01 20 0..946 E 00 n..616 E oo 0.232E 01 21 0.,863 t 00 n., 334E 00 0.167E 01 ?? 0.,832 E 00 0,, V5E 00 0.169E 01 23 0.>858 E 00 0. 621E 00 0.206E 01 24 0. 623E 00 0.-156 E 00 0.276E 01 25 - 20 - URANIUM 215 E'lOF/B-III bHlfcLUING FACTUKS HW fct/.srlC X-SbCTION i, c u GROUP 0.100E 01 0.000E no o .'ipnt 00 I' U.137E 00 0. 1U0E-O2 0. ."0?E 00 ll 0.lilt 00 0. 100E-0? 0, .'»026 00 1? O.100E 01 0.3UUE-U2 0. . 100E 01 13 0.13 4E 00 o.dOoe-02 0, .1076 01 u 0.113E 01 0.I>12E-02 tl. .944E no 15 0.124E 00 0. l'JOE-01 0, . IOBE 01 1* 0.86 Jfc 00 0.821E-01 0, ,197c 01 17 0,4v<;'C 00 U.'.lOt-Ul u,,136 S 01 lfl 0.97JS oo O.orilt-01 0, .2151: 01 11 0.106c 01 0.1131: 00 0. .231E 01 2C J.46t!b 00 o.5'»oe-oi i.. I 90S 01 21 O.lJffc 00 0.200E-0? 0. .100E 01 22 0.137E 00 0.100k-02 c. . 1M0S 01 23 0.8t;lc oo 0.!'J7fc 00 0. .zobz 01 24 0. 124E 00 0.400t-01 0. .212 = 01 25 15L/1. KtlVJN i c n GanuP 0. , DOE 01 [; . TJOE 00 0.000c 00 l" 0. . 100E 01 . ;,JOE oo II.O'IOF 00 u 0, . l.'iOE Oi J. . 'JOUt 00 U.OOOi 00 12 !i. .i.)7t 00 0, ,1O0E-O2 O.I^OF 01 13 0. !U: uo 0. . 20CE-O2 0.1"0E 01 14 J. . i Wfc 00 0. .100E-02 0.1903 01 1*> 0. .<»o:>c oo 0. ,ioie-oi Q.U9E 01 1ft 0. ,4^iif 00 0. ,i>2lfc~01 0.135E 01 17 0. ,'yl2E 00 0, •351E-01 0.130E 01 18 u. .902H 00 0. .561E-01 0.1966 01 I'' J. . ' '. •> ; 00 0. .101E 00 o.2i?e 01 ?" 1. jn 0. .480E-01 0.164E 01 71 0. * .' T ~ 00 0. 1O0E-O2 0.190E 01 2? 0. l i i •: 00 0. . 100F-02 0.1906 01 23 0. b?3r 00 0. , 196E 00 0.196E 01 24 0. • 923c 00 0. .400E-01 0.200E 01 25 - 21 - „ - .: -••jF/ *-i i; iHlELOIUG Fv:i'j, A r. 0 i'lljp 0,.971 E 00 0.. 7 1 2 t -0• 2 u..960 E UC 1" 0.,ain c 00 n.. 7}4E••0 1 n,, 1 1 1 E0 1 11 0,. 76Bt 0 0 0,,')')7E •-0 1 0,.104 E 01 1? 0.,Ub3 E oo 0,. 1 75E 00 0.,l!2 t 01 1 3 0..B63 E 00 0.• 2bSE 00 0.. 1 ? 1 E 01 1*. 0,.ai?z 00 0.. 2 1 H E 00 0.. 120F Ui lc> 0,,8u4 E 00 0,,4<.< H 00 o,, 15 U" 0 1 If. 0./no t 00 0.,bSS E no 0.. 177; 01 17 u., V4 11 uu 0., h 0 1 E ou 0., .91E 01 1R 0,,9fa3 E 00 0.,601 E uu 0.. 2 12E 01 l^ 0., 108E 01 0.. bobE oo 0.. 2 5 0 E 01 20 0.. 102E 01 0..732 ; 00 o..7^1 - 01 71 0,.411 E 00 0,. r) ) 2 F 00 0 ..177 E 01 -> n 0.. 1! 7 d E 00 0..I.H E 0 0 0.. 1 C6F Gl ? ^ 0..a s ?E 00 0., 7U7E 00 0..207 E 01 24 0., 6 SOU 00 0. loOE 00 u.,27« E 01 ?s 1500. KELVI I 0 . luut 01 n,. 3O0E--02 0,. 100E 01 1" 0,.797 E 00 0,. io2t--01 0.. IPSE 01 ]) u . 6 2 1 r 00 0..'..45E --01 0..H9S E 00 1 2 0,. 7 (, 7 0!- 0 0,. ') A 7 E-0 • 1 0,. lOiiE 01 13 1),. •; i 0 " 00 u., 2ulF 00 u.. 11BE ul 14 {,, . .• <: 2 E0 0 n,. 151E 0 0 n,. 11 6 E 01 11 , • • -: 00 0,, 364C 00 0., 140F 01 l'i 0. .Hilt UU 0.. S 7 1 E 00 0., lhOE 01 17 0, ,->->Zc 00 0.,537 E 00 0..177 E 01 IS 0., 9 URANIUM 235 ENOF/E-III SHIELDING HACTURS FUK CAfTURc X-SECTtUN >i c D ofnup 0.797!! 