Adjoint Sn calculations of coupled neutron and gamma-ray transport through concrete slabs

NUCLEAR ENGINEERING AND DESIGN 15 (1971) 319-343. NORTH-HOLLAND PUIiLISltlNG COMPANY

ADJOINT

S n CALCULATIONS TRANSPORT

OF COUPLED THROUGH

NEUTRON

CONCRETE

AND GAMMA-RAY

SLABS*

R. W. ROUSSIN and F. A. R. SCHMIDT**

Radiation Shieldingln/ormation Center, Oak Ridge NationalLaboratory. Oak Ridge. Tennessee37830, USA Received 21 July 1970 The use of the discrete ordinates computer code ANISN to obtain solutions to the adjoint Boltlmann equatitm is discussed. These solutions allow the calculation of transmisssion factors which give the t~,ssuedose equivalent from particles transmitted through a concrete slab due to an incident source particle in a given energy-angle bin. A coupled set of multigroup (22 neutron, 18 gamma-ray) cross sections allowed the consideration of primary neulron, secondary gamma-ray, and primary gamma-ray transport. Tables of transmission factors are presented which allow the calculation of dose equivalent transmission through concrete slabs from 15 to 200 cm thick for any arbitrary neutron or gamma-ray source energy and angular distribution. The use of these factors is illustrated and comparisons are made with other calculations.

1. I n t r o d u c t i o n

If we know ¢(T; z i, E,/a), the fluence emerging from the right surface, z 1, of a slab of thickness T, due to a radiation source incident on the opposite face, z o, we can calculate a "detector reading", D(z 1), by performing an integration as follows: co

D ( Z l ) =f 0

1

dE f dlaF(E,la)~o(T;Zl,E, la).

(1)

0

Here E refers to energy,/a to the direction cosine measured from the slab normal and F(E,t~) to a reaction cross section, detector response function or tluence-to-dose conversion factor, which may, in gel~eral, have angular as well as energy dependence. The purpose of this article is to provide calculational results which will allow the determination of

* Research sponsored by the U. S. Atomic Energy Commission under contract with the Union Carbide Corporation. ** Present address: Institut fiir Kernenergetik, Universit{it Stuttgart, Germany.

D ( Z l ) for a variety of source descriptions and slab thicknesses without having to determine ¢(T; ~;1, E.la) for each case. As will be shown later, this is done by solving the adjoint Boltzmann equation. These calculations were performed in conjunction with the preparation of a review by Schmidt [i ] for the Radiation Shielding Information Center (RSIC). A presentation of equations and background involved in applying the method is given in section 2. This is followed in section 3 with a discussion of the cross sections, conversion factors and oth,,'r data used in running the ANISN [2] discrete ordinates co,~v puter code to produce the desired results. These results are presented in section 4 and are compa~ed with other calculations in section 5.

2. Background information Hansen and Sandmeier [31 have ot, tlined melh~,ds of utilizing adjoint transport calculaliCms '-,r obtaining solutions to certain classes of neutron st:L,rce-det~'ctor problems. We apply these methods for the case of a concrete slab with infinite lateral dimensions and finite thickness. The only source of particles is

R. W. Roussin, F.A.R. Schmidt, Neutron and gamma.ray trattsport through concrete slabs

320

assumed to be incident on the left boundary of the slab, z o , such that S(E, O) dE do = ¢(T; zo, E, O) × 0 dE d/a of them strike unit area of the slab sarface. The quantity ¢(T, z o, E, ~) represents the differential particle fluence incident on the slab surface. Particles entering the slab induce interactions such that the total number of reactions, R, taking place in some volume, V, inside the slab is given by

oo

1

R=fazf f do ¢(T, z, E, O) F(E). V 0 -1

(2)

Here F(E) is a reaction cross section (or detector response). In this case it is assumed to be space and angle independent. If an adjoint calculation is performca in which the adjoint volume source in V is F(E), then, as shown by Hansen and Sandmeier, R may also be calculated from oo

o

~,,

,Zo,E,o.lP

1

0

X~

0

¢+(T;Zo,E,o ) .

(4)

Thus, once tp+(T; Zo, E, O) has been calculated for a given adjoint volume source F(E) and slab thickness T, it can be used in eq. (4) to compute the desired detector reading, D(Zl) , for any arbitrary source, S(E, O) = ~#(T; Zo, E,/a)/a. In the terminology of the discrete ordinates method, eq. (4) is approximated by a double summation over energy and angle as 1 D(Zl) "~ ~ z ~

~ ' i wl'~(r;zo, Ei, o/)

E i •1 X

1

R--f

R

~A7 -Az. f dE f d#~o(T;Zo,E,o )

O(Zl)

E, O)

o

(3) The quantity ¢+(T:z o,E,~) is denoted in [3] as the "source effectiveness distribution". Specifically, ¢+( T: z, E. p) is tha! ,unction which satisfies the adjoint transport equation with volume source term F(E) in V and the boundary condition that ¢+(T; z o , l:', ta) = 0 for p < 0. Hence, the integration in eq. (3) is for positive p only. From eq. (2), we see that R is essentially a "detector reading", D(z), integrated over a volume, V. which for slab geometry can be denoted as &z. lhere is some coordinate Z- in ~z such that

Oj¢+(T;zo,Ei, oj).

(5)

In the above, subscripts i and j refer to the i-th energy group and/-th cosine interval, respectively. The quantity ~0+(T; Zo, Ei, Oj) is the result of the discrete ordinates solution of the adjoint transport equation at position Zo, for the i-th energy group and j-th direction. The quantity w/is the weight associated with the j-th cosine in a Gauss - Legendre approximation to integration over 0, and AE i is the width of the i-th energy group. Thus ~0(T; Zo, El, oil la/AE i wj is the total number of source particles incident on the slab per cm 2 in the i-th group and j-th cosine interval. If we define r(T;

Ei,/all = ~o+(T ;Zo, lz"i, laj)/Ar

(6)

then eq. (5) for computing the detector readirg, such as dose equivalent, may be expressed as

D(z i ) ~ ~ ~ #j ¢ ( r ; z e , ~., U/) R = f D ( z ) dz = D ( z ) A z , Az where DCz-) is the detector reading evaluated at position Z in 2~z. Now, if Az is a very small inteJval near the right boundary, then D(z I ) Az should be very nearly equal to D(ZJ ~ and to R. Hence the quantity of interest D(z I ), may be approximated as

E.

×

%.

L'.,

(7)

in which r(T;Ei, Isj) may be intt rpreted as a transmission factor giving the dose equivalent transmits,.: d through a slab of thickness T due to one partic!e incident on the surface i~ the i-th energy group and j-th cosine interval.

R. W. Roussin, F.A.R. Schmidt, Neutron and ganlma-rav, transport through concrete slahs 3. C o u p l e d n e u t r o n a n d g a m m a - r a y a d j o i n t c a l c u l a t i o n s with ANISN

T h e discrete o r d i n a t e s code A N I S N [21 was used to c o m p u t e ¢ ( T ; z o , E i, lai). Calculations were perf o r m e d for the 22 n e u t r o n and 18 g a m m a - r a y groups w h o s e energy b o u n d a r i e s are given in tables 1 and 2, respectively. The cross sections used were based on a i 22-group c o u p l e d (104 n e u t r o n , 18 g a m m a - r a y ) set which is available at present as D L C - 9 / F A R S f r o m the Radiation Shielding I n f o r m a t i o n Center at O a k Ridge Table 1 Upper boundaries of the 22 neutron energy group scts, fluence-to-tissue dose equivalent factors, and total cross sections for TSF concrete. Group no.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Upper energy (MeV)

Tissue dose equivalent factors [rem/(n/cm 2) I

Total cross section b tcm-- l )

15.0 12.2 10.0 8,19 6.36 4.97 4.07 3.01 2.46 2.35 1.826 1.108 0.55 0.1 ! 1 3.35 1--3) a 5.83 (--4) 1.01 ( - 4 ) 2.9 ( - 5 ) 1.067 t - 5 ) 3.059 ( - 6 ) 1.125 {-61 4.14 I - 7 ) (thermal)

5.640 ( - 8 ) 4.580 ( - 8 ) 4.1601-81 4.105 1-81 3.882 1-81 3.720 (-81 3.607 ( - 8 ) 3.509 ( - 8 ) 3.500 ( - 8 ) 3.549 (-81 3.667/-81 3.143 (-81 1.591 ( - 8 ) 3.548 1-9) i.224 1-9) 1.306 (-91 1.336 ( - 9 ) 1.270 ( - 9 ) 1.222 (-.9) 1.186 (- 9) 1.155 (-9} 1.040 t-91

0.1150 0.1186 0.1119 0.1160 0.1255 O. 1512 0.1992 0.1485 0.1158 0.1658 0.2101 0 2870 0,3796 0.4046 0.4388 0.4430 0.4451 0.4458 0.4466 0.4475 0.4485 0.6244

a Read 3.53 X 10 ' 3 . b These were used for the adjoint cz,iculations whict, considered neutron transport only. The collapsed set used in neutron plus secondary gamma-ray calculations had values of 0.3788 and 0.4061 for groups 13 and 14, respectively. The different values arise because collapsing from 104 gr,,aps was done with a different weighting function.

.,_"~ F

Table 2 Gamma-ray energy group structure fluence-to-,is_,,ue do,,c v,m. version factors and total cross section for ] S l concrete Group no.