00 O.lillE- -01 n.iertc 01 \r 0.B63F 00 0.726E--01 n. nor 01 11 0.S34E 00 U.724E--01 U.IUE 01 12 0.B20E 00 0.216c 00 n.llbi 01 13 o-a*ae 00 0.2 73E 00 0.125E 01 14 u.rs)6t 00 0.422E 00 0.14 2E 01 15 0.873E 00 0.565E oo 0.156E 01 1ft 0.9<:4E 00 0.777E 00 0.197f 01 17 u.yb&E 00 0.610E 00 0.l«Ot 01 IP 0.944c 00 0.684E 00 O.220E 01 1° O.lUlE 01 0.7ME 00 0.252E 01 20 0.973E 00 0.7M6 00 0.241E 01 21 0.S94F 00 0.5U7E 00 0.1B5E 01 22. O.H53E 00 0.551E 00 -0.169E 01 2^ 0.tf44E 00 0.605E 00 0.206E 01 24 o.ftSaE ou 0.169E 00 0.276E 01 2E> A c n GROUP 0.12SE 00 O.BOOf--02 0.100E 01 in O.H72E 00 0.363E- -01 U.104E 01 n O.77oe 00 0.3S2E--01 0.107E 01 12 0.855E 00 0. USE 00 0.101c 01 13 U . !l fa 6 £ uo 0.1796 00 0.122E 01 14 0 . li i ) E 00 0.278E 00 0. 119E 01 IS 0.S12JE 00 0.44SE 00 0.144S 01 16 0.BH4E 00 0.711b 00 0.17Bfc 01 17 0 .9 3 1E 00 0.V1E 00 0.176E 01 1R O.vOvE ou 0.MJ1E 00 0.2026 01 19 0.96 2E 00 0.6U2E 00 0.2315 01 20 0.93'Jt 00 0.6-)lE 00 0.2^4E 01 21 0.901E 00 O.W'c 00 0.175c 01 22 0.H-2E oo 0.490E 00 0.1S9E 01 23 0.»77t 00 0.59SE 00 0.206E 01 2* 0.1U0E 01 0.168E 00 0.26SE 01 25 - 23 - u - 2 3R ENriF/n- i : i SHlELOlNO fACTURi Hi« . .!,,. X-SECTION A c uRIUP 0.3-75E 00 0.611E- -ii I o. I ^ • ••I 1 " u.abzH CO 0. ISht no 0. I'. lr ". 1 1 1 0.912t 00 0.2*!>t j>> u. 1 l.l> Jl 12 0.886E 00 0.3 J*h Jo u. VI 4F: ul 13 0.93 It oo 0. I\ c Ij GS1UP o.aTit 00 0.3'i?E- -01 0 . USE 01 r 0.B39E 00 D.1lRr .10 0. .H7f ul 11 0.00 IE 00 U. 1«£C uu '.).. 1 Un ul 1? O.noOE 00 0.2J ?r" !'0 0. . 1 H r 0 1 13 0 . H H 51 00 0 . J 4 'i t '10 (1 ..'l.li' HI 14 0.HRBfc 00 0.4»9t 00 0 .. 7 1', '• • l\ IS 0.T14E 00 U.421E 00 0 ,.;•?'! • i 1ft 0.lObE 01 0.HJ3E 00 u. . /• 1 fl - :! 17 0.104E 01 0.70«6 oo 0, . -. < o . .. 1 in O.lUfc 01 0.90 IE 00 0. . '-i t. 11 ..' L 1" U.^VE oo O.^IPE 00 0. .339 i. .1 ?n 0.101c 01 0.913E 00 0. .331 = •11 71 o.iooe 01 O.OOOE 00 0. OOOE 00 ?? 0.137E 00 U.200C- -02 0. , 100E 01 23 0.87!>c 00 0.121E- -01 0. H6t nl 24 o.aiyE 00 0.3H1E- -01 0. 147b 01 75 - 25 - U - 236 fNDF/B-lU SHIELOING FACTCJKS FUR CAPTURE x-SECUOM A c D GROUP 0.617E 00 0.605E- -n i 0. .11">E 01 1" 0.897E 00 n-ia6£ 00 0. . 129E 01 11 0.872E 00 0.41!>E 00 0. .156E 01 12 0.934E 00 0.613E 00 0, .1»0E 01 13 0.973E 00 0.74KE 00 0. .,Ju4E ill 14 0.9?HE oo 0.L<-5E 00 n..?79 £ 01 IS O.IOIE 01 o.s't^e on 0. . 24 7E 01 ) h 0.1L0E 01 0.9t,5E GO 0. , 374E 01 17 0.112E 01 0.956E OO 0. . A30fc 01 in 0.U5E 01 0.9/2E 00 0, ,386E 01 19 Q.10HE 01 0.')J2E 0 0 0, .3f.SE 01 )n 0.110E 01 0 . 9 7 1 £ 00 n.. 160E 01 ?1 0.137E 00 0.100E- -02 c. . 190E 01 2? 0.S08E 00 0.111E- -01 0. .•171 = 00 23 0.91.4E 00 0.322E- -01 J. • I SCZ ul 2* 0.719E 00 0.601E- -01 0. .142c 01 25 150J. KELVlf 5RHUP 0.399E 00 0.252F- -01 (1 . 107F 01 10 0.883E 00 O.H'iSfc-- )1 0 . l lot 01 11 0.916E 00 0.258E 0 0 '; . 1 !*•• 01 12 0.900E 00 0.466E 0 0 . 1 -i j E ul 13 0.936E 00 0.652E "0 r . [ •.: ? : -.1 14 0.940E 00 0.7R0E 00 0 .202E 01 15 0.971E 00 0.8 3 7E 00 n,.219 5 01 If. 0.104E 01 0.945E 00 0. ,296E 01 17 0.106E 01 0.V46E 00 0. . 300 E 01 1R 0.106E 01 0.973E 00 0, .357E 01 1° 0.100E 01 0.9S1E 00 0. ,339E 01 20 O.lOOt 01 0.970E 00 0. .331E 01 ?l 0.137E 00 0.1O0E--02 0. . 190E 01 22 0.8riS6 00 0.U1E- -01 0. ,V71E 00 23 0.914E 00 0.322E- •01 0. , 102E 01 24 0.719E 00 0.601c- •01 0. ,1*2E 01 25 - 26 - CU 239 F^OF/D-I[I SHIELDING FACTUKS FUH TuTAL X-SC-CTION A c 0 GROUP 0.925E 00 0.1J1E-01 0.11SE 01 10 0.726E 00 0.361E-01 . 0.U7E 01 11 0.861E 00 0.156E 00 0.13-76 Oi 12 0.Ba46 00 o.i9»e oo o.isoe 01 13 O.b/OE oo U.5I0Z- 00 • 0.173E 01 14 0.8H6E 00 0.42»E <)0 O.WIE 01 15 0.969C 00. 0.595b IK) 0.21SE 01 16 0.1U3E 01 0.609E 00 0.^?5E 01 17 U.IIJSE ul 0./30E 00 0.;5ftE 01 ie O.IOSE 01 0.7T7E 00 0.27SE 01 19 0. ldilfc 01 0.H23E OO 0.2/3E 01 20 0.1U5E 01 0.740k 00 0.?B66 01 21 0.100E 01 0.300E-I12 0.100E 01 22 0.925E oo 0.131t-01 O.UiE 01 23 o.asie 00 0.3'*«E OO 0.192E 01 24 0.101E 01 0.602b 00 0.331E 01 25 1500. KcL'VlV: ft c D GROUP 0.100E 01 0.400E-02 o.iooe 01 1A 0.122E 00 O.UOe-Oi 0.102E 01 11 U.823E 00 0.773E-01 0.121E 01 .12 0.83BE 00 0.U6F 00 0.1406 01 13 O.R08E 00 0.2V3E 00 0.158E 01 14 0.M01E 00 0.3?2fc 00 0.149E 01 15 0.93^u 00 0.519E 00 0.190E 01 16 0.978E 00 0.54HE 00 0.203E 01 17 0.102E 01 0.704E 00 0.236E 01 IB 0.971E 00 0.V61E (JO 0.2496 01 19 0.990E oo 0.bl5t OU 0.255E 01 2" 0.9b8fc oo O.libt 00 O.270E 01 21 0.100E 01 0.3O0E-O2 0.100E 01 22 0.925E 00 0.131E-01 0.M5E 01 23 0.909E 00 0.4O2E 00' 0.195E 01 24 0.B90E 00 0.507E 00- 0.317E 01 ?5 - 27 - PU 239 ENPF/B-lll iHIELDIMli FACTORS FOR ELASTIC X-SECnrif; A C (j GROUP O.IOOE 01 0.9C0E-02 O.lOOt 01 10 0.806E 00 0.261E-01 0.8h9E 00 11 0.8Z4E 00 0.120E 0(1 0.140E 01 12 0.765E 00 0.131E 00 0.144E 01 13 0.844E 00 0.145fc 00 0.171E 01 1* 0.779E 00 0.144E 00 0.162E 01 IS 0.90ZE 00 0.408E 00 0.231E 01 16 0.101E 01 0.356E 00 0.253E Ul 17 0.990E 00 0.480E 00 0.2B1E 01 18 0.95ZE 00 0.351E 00 0.276E 01 1<3 0.997L- 00 0.249E 00 0.262E 01 20 0.939b 00 0.B41E-01 0.250E 01 21 onooe t>i O.OUOE 00" O.OOOE 00 22 o.jooe oi O.OOOE 00 O.OOOE 00 23 0.130E 00 0.260E-01 0-113E 01 24 0.126E 00 0.290E-01 0.209E 01 25 1500. KEIVIM A C D GROUP O.IOOE 01 0.300E-02 O.IOOE 01 in 0.129E 00 0.800E-02 0.1U3E 01 11 0.815E 00 0.552E-01 0.128E 01 12 0.817E 00 0.742E-01 0.14 7E 01 13 0.B60E 00 0.107E 00 0.145E 01 ]4 0.913E 00 O.IOOE 00 0.159E 01 15 0.908E 00 0.373E 00 0.20 IE 01 16 