Upper energy (MeVI

Dose factor,, [ rad/~ 2,, cm - I

lt,tal . r,,'., ,,ec,.,a, I

1 2 3 4 5 6 7 8 9 I0 II 12 13 14 15 16 17 18

10.0 8.0 6.5 5.0 4.o 3.11 2.5 2.o 1.66 133 1.0 0.8 0.6 0.4 0.3 0.2 0.1 0.05 to 0.02

2.42 2.117 1.76

91a 9) 91

1.495 !,27 1.118 9.45

9I 9)

7.22 6.25

Io~ I(~J 1(1~ Ill) I~)) 10) -I01 10; • 11 101

5.05

4.25 3.25 2.41 1.75 i.16 7.64 1.22

9)

IO)

5.48 I 2 ~ 584~ 2~ 6.3hl 2~ 2~ "v.8S 2~ y;.', ?. 2~ 9 7 ~ 2} ]( , t~ 1D' 1.37 I, I;5 I ! 1.:'5 2.O3 t I 2.35 2.1% t~ I 3.394 I I 6.{/8 3.54

a Read 2.42 X 10-9.

National l . a b o r a t o r y . Being " c o u p l e d " means that second~ary ganuna rays p r o d u c e d by neulron inletactions a p p e a r as sources m tile ganlma ray groups through the g r o u p - t o - g r o u p transfer matrix. -file library is described m o r e fully in [I !. An i m p o r t a n t feature is the n e u t r o n g r o u p strt)clure which was designed by Straker 141 to describe well )he o x y g e n total cross.section valley near 2.37 MeV which is very i m p o r t a n t for tran.,port in malerials o f high o x y g e n COlitent. T h e c o m p o s i t i o n assumed for the slabs is thai of T o w e r Shielding Facility ( T S F ) concrelc and is gisen in table 3. T w o sets o f c,dculalions were p c r f t u m c d for seven different slab tllicknesses. T h e first set used as the adjmnt voh~l)lc source, F ( E ) , tile S n y d c r - N e u f e i d 151 neutrtm lhtc,lcc-l~,.d,,,c equivalent conversion (actors tt,r the ,,el.tirol) g ~ m p , and the C h d b o r n e - T r u b e y [(~] g a m m a - r a y Ilucnce-l~,dose convers, ,n factors for the g a m m a - r a y gr,,,~ps. (It should be n o t e d that b o t h these respon';e ll,ncliol~ are based on the m a x i m u m tol:d dose in a 30 cm sial,

R.W. Roussin, F.A.R. Schmidt, Neutron and gamma.ray transport through concrete slabs

322

Table 3 Compositions assumed for various materials. Element TSF concrete

Type 3 concrete

It C O Mg AI Si K Ca Fe

8.50 a 20.50 35.50 1.86 0.60 1.70 11.30 0.19

12.50 5.90 42.10 . . 10.30 8.70 --

2.30

2.31

Density ig;cm3")

Spielberg soil

Spielberg soil

6.63 20.20 . . 1.75 5.70 0.38 0.52 0.52

15.30 46.40

1.00

2.30

4.01 13.10 0.87 1.20 1.20

a in units of 1021 atoms/era s. of tissue.) The neutron and gamma-ray fluence-to-dose conversion factors are shown in tables 1 and 2, respectively. If we now denote neutron group indices with subscript i and gamma-ray group indices with subscript g, the results of the above calculations may be mu:~e clearly Identified ' " as Ct+ (T; z o, E i ~i) and ¢~.( T: z o , E~, laj). The quantfly .~t (T; Zo, E i, pj) gives tile volume integrated total dose in the rightmost interval of a slab of thickness T from both neutrons ajtd secondary gamma rays due to one neutron per cm 2 incident on the left face in the i-th energy group and ]-th cosine interval, and ~PT(T; go, Eg, laj) gives the volume integrated gamma-ray dose equivalent in the rightmost interval of a slab of thickness T due to one gamma.ray incident per cm 2 on the left face in the g-th group and j.th cosine interval. The cross sections used for this set of calculations (neutron plus gammaray adjoint volume source) were produced by reducing the 122-group set mentioned above. Special routines were required in the ANISN code to implement the multigroup adjoint weighting techniques outlined by Mynatt and Engle [7]. The group structure was collapsed by weighting with results of an adjomt calculation for a 75-cm-thiek TSF concrete slab with the above adjoint source. Resulting values of to:~.al cros~ section for neutron and gamma-ray groups are given in tables 1 and 2 respectively. The second set of calculations was run to determine, for the neutron groups, the dose equivalent due .

+

+

.

only to neutrons. This was accomplished by using as an adjoint source the Sayder-Neufeld dose equivalent conversion factors for the neutron groups and zeros for the gamma-ray groups. The result is identified as Cr~(T; z o, E i, laj) which gives the neutron dose equi. valent in the rightmost interval o f a slab of thickness T d u e to one neutron incident per cm 2 o,a the left face in the i-th energy group and pth cosine i,~terval. Naturally, the results for all the gamma-ray groups are zero. The cross sections used were genera*ed by reducing the 122-group set by weighting with results of an adjoint calculation for a 75 cm thick concrete slab with the adjoint source specified above (neutron groups only). The resulting neutron group values for the total cross section of TSF concrete are siaown in table 1. For the thermal group, we assumed the neutrons follow a Maxwell-Boltzmann distribution with a mean temperature of 0.0253 eV. For concretes with low hydrogen content or strong absorption, this results in thermal cross sections which are too high. For either set o f adjoint runs, F ( E ) represt, nts the energy dependence of a distributed or volume source. This distributed source was specified as zero in all except the rightmost spatial interval. For the 15, 30, and 50 cm thick slabs, S16, P5 calculations were performed. For thicker slabs the order of scatter was changed to P8 to improve the gamma-ray group angular results for grazing i~.cidence. For each slab, the size o f the, rightmost interval was set at 0.001 cm. A mesh size of approximately 1.5 cm was used throughout the rest of the slab region for all ew:ept the two thickest cases. For the 150 and 200 cm slabs, a rnesh size of 0.75 cm was used Io help converge the thermal neutron group for runs where no gammaray dose factor adjoint sources were tlsed. The concrete composition used is given in table 3 under the heading TSF Concrete. By dividing the results ~- (T: z,,, E i, laj), ¢+n(T;zo,Ei, t~j),and ¢~(T:zo,Ee,,u/) by A7 = 0 . 0 u l . we obtain transmission fact~rs rt(T; E i, In/), rn(T; E i, laj), and z,r(T; ~g, ~j), rest otively (see eqs. (6) and ('7)).

4. Results obtained using the transmission factors Tables 7.1 through 7.7 list the values of tran~mis-

R.W. Roussin, F A.R. Schmidt, Neutron and gamma-rat transport tltrough concrete x'labs Table 4 Cosines and cosine interval widths for use with the transmission factors.

Table 5 Fraction of neutrons in each source group for :t fisqon source. Group

Direction 1 2 3 4 5 6 7 8

Cosine a

Weight b

0.9894 0.9446 0.8656 0.7554 0.6179 0.4580 0.2816 0.0950

.

.

.

.

.

.

.

.

.

S(/:" ) ,..5.t:" .

.

.

.

.

.

.

.

.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 through 22

0.0272 0.0622 0.0952 0.1246 0.1496 0.1692 0.1826 0.1894

a The cosine of the angle between seurca' particle direction and slab inner normal. b These numbers are twice as large as those used in ANISN because that code requires the sum of weights over all cosines, positive and negative, to be unity.

sion factors for n e u t r o n sources, each table containing data for a single slab thickness. The q u a n t i t y r t gives the total dose equivalent and r n the n e u t r o n dose equivalent only. T h e difference between the two is due to the c o n t r i b u t i o n o f secondary gamma rays. Tables 7.~ tb.rough 7.14 list the values o f r,t(T: Eg, lai). These give the gamma-ray dose equivalent due to p~lrnary gamma-ray sources. Dose-transmission " p r o b a b i l i t i e s " m a y be determined f r o m PT(Ei, l.tj) = laj r ( T ; E i, laj)/F(E i) where

323

.

.

.

.

.

.

.

.

.

.

.

.

F(Ei) are ,_~e fluence to dose equivalent factors given in tables 1 and 2 for n e u t r o n and gamma-ray groups, respectively. These "probabilities" are the dose for a slab o f thickness T per incident dose and are normalized t o unity for zero slab thickness. The transmission factors z ( T : E i. ta/) m a y be used to calculate the dose equivalent transmitted through a c o n c r e t e slab o f thickness T b y applying eq. 17). ()~e first must d e t e r m i n e the n u m b e r o f source particles which are in each energy and angular interval. This

Table 6 Comparison of forward and adjoint transmission results for neutrons at nearly normal incidence on TSI. concrete slabs. Source energy

Slab thick-

Neutron d~':;e equivalent [rem/(ri/cm2)l

heSS

12.2 to 15 MeV

Fission spectrum

Total dose equivalent [rem/tn/cm2)l ........................................

(cm)

Forward

Adjoint

Forward

Adjoint

15 75 100 200

3.04 (-8) a 4.661-10) 6.52(11) 1.67(-14)

3.06 1-8) 4.591--10) 6.341.-111 1.52(-14)

3.08 (--8) 5.061-101 7.51(- 111 3.34(-- 14)

3.101-81 5.01 ( 101 7 . 3 8 ( 111 3.26(14)

1.34 (-8)

1.35 ( - 8 )

1.36 ( 8 )

5.03 (-11) b 5.12 (--111 4.60 (_12)b 4.72 (-2) 3.89(-16)

4.99 (-11)

1.35 (--8) 6.92 (--I11 b 6.981--.11) 8.21 (-- 121b 8.27 (- 12) 4.381-15)

15 75 100 200

a Read 3.04 X 10 -8. b Results with fission-source-forward weighted cross sections.

.