0.H92E 00 0.338E 00 0.23OE 01 17 0.94BE oo 0.465E 00 0.254E 01 18 0.8746 00 Q.34ZE 00 0.2S2E 01 19 0.93UE 00 0.243E 00 0.244E 01 20 0.945E 00 0.780E-01 0.22OE 01 21 O.IOOE 01 O.OOOE 00 O.OOOE 00 22 Q.IQQE 01 o.oooe oo O.OOOE 00 23 0.869E 00 0.271E-01 0.99 7E 00 24 0.147E 00 0.230E-01 0.122E 01 25 - 28 - PU 239 ENOF/b-lII SHIELDING FACTURS FOR FISSION X-SECTION A c D GROUP 0.H30E 00 0.563E-01' 0.10SE 01 1" 0.848E 00 0.645E-01 0.97OE 00 11 0.882E 00 0.283E 00 0.133E 01 12 0.928E 00 0.793E-01 0.144E 01 13 0.914E 00 0.661E 00 0.174E 01 14 U.905E 00 0.649E 00" 0.164E 01 15 O.IOIE 01 0.6B9E 00' 0.194E 01 16 O.lOuE 01 0.7056 00 0.206E CI 17 0.U3E 01 0.754E 00 0.237E 01 18 0.107E 01 0.889E 00 0.265E 01 19 0.108E 01 0.B67E 00 0.266E 01 20 0.108E 01 0.8306 00 0.286E 01 21 O.B93E 00 0.343E-01 " 0.104E 01 22 0.808E 00 0.633E-01 O.illE 01 23 0.8942 00 0.481E 00 0.193E 01 24 O.IOIE 01 0.604E 00 0.331E 01 25 1500. KELVl'J A c —- ' D ' GROUP 0.848E 00 0.292E-01 0.106E 01 10 0.884E 00 0.3736-01 0.104E 01 ' 11 0.834E 00 0.212E 00 0.129E 01 12. 0.800E 00 0.7125-01 0.136E 01 13 0.892E 00 0.585E 00 0.160E 01 14 0.879E 00" 0.527E 00" 0.144E 01 15 0.974E 00 0.S97E 00 0.175E 01 16 0.944E 00 0.626E 00 0.188E 01 17 0.104E 01 0.731E 00 0.220E 01 18 O.IOIE 01 0.870E 00 0.244E 01 19 0.102E 01 0.859E 00 0.253E 01 20 O.IOIE 01 0.826E 00 0.272E 01 21 0.893E 00 0.343E-01 0.104E 01 22 0.808E 00 0.6336-01 Q.U1E 01 23 0.8H9E 00 0.484S 00 0.193E 01 24 0.100E Oi 0.589E 00 0.325E 01 25 - 29 - I'll 239 f.CP/o-iil SHIELDING FACTORS FOR CAfrunr /-su'i:-; A c r. 'J°".,P 0.74 3E 00 0.H.SJ.E--01 0.112!: 01 10 0.839E 00 0. l»5 = 00 0.122E 01 11 0.&76E 00 0.296E 00 0.126Q 01 1? 0.863E 00 C.49BE 00 0.151F 01 13 Callrt 00 0.6«4'£ no 0. l*Ci. 01 14 0.915E 00 0.71SE 00 0.179E 01 11 0.973E no 0.7V5E Ou U.211E ul 16 0.102b 01 0.810E 00 0.229b 01 17 0.lObfc 01 0.872E 00 0.2 746 01 1« 0.105E ol 0.S17E 00 0.277E 01 19 0. 10 ^>E 01 0.b9hb 00 0.279E Oi 20 0.106E ol u.b75E 00 0.^rtH£ 01 21 0.7U3E •j(j C.171E- -01 C.10-4E 01 2? O.tf'iflL 00 0. 543E--01 (>. l!j 7b 01 2* O.tovfc uo 0.49CE 00 o. r-j<.t 01 24 0.10UE ol 0.607E 00 n. i?7t 01 25 l=>u">. KEL^IM 4. r L- ',-nbP O.ttl'lr 0 0 0, . 4 -i 1 E -U• l 0. , 7. r = JO 10 O.clVo^ 00 '),. il 'E 00 f. . losr 01 11 0.«7f>E 00 p. ,;;4t no 0. .121E 01 1 ? U.8SVC uu 1.. . < fr-c 00 0. . 1 VIE 01 1 3 O.EtOuC 0 0 0, . r>l 7E 00 . l",r 01 u 0.»7JE DO . v.i: Oil t,. . 1S3F Ul IS U.945E uO . f. fe,£ 00 0. ,1 4 St 01 16 Q.9U4L OQ Oi , mt 00 0. ,,'OSE 01 17 0.10UE ul 0. ,r. 14 b 00 0. . <",HE ul IP O.'t'Ht no II, ,l>V?f no n. J")?^ 01 19 (l.'I'UE 00 0, , M>St ou 0. .2i.lE ul ?r 0.9'JdE UO 0, . 671 r no 0. . ?m- 01 21 o.vaiE 00 0, 17IE- -01 0. K/4t 01 ?? O.a'KtE ou 0. .S43E--01 0. .lore ul 23 O.6 70E ou 0, ,494 b 00 0. 19SE 01 24 O.BHttE 00 0, 572b OU 0. *i if- ul 25 - 30 - PU-240 ENOFB-III SHIELOINu FACTORS fOH TOTAL X-SECTION A c 0 GROUP 0.801E oo 0.10BE 0 0 o.im 01 10 0.886E 00 0.136E UO 0.1't9E 01 11 0.855E 00 0.142E 00 0.134E 01 12 0.88QE 00 O.280E 00 0.1G3E 01 13 0.926E 00 0.416E no O.209E 01 14 0.965b 00 0.512E 00 0.230E 01 15 O.lOoE 01 U.600E 00 O.PfOE 01 1ft 0.104E 01 0.725t 00 0.293E 01 17 o.nu 01 O.B72E 00 0.343E 01 18 0.10/E 01 0.910E 00 0.358E 01 19 0.987E 00 0.766b 00 0.313E 01 20 0.V71E 00 o. a?e--02 U.960E 00 21 0.751E 00 0.882E--01 0.147E 01 ?.? 0.101E 01 0.980E 00 Q.472E 01 23 0.100E 01 O.703E 00 0.333E 01 24 o.iooe 01 0.700E--02 0.200E 01 25 150 (i. KfcLVIN A c 0 GROUP 0.80VE 00 f. V)3E-01 0.122E 01 10 0.B69E 00 0.C6 5S-01 0.131E 01 11 0.B33E 00 0.-/15E-01 0.131E 01 12 O.iiOVE 00 0.2 Jit 00 O.lfclt 01 13 0.885E 00 0.368E 00 0.187E 01 14 0. 9 c 0 E 00 0.471E 00 0.2CJ3E 01 15 0.102E 01 0.5?8E 00 0.244E 01 16 0.102E 01 0.710E 00 0.263E 01 17 0.105E 01 0.869E 00 0.314E 01 18 0.996E 00 0.909E 00 0.325E 01 19 0.v<;/E 00 0.764E 00 0.2G3E 01 20 O.IOOE 01 O.3OOE-02 O.lOOfc 01 21 0.9U2E 00 0.643E-01 0.133E 01 Z2 0.1Z1E 01 0.93 5E 00 0.4B4E 01 23 0.106c 01 0.7Q2E 00 0.406b 01 24 0. M7t 01 O.220E-O1 0.100E 01 ?5 - II - I'tj-iM! • . '-Hi 01] bL'il'. . '•'••'.I -K'J <••'•' UiSIK ^- -Si C r l '•*: 1U'1, ' L L 7 I". O.htoOfc (li t>, , \Vi A c L. bsoup 0. . C7ot 00 17 . •> >2& -01 n. 12 <> r- 0 1 1" 0. .bSbc 00 0. .S53b- -01 0.]36E 01 1) 0. .bb 3t 00 0. .K33E- -01 0. 1 J.r^t" 01 12 (1. -031fc OO 0, . 2 1 "5E oo 0 . ! f-. t F 01 13 0. . a « ^ E oo 0, . 31.1 E 0 0 o. n HE ul 1* u,, SHIELOIHG FACTORS FOK F1SS1UM X-SFCM1'.' 300. KElVi'l fi c U GROUP O.b^'ik 00 0.213E-O1 Q.577E 00 If 0.665E 00 0.687E-01 0.608E 00 11 0.899E 00 0.222E 00 0.144E ul 12 0.955E oo 0.702E 00 0.19*6 01 13 o.y>ifc DO 0.M2E 00 0.I92E 01 14 u. 1U1E ul 0.H16E 00 0.229E 01 15 0.lOZt 01 0.d98E 00 0.245E 01 16 0.102E 01 U.945E 00 0.284E 01 17 o. loab 01 0.966E 00 0.331E 01 18 0.109E 01 0.'?78E 00 0.359E 01 19 u,1 jut 01 C.971E 00 0.314E 01 20 0. l'j(. •J. KcLVl'i J C 0 GROUP 0. lO'ir 01 i.OOOt 00 O.OOOE 00 10 0.S93E 01 w.? /3E-0I -0.243E 01 11 0.e9:;: 00 0.11 fit 00 0.134E 01 12 0 . 9 1 0 r. 00 o.y>ob oo 0.173E 01 13 l/.V/^c OU 0.59 3E 00 0.166E 01 14 0.972E 00 0.72RE 00 0.204E 01 15 0.101E 01 O.U39E 00 o.^iae 01 16 O.lDOt 01 0.419E 00 0.254E 01 17 0.106E 01 0.959E 00 0.304E 01 18 0.983E 00 0.976E 00 0.324E 01 19 0.902E oo 0.964E 00 0.284F 01 20 0.874E 00 0.'n2E-u2 0.967E 00 21 0.064E 00 0.128E 00 0.1356 01 22 Q.114E 01 0.9S7E 00 0.475E 01 23 0.106E 01 0.6d4E 00 0.406E 01 24 0.130E oo 0.260F-01 0.213E 01 25 - 33 - PU-?<•! »-.