0.o16 ( 2 ) 0.090 ( 2 ) O. 350~ -2~ 1.397 ~ 2~ 3.473 t 2~ 3.522 ( 2~ 10.778 ~ 2) 8.941 4 2J 2.330 ( 2~ 12.091 I 2) 21.913! 21 19.937 (- 21 13.605 ( 2 ) 1.557 ( 2~ 0.0

4.59 (--121 3.831-16)

696 ( - I11 8.31 ( -121 4.591-151

anJSLE , ANnL ~ ? ~LJ= 0.0~¢)~ ~U= O.~G~ 3.0~rc-OS }.OloP-On 2.&7~r-O~ 2.560~-0 g ?.&ogF-08 2.&qGF-OS ~.4~Or-O~ 2.&6?F-O£ 2.&AIF-O8 ?.4~-0 o 2.4~8~-08 2.407c-08 3.02]E-08 |.q~I:-08 ?.724P-08 ?.~q|~-OP 2.434F-08 ~.%|A~-OB I.O&OE-O9 I.~06E-08 |.~19E-08 1.273F-08 5.~83F-09 5.KO|F-OO 1.58gF-OO t.~08c-OO 6.|4=F-lO fi.9llF-IO ~.205E-I¢ ~.O&OF-|O ~.oI~-I0 A.76[P-[O &.%QGF-~O ~.&ABC-~O ~.2o7E-|0 4.156E-~0 ~.qOkF-|O ~.772E-10 ~.&?RE-IO ~.~06F-~O 2.P&AF-IO ?.7~9F-10 1.612F-10 1.563F-I0

A'JOl : % WU= 3 . 8 ~ h P.~qIF-O~ ?.¢20E-08 2.48)~-0~ 2.4~&F-08 ?.G)~r-O~ 2.~c-0~ 1.89~-08 7.|~7~-0~ 2.762F-08 1.805F-08 1.18&~-08 ~.07or-O~ ).372E-0 ~ ~.=||E-)O ~.77~E-I0 4.~q~F-IO 4.]OOE-|O ~.qoBF-lO 3.&~Oc-lO 3.094~-|0 2.55~F-10 I.&76F-IO

A%GLF ~ MU= 0.~550 ?.~66F-O8 7.~I~F-O~ ?.406F-OS 2.~6~F-08 ?.~2)~-08 ?.186E-08 1.759~-08 I.qROE-O~ 2.?&GE-OP ].551E-O@ 1.050¢-08 &.3RRF-O9 1.|99E-09 4.WBOE-[O &.~aOF-IO &.~?[E-IO ~.~-~0 ~.567E-I0 3,222F-10 ?.805~-10 ?.~O~E-IO 1.35Qc-I0

ANGLE 6 MU= 0.~5~0 2.017¢-0R ~.7~&F-08 1.7RSF-08 1.742E-08 1.707c-08 1.56?E-08 |.27~E-OS ~.&~E-08 |.E29F-O8 i.]I6E-O8 6. 7 9 1 ~ - O q 2.935E-Oq 8.330E-10 3.bgTE-lO 3.36&E-I0 3.|4|E-10 2.904E-[0 2.685E-|0 2.~06F-10 2.070E-10 1.GBO~-[O I.O&RF-IO

O.O ~ead 1 5

---&.14~-O7 x I~ ~

2.qOF-Oq---!.OlF-O~ t.OTC-OS---2.WOE-O~ ~,06E-OG---1.OTF-05 ~.12~-06---~.06F-0~

~NERGY GROUP (MFV) 1.27~ 0 1 - - - I . ~ 0 F 01 I.OOE O l - - - I . ~ 2 F Ot ~.I~F O 0 - - - I . O Q E Ol 6 . ) 6 F O 0 - - - Q . I ~ F O0 &=qTF 0 0 - - - 5 . ~ 8 E O0 07F 00---~.97F O0 ~ . 0 1 F O 0 - - - ~ . 0 7 E O0 ? . ~ 6 ~ O 0 - - - ~ . 0 1 F O0 2 .~ 5 E 0 0 - - - 2 , ~ 6 F On ~.8~ 0 0 - - - 2 . ~ 5 E O0 1 . t I F OO---I.~BF O0 5 . 5 0 F - O I - - - I . I I F O0 IolIF-OI---g.5OE-O] 3.~SF-O~---I.IIE-OI 5.~c-O~---~.?~E-O~

~NGL ¢ ! MtJ= O . ~ q ~ 3.0q6c-0~ ?.~08~-0~ 2.523E O~ 2.~78F-08 ?.469F-08 2.~1F-08 2.022F-08 ?.72~F-08 2.~3|E-08 I.q~BE-O8 /.31q~-08 5.917F-Oq 1.668E-09 ?.349F-10 ~.5~6E-~0 6.52BE-10 6.~77F-|0 o.3¢~F-10 ~.054E-I0 ~.~26~-10 A.qGtE-lO ~.18~E-10

AN~LF ? mU= 0 . 9 ~ 5 ~.077E-0~ 2.~F-O~ 2.~25E-08 2.~ROF-OR ?.~6~F-08 ~.~OqE-O~ 1 ,O R I E -O P 2.IqOE-O8 ?.~ItE-OR 1.89~E-08 1.277r-08 5.6?6E-Og I.SR~E-O~ 7.0gSE-IO 6.369c-10 6.~3E-lO ~.~q6E-tO ~.175E-10 ~.BQOF-IO 5.4~lE-lO 4.~12E-IO ~.tO2E-~O

ANGLF 3 MU= O . P 6 ~ 3,0~0E-08 2.~54E-08 2.~lOE-O~ 2.~B2P-08 ?.~31E-08 2.335E-08 I,R97E-O~ 2.llGE-08 2.359~-08 1.80~c-08 1.18~F-0~ 5.IISF-Og ~.~BF-OO 6.65~E-10 b. OS)E-IO 6.02~-|0 5.q75E-[O 5.85~E-10 5.571E-IO 5.l~TC-lO 4.5~7E-10 2.95~r-I0

ANGt c ~ mU= 0 . 7 ~ 0 ?.qO6E-08 P,4~OF-Oe ~.~3~F-08 ?.~82F-08 ?.332~-08 ?.t~E-OR 1o753F-08 t.qTgE-O8 ~.2~c-0~ t.~gE-O~ 1.0~OF-OR ~.~22E-09 l.?71E-OO 6.060E-10 5.60tF-lO 5.570E-10 5.5~0E-|0 g.~O~E-]O =.13~r-lO ~.752P-10 ~.t??E-IO 2.7~6E-I0

ANGLE 5 MU= 0 . 6 1 7 a 2.616E-08 ~.~ttF-08 2.230E-08 ~.I?OE-O~ 2.!08E-08 1.93~c-08 1.S~1F-O8 1.751F-08 ~.Ot~E-O6 1.~tGF-08 ~.7~2E-Oq 3.~B3E-O9 1.080E-09 5.354E-10 F.O32E-IO ~.qq8E-tO ~.9~8F-|0 ~.8BTE-IO 4.586P-tO ~.231E-10 ~.70[E-tO 2.~8~E-10

ANGLE 6 wU= 0 . 4 5 ~ 0 2.056F-08 1.7~7E-08 1.81~E-08 1,760E-08 t.TtSE-08 1,56~E-08 1,276E-08 1.~2~E-08 1.627¢-08 1.115E-08 6.800~-0~ 2.871E-09 8.92~E-10 ~.575E-10 ~.~59E-10 ~,325E-|0 4,27~F-10 ~.170F-IO 3.943E-[0 3.621E-10 3.150E-10 ?.176E-~0

SCALAR ADJ~INT 2.025E-08 1.7~2E-08 1.75bE-08 ].727E-08 1.718E-08 1.623E-08 |.5~5E-08 ~.4@~E-08 ].6~BE-O8 1.203E-O8 7.6~E-09 3.25[E-09 9.265E=I0 3.9#IE-~O 3.500E-~0 3.2goE-tO ~.O~E-|O 2.82gE-~0 2.5~6E-10 2.199E-10 1.Tg2E-|O 1.103E-10

ANGLF 7 MU= 0 . 2 ~ [ 6 |.329E-08 t.I9SE-08 1.236E-08 1.2[OE-O8 1.221E-08 1.153E-08 1,002E-08 1,065E-08 1.12t~-08 8,II3E-09 5.068E-0~ 2.206E-09 7.126E-10 3.737E-10 3.595E-IO 3.564E-10 3.516E-10 ~.~72E-10 3.224E-10 2,g42E-lO 2.515E-10 t.827E-IO

ANGLE fi MU= 0 . 0 9 5 0 8.071~-09 7.625E-09 7.816E-09 7.783E-07 8.132E-09 7.861E-09 7.35~F-09 7.5~2E-09 7.LI3E-09 5.597E-09 ~.Sq~E-09 1.605E-09 5.~54E-I0 2.863E-10 2.686E-~0 ~.65~E-lO 2.609E-[0 2.53~E-10 2.376E-|0 2.1~7F-I0 1.808E-IO 1,235E-10

SCALAR ADJOINT 2.06[E-08 |,773E-08 I.TB2E-08 1,74~E-08 I.725E-08 1.525E-08 1.3~6E-08 1.~85E-08 1.637E-08 1.202E-08 7.650E-09 ~.285E-09 9.86ZE-10 ~.829E-[0 4.503E-10 6,~72E-[0 ~.~2~E-IO 4.322E-10 4.0gZE-IO 3. TbbE-IO 3.2~9E-10 2.~OE-|O

15 CM TSF CONCRETE SLAB

ANGLE g MU= O.Og50 7.819E-09 7.&O.E-09 7.6]OE-Oq 7.662~-09 B.OB)E-09 7.846E-09 7.3~BE-Og 7.553E-09 7.~17E-09 5.600E-Oq ~.583E-09 I.SBOE-09 5.070E-10 2.29B~-|0 2.0~5E-[0 1.956E-|0 [.80~E-~O 1.655E-~0 1.47|E-10 [.2~5E-[0 q.803E-11 7.173E-11

I = Cq TSF COnCrETE SLAB

ANGLF 7 MU= O.2el~ 1.295E-08 ~.[66E-08 1.211E-08 1.194F-08 ).214E-08 I.ISIE-08 |.002E-08 ~.0~5E-|)8 I.I22E--O8 8.IZOE-Oq ~.0~6E-09 2.17&E-09 6.625E-I0 ).O0|E-[O 2.758E-10 2.567E-10 ?.~66E-|0 2.180E-I0 1.9~5E-10 1.659E-IO I.~OE-IO 8.633E-11

'I~ITP)% [+~5F FQJIVALFNT NFUTPFN ) l ( C M i = ' ) | )

ANGL~ 5 MU= 0.617q P.~73E-Og 2.[76~-0g 2.?00~-08 2.]51F-08 2.100~-08 I.qB~F-OP 1.5~0~-08 ~.7~2~-08 ?.OIRF-OP I.~tBE-O8 8.737~-0 o ~oRq~-O9 |.O]BE-D ° ~.362E-~0 ?.?|2~-10 ~.663F-|0 3.~qBE-|O 9.[5~E-IO 2.937E-10 2.~57F-10 ?.OlOE-IO I.?14F-IO

T:'~%C-*I£
FN~:RGY AND A~"GUL^R I)EPFND~NT T;'~NSWISSIBN '=ACTORS N~IJTRON PLUS GAMMA-RAY DOSE FC)UIVALF~T N;JTRON GROUPS (RE'wS/((SOUPCE NFUTRPN )/(CM~'.'21))

FWrOGy Cp (IUP (MEV) 1.22F 0 1 - - - 1 . g O F ol I.OOF 0 1 - - - 1 . 2 2 F Ol 9 . t q F O0---I.OOE 01 ~.~GF O 0 - - - ~ . l O F O0 4.07F O 0 - - - ~ . ~ G F O0 ~.9"~F 0 0 - - - 4 . q 7 ~ no ~.01~ 0 0 - - - 4 . 0 7 F CO ?.&GF O 0 - - - ~ . O I F O0 ?.3 ~c 00---2.¢,6F O0 I . Q " F 00---2.~'5E o o 1.11F 0 0 - - - ] . ~ : O0 5 . 5 0 F - 0 1 - - - ] . I | E O0 I. l IF-OI---5.50F-Ol 3. ~ S F - O ' ~ - - - I . I 1 F-Ol 5 . 9 3 E - 0 4 - - - 3. ~ K F - O ~ '~. 0 1 C - 0 ~ - - - ~ . 8 3 E - 0 ~ 2. o O E - O ~ - - - 1 . O l F - O ~ I . O?F-O'~---2.qO~-O~ .06E-OG---I.O7E-O~ 1.12c-06---% 06E-06 ,:,. 1 ~ F - 0 7 - - - I . 12E-06 o.0 ---6.1&E-07

F~IFcf-,y &,.,.r~ '~N,.,'~[ #r

%

~j

q

!

4-

Ol Ol O! O0 O0 00 O0

1.053~-10 °,2lbF-ll 8.O~F-II 7.2S*F-II ~,381E-11 ~.~25E-II ~.&IOE-II 9.6~IC-II

1.091~-10 o.5~E-II R.38TE-]I 7,531F-II 6.628F-11 5.6&IC-ll A,589E-ll 2.¢60F.11

ANGLE | MU= O . q ~ 4 1.24~E-0~ Ol 1.045F-OR Ol 1o057E-08 Ol !*02RE--OR O0 l.O|9~--OB O0 goO52E--09 O0 6.06~E-Oq O0 7.20|~-09 O0 ~.72¢E-09 O0 ~.905E-09 O0 =.310E-Oq O0 7.~-;0 2.~¢8F-10 !.llP-Ol---S.5Of-Ol 2.3~1F-10 ],3S~-O3---I.IIE-OI ?.~SF-lO 2,271~_I0 ?.t55F-IO ?.qOF-OS---I,OIE-04 ~.o~-to 1.07F-05---?.90~-O~ l.RqTc-lO ~.05E-O6---I.OTF-O~ 1.~lO~-lO t,l?r-O6---3.O6F-06 1.672E-10 4.16F-07---|.|2~-0~ ~.InO~-ll 0.0 ---~.14F-07

: , . . ~,~

~. ~

x

l~ '

FNFRGY GPOUP |MFV) 1 . 2 7 E 01. . . . . 1.50E 1.00 ~ Ol---!.?2E 8.19~ O0---I.OOE 8.3~¢ O0---~.I~E 6.O7F 00---6.36F ~,O?r 00------6.q7¢ 3.OlE 00---6.07¢ 2.66E O0---%OIE 2. 35 E 0 0 - - - 2 . ~ 6 E I.~3F 00---2,~5E 1.11~ 00---1.83E

9.88?E-l! 8.b37E-11 7,~67E-ll 6.782~-11 5.95BE-If 5.057~-!I ~.IO~E-ll 2,3~5E-I!

ANGLE ~ MU= 0 , 8 6 ~ 6 I.052F-08 ~,P75E-09 O.IOOE-Oq P.BT~F-Oq 8.RO~E-Og 7.~14¢-0q 5,164F-Og 6,0~3E-Oq 7.31?E-Oq ~.9~2E-Oq ].7~3E-Oq 5,053E-I0 1.605~-!0

-

q,oo6E-ll 7.85qE-11 6.873F-11 6,15IE-tl 5.~q~F-I1 ~.5b~E-ll 3.696~-lI 2.157~-II

~NGL = ~ ~U = 0 . 7 ~ 5 0 ~,go~E-Oq T.SRl~-Og 7.~33E-Oq 7,635F-09 7.593E-09 6o62g~-Oq ~.50gE-09 5,lSOE-Og 6,121F-09 3.2S?F-09 I.~E-Oq ~.316F-10 1,~43E-10

:

7.953E-11 6.q~lE-ll ~.O~OE-II 5,~0~E-11 4.728E-II ~.oR~-ll 3.215E-11 l,O2~C-ll

b.7R1E-I1 5.90IE-II S,I~OE-II 4,580E-II s,qocE-II 3,35~E-11 2.685E-II 1,665E-11

ANGLE & ANGLE ~ ~,J= 0 . 6 1 7 g MU= 0 , ~ 5 8 0 ~.RSgE-O q ~.O00E-O° 5.g6OE-Oq &.~2IE-Oq 6.186F-Oq ~.&6OE-O ° 6,056F-Oq ~.428E-0 ~ 6.103~-0q ~.588~-0 ~ ~,~T&E-O9 ~.132F-0 o 3.785E-09 3.072¢-0 ~ ~.I~TE-O@ ~.168E-Og 4.b75E-O0 ~.2~lE-Oq 2.525E-09 I.R6qE-O~ 1.15?F-Og 8.R3~E-IO 3.572E-10 2.877E-I0 1.260F-10 1.066E-I0

2.323=-I0 2.201=_i0 2.088E-I0 ~.992~-I0 1.836E-I0 1.655E-tO 1,42~E-10 q.882E-|l

ANGLE ? ~U= 0 . 9 4 4 6 1.187E-08 g.QROF-09 1.O!4E-08 g*~¢F--Oq g.?~?E--09 ~=605E--00 5.767E-~g 6. R2~F-OQ 8.273F-0O 4.~q~F-Oq ?.|54F-Oq 7.O00E-tO 2.823~-10 2.25qE-10

ANGLE 6 MU= 0 , 7 5 5 0 g,148E-Oq 7.7°5F-09 R'O~4~r'00 ?'78q~--09 7.703E--09 6°72~F'09 ~.bO2E-09 ~,765E-0 Q 6.2~3E-Oq 3o~84~-09 |.SR?F-Oq 5.503E-10 ?.~12E-iO l.qS~r-IO ?.lgSE-IO ?.OIqE-IO 2.079¢-I0 l.gll=-lO I.~?IE-IO I.~I0~-I0 l . RTO~-lO IoTISF-IO 1.731E-lO 1.5~6E-lO l.~5~F-lO I.~?~E-iO 1.3~qP-lO 1.223E-10 8.&48~-lI 7.R41E-II

ANGLE ~ MU= O . ~ 5 b lo07qE-Oq 9.102E-Oq 9.~1~-0 q q*O34F--Oq R*~IRE--OO 7"812E'0 ° 5.26tE-Og 6.161F-09 7,~44c-0q ~°ObR~-Oq 1,8q3F-Oq b.32|F-|O 2.6~6E-10 2.132F-10

ANGLE 5 ~U= 0 , 6 1 7 9 7,08~E-oq 6,155E-Oq bo~TOE--Oq 6*lOOE--OO 6,FO6E--O9 5,Ab3E--O~ ~.877F-00 ~,2~7E-OQ 4.RO~E-09 2,54BE-09 I.?TIF-OO ~,b~-tO ?.I]~F-IO 1°765F-10 1.~02~-I0 1.70&F-IO l.bl2F-IO 1.575~-I0 I.~ORF-IO 1.?~?~-!0 1.080F-IO 7.08IF-If

ANGLE 6 MU= O,~SBO ~.P92F-Oq 4o488E-09 4 ,~ 1 9 E- - 0 9 ~.$~'--09 ~'68~--09 ~*212F--Oq 3,ISlE-O o 3o, 268E-Og 3.359E-09 |.980F-Oq g.RR&E-tO ~.BI|E-iO 1.820F-IO t.6OIF-IO Io551F-lO I°465E-I0 1.3~F-IO 1.307E-I0 1.304F-I0 1.075F-IO q.I~RE-I1 h.18?F-II