• 11>i- r- -111 SHlEUjJ/.G FACIl'j ' J CAPIUlif- J-iUM "' A (. li ...or, UP 0. .'('JOE 00 p. , i o ;• t ' 'ii M ,,11 ' 1 lo 0. .BBUt oo 0. . .' 'j •> i 00 n .. ] ,' 7 = .! 1 1 1 u..r>7i h Ou 0. ,*:•>£ '10 n. . 1'.Oc > ' i 12 0. ,vlflE Jl 19 0. . lljutr 01 n. .'Jtjhc '10 0. . 117fc 01 20 0. ,h6Vb 00 0. .•<. ME--01 0. . 1 l A c D GROUP 0.P53F 00 0.4^3E- -01 0 .'159E 00 lr U.B57E 00 0. ICE oo 0, .122E 01 1 1 0.U61E 00 0.lhOE 00 0, . 125E 01 12 0.A71E 00 i;.>W<,fc 00 U. , 15oE ul 13 0.93UE 00 0.M5E 00 0, • 171E 01 1*. O.^iaE 00 0.71hE 00 0. , 1S9P 01 15 0.103E 01 0.t<42E 00 0. . 220E 01 1A 0.101E 01 0.920E 00 0. .256E 01 17 0.107E 01 0.4t)VE 00 0. . 3U6E 01 18 0.9U7E 00 0.97(,fc (10 0. ,3?t>E 01 1 ° O.'i'tdi: 00 0.'?b3E 00 0, ,283E 01 20 O.Wtbc OO 0.332E- -OL II. , 112c 0 1 21 0.858fc 00 0.207E 00 0. ,133E 01 ?? 0.U3E 01 U.^tJ^E 00 0, A73E 01 23 0.970E oo 0.646E 00 0. 395b 01 2*. 0.157E 01 0.220E- -01 0. 100E 01 25 - 34 - PU 241 fc'IOf-/B-1 I 1 SHIELDING FACTORS FOR TOTAL ^-SECTION A c D GROUP 0.773t 00 0.101E- -01 0.969E 00 ir> O.IOOE 01 O.30OE--02 O.IOOE 01 11 o.aabE 00 0.392E- -01 O.lllE 01 12 0.848E 00 0.131E 00 0.135E 01 13 O.H/BE 00 0.156E 00 0.136E 01 14 0.tt)2E oo 0.245E 00 0.139E 01 15 U.93BE 00 0.476E 00 0.185E 01 lfa 0. PU 2<.i r; .• D F / a -111 ShlELOlNG FACTORS MMl ELASTIC X-SFCUOK A c D G'^UP 0.• 100E ni o.'toob---. , 0.1C0E Ul 10 0.. luOE 01 o.noot nr O.^OOt 00 11 0,.87S E 00 0.121E-->>l 0.1165 01 1? 0,, (I04E 00 0.3m- -1: L 0.139E 01 13 0..1567 b no 0.Jf.lt--"H 0.119E 01 14 0,.872 E 00 0.25LE--Ul 0.142E 01 15 0,.H38 E 00 0.137E 00 0.197E 01 16 u.,H9B E oo 0.10AE 00 0.207E 01 17 0., V02E uu 0.C51E--01 0.215E 01 1^ 0..B52 E 00 0.360E--01 0.113E 01 19 0..VKS E 00 U.2 J1E uu 0.v6SE 01 20 0.. 129t 00 0.29PE--0 1 o.mr 01 2! 0.,885 E oo 0.721E--01 0.245E 01 22 0..100 E 01 O.OOOE 00 O.OUOE 00 23 0,. lOOE 01 0.900E--02 -0. 779E 07 24 0..100 E 01 0.110E-•Ul 0.lOOE 01 25 A c D MOUP 0.1J7t 00 0.100E-02 0 . l^OE 0 1 in 0.lOOt 01 O.OiiOE 00 0.. 000 S 00 11 o.ione 01 0.4<>GE-02 c.,100 E 01 12 0.100E 01 0.140E-01 0.• lOOt Ul 13 0.8H2E 00 0. IblE-Ol 0,,1141 = ul 14 0.100E 01 0.1 J0E-01 0,.lOO E 01 15 0.830E 00 0.112E 00 0,, 1B0E 01 16 U.'/OvE 00 O.tfl lt-01 0.,193 E 01 17 0.9'>1£ oo O.Mlt-01 0,, 189E 01 18 0.102E 01 0.321E-01 0. 188E 01 19 O.S3bE 00 0.221E 00 0. 252E 01 20 U.1S7G 01 0.261E-01 0., 300E 00 21 0.d65£ 00 0.640E-01 0. 226E 01 22 0.100E 01 O.OOOE 00 0. 0006 00 23 O.IOOE 01 0.V00E-02 -0. 779E 07 24 0.100E 01 O.VOOE-02 0. lOOE 01 25 - 36 - PO 2M EN0F/B-I1I bHIELUINU HACTliKS FUK FISSION X-SECTION 300. Kf.LVl.J 4 C 0 GROUP 0.82/E 00 0 .if'WE--01 0 . 1066 01 ln 0.B34E 00 0. ."U3E- -Oi 0. .9336 oo 11 0.873E 00 0, . i-iae 00 0. .125E 01 1? 