4,158E-11 ].610E-II 3.13~E-II ~.176E-II ~.403F-11 I.qR~E-II 1.5~8F-II I.O~3E-II

~NGLE 8 NU= 0 . 0 9 5 0 ~.076E-09 2.012E-Oq ~.025E-09 ~.OgOE-Oq 2.252E-09 2.063E-OQ 1.768E-09 1.671E-00 I.~9E-09 q.lq~E-lO ~.693E-I0 1.6~E-IO ~.~qSE-ll T,I&TE-1I B.230E-II S.43?E-II ~.854E-II 4.2~]E-II ~,571E-II Z.86SE-II 1,737E-II

SCALAR ADJOIN/ ~.gRIE-Oq S.2PRE-09 5.3~F-09 F.292E-Oq S.377E-Og 4.78~E-09 3.429~-09 ~.T28E-09 4,091E-09 2.~OOE-og 1.065Eo09 3.277E-10 1,139E-I0

ANGLF ? MU= O . Z 8 1 6 3.36qE-09 3.14gF-Oq 3 .1 0 ~ F- - 0 9 30208E--09 3.38~--09 ~ 'lO9 ~- - Oq 2.~F~E-09 2.~38F-09 ~.~2gE-og 1.435F-o9 7.;71E-10 3oOOBE-IO |.~9SF-IO I.?~IE-IO I,Z73E-IO 1.2~I~-I0 l.l~E-lO I.O~BE-IO 9.83qE-I! 6.TO3F-It 7.3~E-II 5.17~F-II

ANGLF 8 MU= O.Oq50 2.188E-09 2. l 1 3 F - O q 20120E--09 2,165E--09 2,307F--09 2.1l|~-nO l,@18E-Oq l.7~3~-Oq 1.420F-Og o.86~E-lO 5,3)2E-I0 2.209E-10 t.I~OE-IO q,304F-ll 9.623E-I1 g.07~-ll 8.~3E-II 8.03~E-It 7.~45F-11 ~.6~RF-ll 5.~5~E-ll ~,O0~E-II

SCALAR ADJ31NT 6o177E-09 5,~98E-Oq 5"5~5E'09 5.~[6F--09 5,657E--09 ~,858E-09 3.506E-Og ~,825E-09 4,20~E-09 ~.&O8E-09 l.t?OE-O9 ~,2~2f-tO t.92~E-tO t.5b7E-IO |.blTE-lO 1.62qE-10 I.~5E-IO 1.~67E-10 1.260F-I0 t.127E-IO q.bObE-lt 6onqOF-l[

30 CM TS~ CONCRETE SLAB

5.5~2E-11 ~.TqOE-ll ~.ITIF-I! 3,TOTE-If ~.~2E-ll 2.b~SF-II 2.126~-II I.~7~E-II

ANGLP 7 MU= 0 ° 2 ~ 1 ~ 3.216E-09 3.013E-Oq 3.0bSE-OO 3.106E-Oq 3,30~E-09 3.0~4E-09 2.~O~rE-Og 2.)SiE-Oq 2.129E-09 1,3~F-O~ 6,606F-I0 2.~OE-IO 8.6~SF-ll

30 ~M TSF CONCRETE SLA~

T~ANSMIssIqN FACTORS ~¢(30;lli'u] NFUIRON PLUS GAWMA-RAY DOSE FQUIVALPNT NEUTRON GROUPS IREMSI|(SOURCE NEUTRON I / | ~ M ~ * ~ I ) )

ANGL~ 2 M3= 0 . 9 4 ~ 6 !.150E-09 q.746F-Oq g.99~-Oq q.~gOF-09 ~.632E-Oq 8.~06E-OO S.6bgF-09 ~.703E-Og ~,l~tE-Oq ~.~SRF-09 ?.014E-09 ~.676E-I0 1.732E-I0

ANGLE 1 MU= O . q q o ~ I.?17F-9~ 1.02!E-O~ 1.03~E-O~ !.Ol?F-O~ 1.o08r~OR R.q6~E-oq 5.g~SF-Oq 7.080~-0q q. SQSE-09 4.767F-09 2.1~=-Oq 6.070E-IO 1.808~oI0

FNFR5Y AND ANGULAR D E P F N q E N T

1.01F-O~---5.8~E-O~ ~.qOF-O~---1.01F-04 !oO?E-OS---2.~OE-O~ ?.06c-0~---1.07F-0 = I.I2F-O~---~.O6F-O~ 4.14F-OT---l.l?g-o6 0.0 ---6.14g-07

?.35E 00---?.6~ oo 1.83F 00---2.3~F ~0 1 . 1 1 ~ 0 0 - - - ! . ~ 3 ~ O0 5.gOF-O|---|.I!E O0 1.11E-01---5.¢0c-0! 3.35F-O~---1.11F-01

ENERGY GROU~ (MFV} 1.22F O I - - - I . 5 0 E I.OOF O l - - - l . ? ? r q . 1 0 ~ O0---l.OOE ~ , ~ 6 ¢ 0 0 - - - ~ . 1 9c 4.07F 0 0 - - - 6 . 3 6 E ~.OT~ O0----&.qTE ~.OIF O0---~.07F

•

~ (30,E.,~.) NEUTRON DOSE EQUIVALENT ENERGY aND ~N~UL~ DEPENDENT TaANSMISSION FACTOQS NELFrRON GgOUoS ~PFMS/(ISOU~CE NEUTRON } / ( C M t t 2 } I |

TA~LK 7 2 NEUTRON :;~OIJY TPANSMIS!~ION FACTORS FCF A 30 CM TSF C?NCPET~ bLAB

*j,

R

.=

.~

AND

~

.

.

.

.

.

.

ANGLE ~ H~= o . q ~ 4 b 2oT~6E-og 9.75~E-09 ~o3~8c-0q Z.~|OF-Og 2.19q~-09 |.625E-0~ 8.438E-|0 l.O&&E-Oq l.&ISE-09 ~.9|?~-10 1.S27~-10 ~.88gE-ll 1.604F-ll I.IOSE-II l.O06E-ll q.SElE-12 7.3~qE-[? 6,5~6E-12 5.7~2F-12 4.856E-12 3.?&2E-12 2.217E-12 |.~0°F-09 2~OZ?F-Oq |.966[-0. |.BR6E-O~ ].40&E-09 7.50TP-lO 8,ql~F-lO l.l~7~-Oq 4.092F-lO 1.30OE-lO 3.52~-11 1.4q5F-11 I.O~SE-I! 9.410E-12 7.qngE-12 6,87qE-]2 6,|l~F-I? 5.~&gE-|2 4.526F-12 3.669E-|2 2.095E-12

2.~12~-0 o

~NGLF ~ MU= 0 . ~ 5 5 6

ANGLE & NU= 0 . 7 5 5 0 ].778F-0 o [°4q&E-OQ [.57¢F-0 n |.547F-09 1.508P-09 |,|AB~-O o ~.~q~F-[O 7.15IE-IO R.E13~-IO ~.182F-10 1.06~F-lO ~.O~OE-tl l.~5~E-ll 9.356F-1~ 8.546E-12 7.762F-12 6.240E-|2 5.542E-|2 4.841E-12 4,0S6E-12 ~°~04E-12 1.qZ7~-12

:

~!

~ A

2,~00E-12 I.A~BE-IZ

2.99qF-|2

A'~St ~ h MU = O , ~ S P O 8.a24~-|0 7.7|2~--I0 7. P 4 7 ~ - 1 0 8,048F-|0 R.?~SF-IO 6.~7~F-]0 A.29~F-lO ~.067~-10 ~.601F-10 1.70~F-IO b.~TF-11 2.141F-11 l.OOTr-ll 6.977E-12 6.~9oE-|? 5.~31E-12 4.656E-17 6.121E-12 ~,~82E-12

*Read 1.5 x 101

ANSLE I ENERGY MU= 0.98q4 GROUP l~EVl 3.167F-09 1.22E 0 1 - - - I . 5 0 E 01 2.588E-OW I.OOE 0 1 - - - 1 . 2 2 E O1 Z.T~E-09 B. lqE 0 0 - - - 1 . 0 0 ~ 01 2o626E-09 6.$6E 0 0 - - - 8 . 1 9 E O0 2.48SE-09 ~.BT~ 00~-6.36E 00 I.857E-09 4.07E 00-°-~.97E O0 g.868~-|0 3,01E 00---4.07E 00 1.248F-09 2 . 4 6 E 00 - - ~ , O I E 00 1.708E-Oq 2.35E 0 0 - - - 2 . 4 6 E 00 6.~10E-10 1,83E 0 0 - - - 2 . 3 S E 00 2.513E-10 1.11~ 0 0 - - - 1 . 8 3 E 00 1.01~E-10 5 . 5 0 F - O l - - - 1 . 1 1 E 00 5.705E-11 I.IIE-0I---S.50E-01 4,806E-11 ~.35E-O~---I.IIE-OI 4.796E-II 5.~SE-04---3.35E-0~ 4.450E-|I |°OIE-O4---5.83E-04 4.159F-11 2°90E-OE---loO|E-04 ~.917E-11 !,OTF-OE---2.90E-05 ~.611E-11 ~.06E-06---I.07E-0~ ~.243E-II |.12E-O6---~.O6E-06 2.78bE-!I 4,14E-OT---1.12E-06 1.729E-tl ~0 ---4.|&F-07