0.HS3E 00 0. , i>lt 00 P. . me 01 13 0.H75E 00 0, . V8E no 0, . 132E 01 l<* o.u?9E 00 0. , WfE 00 0, , K.4E 01 15 0.1»4'.E 00 0. ./SV/F uu 0. .17«t 01 16 0.96VE 00 0, ,&95F 00 0. , 195E 01 17 0.9bOE 00 0. , 710E 00 0, .191E 01 18 0.99HE 00 0. .hiOE 00 0, .205E 01 19 0.11*E 01 0. >' 10E 00 0, ,?-55E 01 20 0.921E 00 0. S >hfc 00 0. • 71BE 01 71 0.967E 00 0. •V09E Ou 1). 2/bE 01 2? 0.H6OE 00 0. 2«fc--01 0. 107E 0 1 23 0.8486 00 0. 347E 00 0, .172 = 01 2* o.avat 00 0. 635E 00 0. 300E 01 25 A c D GROUP 0.8h3fc' 00 0.453E- -01 0.774E 00 10 0.6726 00 0.272E- -01 0.107E 01 11 0.D63E 00 0.U6G 00 0.110E 01 1? o.tswe 00 0.290E 00 0.127E 01 13 U. to 2 E 00 0.2-J2E 00 O.^'.E 01 n 0.J6 7E 00 0.333c 00 0.130E 01 is 0.91QE 00 0.5b3E 00 O.loOE 01 16 0.94OE OU 0.629E 00 0,la^E 01 17 0.957E 00 0.630E 00 0.179E 01 IB U.9'JO£ 00 Q.601E 00 &.201E 01 19 0.1<> FU 241 E «Dh/h-II 1 SHIELDING FACTOKS Fin* CAPTURE X-SECTIO" A c 0 GROUP 0, .«•><;£ 00 O.fcS'iE--01 n.nnt- 01 1" 0, ,H5bE 00 O.33?E- -01 0.112E 01 11 0. .I17yb 00 0. IKSE 00 0.126E 01 12 0, .B64E 00 0.35AP 00 0.1J5K 01 13 0, ,so2E 00 0.445E Ou o.naE 01 14 0. ,H34E 00 0.420E 00 o.i ise 01 15 0. .961b 00 0. /6lb 00 0.20bt 01 16 0. ,94BE 00 0.7T4E 00 0.20HE 01 17 0, .101E 01 0.7V«C 00 0.214E 01 is 0. ,9fi2E 00 U.598E oo 0.2U5E 01 19 0, , 11 IE 01 0.06?E 00 n.?71fc 01 21 0. ,1U0E 01 0.4 ?4E 00 0.23SE 01 21 0, , LOUE 01 0.912E 00 0.2H4E 01 22 0. ,617E 00 0.161E- -01 0.113E 01 23 0. ,884E oo 0.315E 00 0.172E 01 24 0. ,910E 00 0.6J1E 00 0.29BE 01 25 A c 0 GROUP Q.321E 00 0.342E- -01 0.109E 01 10 U.944E 00 0.172E- -01 0.96 5b' 00 11 0.872E 00 0.115E 00 0.110E 01 12 0.842E 00 0.241E 00 0.124E 01 13 0.H/5E 00 0.324E 00 0.120E 01 14 0.8A5E 00 0.291E 00 0.126E 01 1? 0.916E 00 0.692E 00 0.103E 01 1ft 0.919E 00 0.6B9E 00 0.1«2E 01 17 0.950E 00 0.745E 00 0.19 IE 01 ia 0.941E 00 0.550E 00 0. ITtlE 01 1° 0.104E 01 0.H39E 00 0.251E 01 20 0.978E 00 0.4 32E 00 0.222E 01 21 0.956E 00 0.910E 00 0.274E 01 22 0.817E 00 O.lblE- -01 0.U3E 01 23 0.b6/E 00 0.317E 00 0.172E 01 24 0.922E 00 0.62 IE 00 '.296E 01 25 - 38 - PU ?42 FNUF/b-ItI SHIE101.NO FACTUKS Fim TOTAL X-S6CTI0N A c 0 GRnuP 0.100E 01 O.OOOt 00 •O.OOOt 00 in O.IOOE 01 O.POOE 00 O.OOOE Of 11 0.UB2E ou o.^ifc oo 0.195E 01 12 0.959E oo 0.553E no 0.223E 01 13 O.B93E 00 •j.2o5E Uu 0.191E Ul 14 0.9H3E 00 0.535E 00 0.245[- 01 15 0.1O7E 01 0.70 IE 00 0.2B9E 01 16 0.102E 01 0.650E 00 G.2U9E 01 17 O.llbE 01 0.U65E 01) 0.357E 01 1R 0.891E 00 0.235E Ou 0.213E 01 19 O.M31E oo 0.151C-01 0.104E 01 20 0.1<>9E 00 O.HOOE-02 0. 103E 01 21 0.122E 01 0.96 4E 00 0.423E 01 22 0.112E 02 0.241E-01 -0.236E 01 23 0.117E 01 0.2bOE-01 0.480E 00 24 0.b65r 00 0.530E-01 0.163E 01 25 A c D GROUP o. luuE 01 O.OOOfc 00 O.OOOE 00 in O.IOOE 01 O.OOOE 00 O.OOOE 00 11 0.90 IS 00 0.369E 00 0.177E 01 12 0.91HE 00 0.511E OU 0.202E 01 13 O.rthOc 00 0.227E 00 0.172E 01 14 0.930E 00 0.504E 00 0.218E 01 15 0.1u2fc 01 0.6H8E 00 0.265E 01 16 0.9&4E 00 0.639E 00 0.260E 01 17 0.114E 01 0.H62E 00 0.336E 01 IB O.hOlE 00 0.217E 00 0.179E 01 19 0.8'UE 1)0 0.151E- -01 0.104E 01 20 0.129E 00 0.800E- -02 0.103E 01 21 0.119E 01 0.964E 00 0.409E 01 22 0.4UE 01 0.250E- -01 -0.299E- •01 23 O.ll/E 01 0.260E- -01 0.4b0F 00 24 0.h65fc 00 0.530E- -01 0.163E 01 25 - 39 - Pu 242 FNOF/P-l I 1 SHlELhlNO FACTOKS FOR CLASTIC X-J6CTIOM A c o uRDUP 0. , 100E 01 O.noOF 'M) O.OOOF 00 10 0. , 100E 01 O.OOOE Ul) O.OOUE 00 11 0. .K'J'IE 00 0.41<>fc ()0 n,W5fc 01 1? 0, .^it 00 0.b45E no 0.227E 01 13 u..B77 E uo 0.2G5E no 0. 19/E 01 14 0. .•*3db 00 0.4ft4E 00 0.250E 01 IS 0. . 104E 01 0.t>f>2E 00 0.2V6E 01 16 0. .9HB6 00 0 . 0 I 7F 00 0.2-74E 01 17 0, .116E 01 0.80BE 00 G.367E 01 IB o..100 E 01 0.400E- -02 U.100E 01 1° c.. .•U7E 00 0.141E- -01 0.11/t 01 20 (.•• • HIE oo 0.60UE- -02 0.104c 01 21 0. , 132fc 01 0.742E 00 0.436E 01 22 0. .100E 01 O.OOOE 00 o.ooot 00 23 0. . 3 (i 7 E ul G.l^OE- -01 -0.360E 01 24 0. looe 01 0.2 70E--CI 0.100E 01 25 A c D G"*OUP 0.100E 01 O.OOOE 00 O.OCOE 00 10 0.100E 01 O.OOOE 00 O.WOE 00 11 0.fer>4E 00 0.369E 00 0.178E 01 12 0-nvjE Ou 0.b07E no 0.20SE 01 13 ri.iWoc uo 0.1/9E 00 0.167E 01 14 0.«>-'Ofc 00 0.443E JO 0.223E 01 IS O.SvJ(.E 00 0.6S3E 00 0.272E 01 1ft O.'JHt 00 O.S09E 00 0.26BE 01 17 0.luoE ol 0.B06E 00 0.340E 01 IP 0.1OOE 01 0.3U0E- -02 -0.77-iF Ob 10 0.S17F 00 0. 141E--01 0.112E ol 20 0 . 11 1 b ou 0.600E- -02 0.104E 01 21 0. llJhc 01 0.792E 00 0.398E 01 22 0.100E 01 o.oooe ou O.OOOE 00 23 0.387E 01 0.160E- -Ul -0.360E 01 24 0.100E 01 0.£70E- •ul U.100E 01 Zb - 40 PO 242 ENDF/B-Itt SHI6L01NG FACTOflS FOK CWTUkt X-S6CT10N 300. KELVIN 4 c 0 G»nup 0. . louE 01 n.ouof 00 o.nooE 00 m 0 . 1OOE 01 D.OOOt 00 o.onoE 00 11 0 .928E oo O.'./DE no 0.169E 01 12 u .96*E OU O.ftdMfc 00 O.l'jfE 01 13 0, .'(?dk no n.?i2E oo 0.167P 01 14 0. . 102E OL O.rt'JhE 00 0.236E 01 IS 0. .lct>r Jl A c D GROUP 0, . 100E 01 O-OOO-: 00 0.000c 00 in 0, .100E 01 0.0006 00 O.OOOE 00 11 0. ,90faE 00 0. 3>4t 00 0.1S4E 01 12 0, ,921F 00 ().'>!?{ 00 0.178E 01 13 0, ,fWiE 00 0.577E 00 O.lblE Ul 14 0, .11 )c 00 0.7S3C 00 0.2O8E 01 15 0. • lUbc 01 0.R74E 00 0.2426 01 16 u.,9fi2 E 00 0.923E 00 0.2<>4t 01 17 0. , Hue 01 0.963E 00 0.321E 01 1H 0. ,Hb()E 00 0.793E 00 O.H.BE 01 19 0. ,.><-U 00 0./4Sf- -01 0.1l?E 01 20 0, .nlit 00 0.653E- -01 0.123E 01 ?1 0. ,luut 01 0.9t)l£ 00 0.396E 01 22 0. , bt>3t 00 0.48U- -01 0.178E 01 23 0. , 19S6 01 0.3416- -01 0.654E 00 24 0. , tit fit 00 0.650E- -01 0.K.2L- 01 25