~NGLE ? MU= 0.94~5 2.8~0E-09 2,~7~E-0 o 2.509F-Og 2°41~E-09 2.S91E-Og l.717E-Oq g. s o l F o | O 1.149E-09 I°5#~E-09 5,94~E-~0 2.~41E-I0 q.7?lE-11 5.51'T-II 4.651E-II 4.642E-II ~.309E-1! 4.026E-II 3.7q2E-II 3.495~-11 3.137E-11 2.Bq5E-II 1.68~E-II

ANGLF 3 ~U= 0.8656 2.438F-09 2.021F-Oq 2.136E-Og 2.064E-09 |ogT~F-09 1.493E-Og 8.310F-|0 q.91q~-lO I.277c-09 5.066E-10 2.075E-I0 q.Ol7E-l! 5.198F-I1 4.38ZE-II ~,~79E-11 4.06~F-11 3.796~-11 3.~73F-11 ~.292E-11 2.q53E-ll 2.5~5E-II 1.601~-11

ANGLE 4 ~U= 0.7550 ]-BglE-Oq 1.596F-Oq 1.67gF-Oq 1.636E-09 1.S90F-Oq ~.Z~4E-Og T,I4[E-IO 8.07qE-~O q,520E-lO 6.0TSE-[O 1.767E-I0 8,107E-11 4.762E-tl 4.017~-11 4.018E-11 ~.7~8F-11 3.481E-11 3.27~E-11 ~.014~-11 2.700~-11 ~.315F-11 !.486~-11

ANGLF 5 MU= 0.617q I,~62E-Og |.181~-09 |,226E-Oq |,2|6E-09 |.208E-Oq 9.565~-I0 5°q~IE-lO 6.296E-10 6.670~-|0 ~.|45E-I0 l.&Eq~-lO ~.061E-11 4.233~-11 9.572E-ll 3.576E-1~ 3.~ITF-II 3.095E-11 ?.~oqF-ll 2.674E-11 2,~91E-11 2.045E-II 1.343~-11

ANGLE 6 NU= 0.4580 9.426E-I0 e.445E-10 8.~q7E-[O 8,7||E-i0 8°848E-I0 7o190E-|0 4.787E-|0 4.771E-10 ~,&IqE-|O 2.362E-I0 1.170E-10 5.q~SE-11 3.6~2E-1! ~.064F-11 3.071E-II 2.848F-II 2.655E-11 2.~qZF-ll 2.28bE-11 2.037E-II 1.7~4E-ll l.lT4E-11

S~L~= ADJO[NT I.~OBE-09 ].0~E-09 1.076E-09 1.073E-09 ].0SoE-09 R.I~-IO &.8~IE-IO F.141E-10 5.610E-lO 2.255E-10 7.890E-11 2.~b8E-ll 1.070E-II T.399E-12 6,769E-12 5.7~8E-12 4.g33E-12 4.371£-12 ~.807E-|2 9,195E-|~ 2.SbIE-|Z 1.552E-12

ANGLF 7 MU= 0.2816 6,&3OE-IO 5.q49F-10 t.gStE-lO 6.152E-I0 6.~13E-10 5.ZO|F-|O 3.741E-I0 ~,S~OE-IO 2,889E-~0 |.725E-10 q.O41E-ll &.T57E-ll 2.q76E-II 2.50qE-II 2.516E-I1 2.332E-11 2.171E-ll 2.0~4F-I1 !.861F-11 1.64qF-ll l.SqlE-ll q. R I 8 F - I 2

ANGLE 8 MU= 0.0950 4.218E-I0 4.024E-|0 3.983E-I0 4.|86E-I0 4-284~-I0 3.506E-I~ 2.7495-10 2.497E-10 ~.820E-10 |.188E-10 6,507E-II 3.514E-11 2,251E-11 1.895E-II 1.q01E-ll 1.7~IF-II 1.637E-II 1.530E-11 1.~95E-ll 1.22~E-~l l.Ol5E-11 T.611~-12

SCALAR ADJOINT 1,29~E-09 |.114E-09 ].tSbE-09 |.IWSE-09 I.IZ~E-09 S=78|E-|O 5°~28E-|0 5.871E-I0 6,~5~E-10 2.94TE-I0 1.336E-I0 6.~4~E-I1 ~.804E-ll 3,208E-II ~.2IIE-II ?.qT8E-ll 2.777E-II 2.609E-II 2.395E-11 2.136E-II 1.819E-II 1.212E-II

~0 CM TSF CONCRETE 5LAB

A:~StP ~ MU = O . O g ~ O ~.773E-I0 3.b05~-|0 ~o~63E-I0 ~,815E-|0 3.°3TE-|O 5.I~gF-IO 2.~q4E-lO 2.0RSE-10 1,3qOE-tO 8.154E-11 3.~76E-II 1.238F-11 6.15qE-12 4.2~8E-12 9.911E-12 3.316E-12 2.8~4E-12 ?.496E-12 2.!S~E-12 |.TT4E-12 1.375E-12 q.~IOE-13

<,0 C'a 7':,F rr)~,~('wET- C L ~

A'~Gt P 7 MU = 0 . 2 8 1 6 5,80SE-I0 ~.~bBE-|O 5,353~-|0 5.b~O~-lO 5.92~F-10 4.71|F-|0 3.257E-10 2.q65F-lO 2.25qF-10 1.204E-10 &.~BlE-II 1.687E-11 8.17qE-12 5.~6~E-12 5.200E-t? 4.411F-12 3.776E-I2 3°33&E-I~ 2.88RF-12 2.402E-12 1.900E--|2 t.2?OE-12

~!F.ITOFS~I F)n~ C~!!IVAL~:HT ,'lctllCF~.~'~ | / ( ( ~ ' ~ 9 ) | )

.

tHCLF £ MU = O . ~ l T q 1.265F-0o |.O~--OQ |.|~6F-Oq I.[37E-09 |.|36F-09 8.~7~-10 5.261E-10 5,470E-10 5.68qF-10 ?.]EqE-lO 8.426E-11 2.bOqF-1| I.IBTF-II 8.221F-12 7.525F-12 6.)qlE-12 ~.485c-12 4.865E-|2 &.Z&IF-12 ~.567~-12 2.874E-12 |.72~E-12

:

ENERGY AND ANGULAR DEPENDENT TRANSMISS|Cq CACTORS ~NCUTRON PLUS GAWMA-RAY DOSE FOUIVALffNT NEUTRON GROUPS (REMS/||SO'JRCE NEUTRO~ ) / ( C M * * 2 ) | ;

ANGLE I MU= O . q B q 4 ~.027F-09 2.46&E-0~ 2.60q[-09 2.5|9~-09 2.SqlE-Og 1.762E-09 g.02~E-tO I.I40F-O~ 1.580E-Og ~°~47E-I0 1.672E-10 4,1IWE-~I 1.66BE-ll 1.148E-ll 1.044E-II B.876F-|2 7.6~0E-~2 6.800E-12 5.g~6F-12 ~.051E-12 4.I03E-12 2.287E-12

~J FACTOpq &'~'G[ILA° DF pc Nr)E~! T~ %~%~4I r.,SI. ~!JTPCI~ G-r)LIpS ( R C u ( / ( ( S f ' J [ ' ( "c

EI;FRGY G~OUP (M~V) 1.22E O I - - - I . ~ O P CI |.OOF 0 1 - - - 1 . 2 2 F O1 B.tqE 00---1.00F 01 6.36E 0 0 - - - 8 . l q E oo 4.97F 00---6.36E OO 4o07E O 0 - - - ~ , q T E 00 ~.O|E 00---4.07F 00 2.46E 00---3,01E 00 2 . 3 5 E 0 0 ~ - - 2 . ~ 6 E O0 1.BSE 0 0 - - - 2 , 3 5 E 00 I.llE O 0 - - - 1 . ~ 3 E 00 5.50E-OI---t.11E O0 1.llE-OI---5.50E-OI 3.35E-O~---I.IIE-Ol 5.83E-0~---3.35E-03 1.0tE-O4---5.B3F-04 2.90E-05---l.01E-04 1.07E-OE---2.qOE-05 3.06E-06---l.0TE-05 I.lZE-06---3.06E-06 4.14E-0T---I.lZE-06 0.0 ---4.14E-07

ENFRGY

•

9

.%

P~

>=

% ..%

o~

ej,

ANGLE ? wU= O . q ~ 6 6,009~-10 3,113E-10 g.66?E-lO 3.2~F-10 ~.~SqC-lO 1.650~-10 6.~q6F-11 O.40qF-II I.~q!F-IO ~,655E-1! 6.408E-17 1.ql~F-12 8.020c-13 ~,45~E-~ a.OOOF-13 6.lg~F-l~ ~.~70F-13 x.177g-l~ ~.7~-1~ ?.xhOr-13 l.c17E-13 1.07qF-1~

ANGLE ~ ~U= 0 . 0 6 ~ 6 3.1q6F-lO 2.~85E-10 2.72q¢-10 2.6?qE-lO ?.3?7F-10 1,~75F-10 ~.797E-11 b.qSOF-tI q.527F-ll 2.137F-11 5.510¢-12 1.~6~-!? 7.a73F-13 5.OqBg-13 4.g83;-13 3.4845-13 ~,~3~-13 2.q6~E-I~ ?.gqT;-l~ ?.19~¢-!3 1.~P~F-I~ 1.020¢-13

ANGLE 4 ~U~ 0 , ~ 5 0 ?.767E-10 1.826E-10 I.q61E-IO I.q0~F-IO !,,757E-10 1.076~-19 4.86TE-11 ~.3=1r-11 6.?18E-11 1.61~F-ll 4.53PF-12 I.~=?F-I? 6.75~r-13 4,616g-13 a,161F-13 q.g2~E-13 3,02~F-1~ 2.bgOF-13 2.~51¢-13 l.gBbF-13 1.607F-13 q.3~F-16

ANGLE 5 MU= 0 . 6 1 7 o 1.53&c-lO 1.274F-10 1.:31F-IO 1,356F-10 1.259E-]0 ~,021g-ll 3.956E-11 3.980E-11 3,750E-11 1.17~F-1I n.611F-13 1.261~-12 ~.O27E-13 q.052~-1 a 3.662F-1 g 3.10~r-13 2,~2E-13 2.361¢-13 2.060F-l? 1,736~-13 1.aaSF-I ~ B.~7~-14

ANGLE 6 MU = 6~80 l.r =-L~ 8.7,8E-11 8.8~0F-ll q.?qo~-ll 8.7~6E-11 ~.7~6c-11 3.1~1E-11 ?.gOOE-ll 2.218~-11 n.~70F-12 2.807E-12 1.022E-12 g. OlqF-13 ~.636~-1~ 3.113F-13 2,6~7C-13 2,2~F-13 ?.O01F-13 1.760F-13 1.4~-!~ 1.16~F-13 7.96gco16

7~

Ol O1 O! {'10 0(3 O0 O0 O0 O~ 30 0n 03

I. l"r-n~---~-O'r-O ~ e..tac-O7---1.l ?r-'wU.O - - - ~ * . I ~ - 2~

qor-Oc--~., ?.! v - q 4 ~.. ')7 c - O C - - - ? . ~C~r - n r

-~. - ~ = c - 0 ~ - - - 1 . I I r-~1 ¢.~e_OZ,--?.?~---r~

E~'cg GY GQOUP IM~V) 01---1,=OF 1.29F I .00F 0 1 - - - :.~2~ n.lqF 00---!. O0 r ~ . ~ 6 c 0 0 - - - S . 1 (~c 4.g7 c 00---6. "~h ~ ~ . 07c O 0 - - - & . q7~ -3.01 ¢ 03 .... ~.07c O0---~.Ol ~ ~ "J{¢p 0 0 - - - ? . ' ~ - " I , 8 ~ F 0 0 - - - 2 . ~=F t,1]c On---t.R~r *;. 50C- q l - - - ~.. I | ~

~.lOqr-l? g.lOPr-l? ~.~66c-12 ~.?~TC-l? ~.~gr-~

~.==l:-I ~ ~ =cay_12

c.O~qF-l! l.laTE-lO 1.~76~-13 =o!=lC-ll ).~l~C-ll 1.2lq~-ll

g,~&4r-~l I.?~,0F-IO 1.9~=~-10 =.~6~c-1~ ~.¢a~-l] 1.2~7"-1l

e.~OTr-!~ 5.og6~-!2 g.~37r-12

AN~L~ ~ MO= 0 . o 4 ~ 4.&!~r-!O ~o~74F-10 ~.0~15-10 ~.~??c-ln ~.l~r-lO

~%0LE 1 uU= O . O ~ q ~ ~,OIOC-ZO 3.~17c-10 ~,3~c-10 ~.076r-13 ~.~=3r-lO

6.4aor-12 6.qOeC-I ~

5.7~SF-1P ~.a~2c-12 g.O~?r-12

~.O~a~-ll q.7a?r-ll |.:O~r-lO ~.~C-ll ~.lOlF-I! 1.13~r-ll

ANGLE 3 MU= O . 8 ~ S ~ ?.57~c-10 ?.813F-10 ~.06~r-lO 2.~c-19 ~.626r-~0

6.070g-1) ".~7|r-I~

g,~o~F-12 a.°~IC-l? &.666F-l?

6.q?Ot-ll ?.Q~n~-lI ~.~a!F-ll 3.6~7F-11 1.~40~-11 I.O?~F-II

ANGLE 6 uU= 0 . 7 ~ 5 0 ~.~P~g-lO >.~I]F-IO 2.~¢o~-I0 2.~0~¢-10 ".OP1F-~O

?.516c-1P a. PS~ro|2

6,715¢-12 4.601r-1? ~.lgTE-I ~

g.7~OF-11 5.114¢-11 6.?3~F-I1 ?.gO6F-11 1.~58~-11 ~.~70g-lP

A~J~LF ~ ~U= O . ~ l ? O 1.7q3~-10 I.~I?F-tO 1.578~-10 1.qBO=-lO I,#~?E-IO

~.Oo~c-]p p.77oc-t7

a.OgX¢-l/ ~.7~?c-12 3. g~?F-12

~,~47F-11 a.~aO~-lt 4.1~=:-11 ?.?~4r-ll l.~C-ll ?,s61~-l?

AMGL~ 6 MU= O.~SSO 1.??~F-IO 1.06~F-tO ~.O~=E-IO lolllc-TO l.O~OF-lo

AN~ ~ 7 MU= 0 . 2 8 1 A ~.~OqE-ll 7.~F-~| 7.*77F-tl 7.~OF-ll ?.~3IF-II

7.q~6~-i2 2.PqaF-12

3. ~?)F-I? 3.100~-17 ?.oOqF-l?

3.~8E-11 n.aaaF-ll ?,7~2r-lI 1.673F-11 ~.oa~r-12 ~.07nF-t?

SCALAR ADJOINT ~.555F-10 1.279E-10 1.35°E-10 1.356E-10 1.729E-10 7.600F-11 3.b59F-l/ 3,q65F-|l 6.227E-1| I.ISIE-11 3.367E-12 I.I~?E-12 5,a~SE-13 3.6~8F-13 3.?gSE-13 ?.79lF-13 2.~6g-13 2.122E-13 l;R6q~-l~ !.¢53f-13 1.36bf-13 8.185F-16

I.qo~F.IZ I.~76g-12

2.girl-I? 7.34~r-I? ~,tq6c-~?

2,~77¢-i1 2.a37E-l! 1.730F-11 1.1~2F I1 7.202g-12 a.a~qF-l~

&NOL~ 8 ~U= 0 . 0 o ~ 0 5.65&F-|i 5.0~GE-II 5,0=~F-I! ~,t0~F-11 5.003F-11

x.p~,~r-12 ?.ooqr-12

4.23~F-12 ~.Qgl[-12 ~.711E-[2

5.272E-11 5.755~-11 5,a22F-ll 2,6q6E-ll l.tOIE-ll q.O~lE-12

SCALAR ADJ]INT 1.7qQF-Io l.~qBF-lO t.=80E-IO 1.558E-10 1.~28¢-10

7~ r M TSF CqNCR=T= SL6~

ANGLE 8 MU= 0 . 0 9 5 0 ~37=¢-!! ~.06~E-ll :.qq?E-ll 4.3~0E-11 6,03qE-11 2.67qE-11 1.768E-1! 1.668F-11 7.861E-12 3,968E-12 1.512~-12 5.q?SE-l~ 3.Ob6E-13 2.0~5F-13 l.qOOF-l? 1.blOg-|3 1.~75E-13 1.212F-13 l.Oa~-I~ ~.627c-16 6.68q¢-la ?.9OqF-14

C~ TSF CONCRETE SLAB

ANGL~ 7 WU= 0 . 2 ~ 1 6 ,=771F-11 6.OlqE-tl 5.0~5-11 6.606F-11 6.Og~=-ll ~.052F-11 2.415E-11 2,08IE-II 1.~23E-11 ~.805E-12 2.119E-12 n.OT~F-13 6.073¢-13 2.7~7F-13 2.5~0E-13 ~.1~2=-13 1,8~?~-tg !.61°F-l~ 1.40?c-I a l.l~C-l~ q.2~¢-l~ g.q~?r_!~

hEUTP[0N OOS~ F Q U ! V A I E N T NEUTPON I / | C M * * 2 | | |

MCUTRON PI.I~S GAM~'A-RAY n Q ~ c ¢QJIVALENT ENrRGY ANq A',IG'JL ,e.~ r)EPE'~nENT TJANSHISS[0% ~:ACTQR~ N~JT~,Q~? P-ROUPS I R r ~ S / I i S g U R ( ] ; NFUTQON I / ( C ~ * * 2 I I |

1.07P--O=----?.qOC--O = ~.06~-0~---~.07Fo0¢ 1.12~-06---~.OEFoO~ 6.14E-07---1.t?c-0~ 0.0 ---4.14E-07

~

Ol 01 0! O0 O0 O0 90 O0 O0 oo oo oo

ANGLc 1 ~U= O . q ~ q ~ A.Sa6F-IO 3.53qE-10 ~.O~TF-lO ?.721c-10 3.Z12EoIO !.~3?~-10 7.113C-ll o.4~¢-11 !.52q~-10 3.0?Og-ll 7.01~F-12 l.ql4F-12 9.3&~=-13 5.57~e-~? 5.085;-1~ a.3!1c-]3 3.707F-!3 ~.~-I~ ?.~OIF-13 ?.45~¢-1~ l.qn~C-l? I.II~P-~ ~

~r.(75 ; [ i , v ~ ) AND ANCAJLAn DEPFNDFNT TR~NSMISSIqN FACT0~ N~t~TPqN ~ROUPS (R~US/{{SOUR~F

ENERGY GROU~ (MFVI I,??E O I - - - I , = O E I,OOE 0 1 - - - I . 2 2 E ~.lqF 00---1,00= h.~6F O0---B.IOF ~,qTE 0 0 - - - 6 , ~ 6 ~ 6,07F O0---~,~7F ~.Ol~ 00---4.C7E 2.~6~ O0---~.O1E 2,35E 0 0 - - - 2 . ~ 6 F 1.8~F 00---2,?~E 1.11E O0---1.~0E 5.gOE-OI---1.11F 1.tl~-O1---~.5OF-O1 3.35E-O0---!.11E-01 g.83E-04---3.~c-o |.0IE-O6---~.P~E-06

eNErGY

T,; ;d,t. 7 . 4 ,'~t!fl"RO~; G~OUF TRA,;:,~I::-LY.",q FACTOP5 F~)R A 75 CE TSF CO;~CRLTL ~LAL

-J

P~

aq

,w

Ol Ol O0---I.OOE Ol

O1---I.?~F

1,0~1~-11

q,g?SE-la *,q4&~-14 ~.~@Sr-la ?.~|qE-la 9.0~Ow-14 l.?Ba¢-la 1.~71~-14 1.~77~-1~ 1.~68¢-14 q.a@Yr-1~

1,~I~E-11

g,~FO¢-14 4.|06F*14 ?,?o4r-la ?.~OTE-la ?.128E-14 l.q~sr*I4 I.b32¢-14 1.4~0K-14 ~.~I4F-I4 q.s?~¢-l~

#~ea~ 1.5 x I~~i

2.goE-oS---I.G~-O~ 1.07E-OS---2.90E-05 ~.06F-0~---I.07~-05 l,l?E-O6-,-~,OBE-Oh &.I&E-OT---|.I~E-06 0.0 ---~.|&F-07

~,97F O 0 - - - 6 , ~ F O0 &.OTF O 0 - - - ~ . ~ T F O0 ~ . 0 1 F O 0 - - - 4 , 0 1 E O0 2 .&& ~ O 0 - - - 9 . 0 1 F 00 ~.~F O0---2.~E 00 I . B 3 F O 0 - - - 2 . ~ F 00 I . I I F O0---!.6~E 09 ~ . ~ O E - O I - - - I . ~ ! F O0 t.1~F-0!---5.¢0~-01 ~.~&E-O~---1.11~-O1

ENERGY GQOUP !MFV) 1,22F 0 1 - - - 1 . 5 0 E Ol I.OOF O I - - - I . 2 ~ F 01 8 . I q E 0 0 - - - I . 0 0 ~ Ol

I.ORTT-Ia ~.~77E-|4 ?,50~F-Ia 2.75o~-1~ I.~17~-1~ 1.~0E-14 1.46.~-~4 1.2~C-l~ 1.0~*=-1~ m.~?OF-l~

7,|~E-I?

7.1~IE-Ia ~.~74¢-|4 2.277F-Ia ?.O~IC-14 1.TalE-14 1.497F-Ia 1.~0F-14 1.169F-14 g.~?E*I~ ?.WS~F-15

4,2?~[-12

ANGLE ~ ANGLE ~ MU= 0.SbS6 MU= 0.7550 ~.058E-!I 2.79gE-11 ~.0~?~-I~ 2.132w-I1 ~.~OqE-lt ?.3~?F-II 1.Baqr-II ?.2~2F-11 2.~F-ll !.87~E-II 1.1~4F-11 q.09~-12 ~.I?OF-[? q,~37~-~2

6,0~¢-|4 ?,RI4F-|4 t.oq4E-l~ 1.80~F-I~ 1.5~2F-14 l,~lBE-14 1.1~8F-~4 l.OlqE-|4 P.SO1F-15 6.qlTE-15

2,aI?~-|2

ANGLE m MU- 0.6179 I.A~?F-11 1.441~-11 I.~25F-ll 1.544E-11 !.294F-11 ~.~|~-I? ~,T?S~-IZ

K,OO6E-I~ ?.46Q~-|4 1.691~-14 I.~BE-14 I.~02E-14 I.IITF-Ia e. OeAE-|5 8.610F-15 7.214F-15 ~,TTT¢-|~

1,361E-|2

~,qSSE-I~ 2,00WE-|4 I.~7~E-14 1.2~B~-1~ 1.059E-I& 9.059E-15 8.OOBE-I~ 6.q43~-15 5,778E-15 4.57~E-15

7,76~E-1~

ANGLc 6 ANGLF 7 MU= 0.4E30 MU= 0.2816 1.17BE-11 7.70qF-12 ~ . a o S E ~ 1 2 6.b13E-12 9,921F-12 ~.60BE-I? I.O~?F-II 6.~M78~ -12 @.7~6F-12 5.8g4F-12 a,66qE-t2 3.215E-12 2.|8~F-12 1,6BSE-I?

?.903E-14 1.50wE-I~ 1.032E-14 o.386E-15 7.O52E-15 6,BOOE-I~ 5.Bq5E-15 5.176E-15 4,26qF-15 3.30qE-15

&,42WE-13

ANGLE 8 MU= 0.0950 C.977E-12 ~.~BqE-12 4.410E-12 &.72BE-I? 3.qB2E-12 2.102E-12 1,230E-12

8,b&~;-|~ 8.214E-1 ~ 7.B~&E-13

b. Ba~E-13 ~.7B~E-I~ ~.712E-I~

@.9~9E-19 ".WTAF-13 8,084~-~9

6.~5~E-13 5~q71=-I~ ~.811~-I~

6.271~-1~ 5.45~-13 ~.537E-13

B,|bB~-|~ 7,TSgF-1) 7.~99F-I~

5.753~-1~ 4.qBO~-l~ ~.792~-13

7,50qF-13 7.1~2E-I~ 6.79BE-1~

6NGL = I ANGLe ? ANGLE ~ ANGLF 4 MU= O. OBQ& WU" O.g&4~ NU- O.P~5~ WU- 0 . ? ~ 0 7.~q3E-11 &,~OC-ll 4,qO~-ll ~.4q]¢-11 ~.$1&E~!! ~.7q2¢-II ~.T72¢-1! 2.76~F-II 6.31~-11 5.~3~E-!! 4.?O~E-II 9.~g8¢-11 5.BIIF-II ~.OSlF-ll ~.~74E-II ?.901E-!I ~.a~OF-II ~,078E-ll ~.78~c-II 2.#?0¢-II 2.~q~-ll 2.1~aE-11 I.RISF-I! I.~46E-II ~.OI~F-I~ 9.~I~E-12 ~.~48F-12 7,~91F-12 !.~4]F-II 1.22S~-11 I,O&~E-I] 8.507F-12 ?.16~F-l! |.S42E-II |.~06F-11 I.O01E-II b.ZA~E-12 ~.~O~F-12 5.10~F-I? ~.~0~-12 ~.18~-12 ~ . 0 2 @ E - 1 2 2.77~E-12 2.~5~F-12 1.7O?F-l? 1.775E-12 1.611E-12 I.~5q~-12 1.0~?~-12 1.0~8F-1? 0.88l~-13 o.065E-1~ g,277=-I~ 8,q85~-I~ 8,47qF-1~ 7,78~E-1~

5.1lIE-13 ~.~3F-13 2.Bq~F-13

6,698E-I~ 6,%5w6-[~ 6.057F-I~

aNGLe 5 MU" 0,6170 2.385C-11 l.qSS¢-ll ?.0~3E-11 2.035E-11 1.781F-II I.I07E-ll 6,I~IE-I? b,72~-12 6.937E-12 ~.507E-12 ~.097E-12 1.279E-12 8.071F-13 6,~2E-1~

4.370E-19 3.774E-I~ 2.616E-13

5,76&E-|~ 5,46R~-13 5,203E-I~

6NGLF 6 MJ= 0.4580 1,613F-11 1.369E-11 !.3POE-El 1.61~E-II 1.257E-II 8.212F-12 5.0~0F-12 5.181E-12 4,770E-12 2.765~-12 1.728E-12 I.O81E-12 6.q37E-I~ 5.958E-1~

3.548E-13 3.03~E-I~ 2.195E-13

4,728E-I~ 4,4BIE-13 A,257E-13

ANGLE 7 MU= 0 . 2 8 t 6 I.OO3E-I1 9.626E-12 q.627E-I2 q.S#IE-12 B.752E-12 5.~n3E-l~ 3,~68E-12 3,q82~-12 3.226£-12 2.090~-12 1.~5BE-12 B.BgSE-I] 5.6~0E-13 ~,~84E-13

2.b42E-1~ 2.222E-I~ 1.708E-I~

A,SY4F-I] 3,38~E-I~ ],206E-13

ANGLE 8 MU= 0.0~50 7.197E-I2 ~.57qE-12 6.5|2E-12 6.70~E-12 5.Bb4E-12 ~.qSIE-12 2.926F-12 2. TSBE-12 2.060E-12 I.~b~E-12 g.R~F-13 6.~3E-13 4.307E-1~ ~.~9~E-I~

~.566E-13 ~.q~SE-13 2.bqSE-IB

6,011E-I~ 5.704E-I~ 5.~2qE-~

SCALAR ADJOINT 2.46]E-11 1.975E-ll 2.126E-11 2.062F-II 1,750F-II 1.03qE-II 5.660E-12 6,SBBE-12 7.144E-12 ~.204E-12 I.B85E-12 1,146E-12 7.252E-1~ 6,225E-[~

SLAB

¢,WqmF-I~ 2.BZTE-I~ 1,79&E-14 1.625E-14 1.37BE-l~ I.IB3E-14 1.049E-1~ q.147E-15 7.685~-15 6.16WE-IE

3,04]E-12

SCALAR ADJOINT I.g48E-lI 1.50BE-E1 I.O~3E-II l.blSE-ll 1.510F-II 6.3~7E-12 7,~78E-12

~t(iOO;Li,~j) IR~NSNIS~[ON ~ A f T o P S NE@TegN PLUS GAqMA-RAY POSE EQUIVALFNT 100 CM TS= C O N C R E T E NEUTRON GROUPS ! R r N s I I ~ S O U R C E NEL*T~N ) / | C M e e S | ) )

ANGLE ? WU= 0.q4~6 5.]@1~-1! 3.~41F-11 ~.~OE-I ~ t.2~IE-ll 3.2qSF-|I 1.467F-11 a.790¢-19

ANGL~ I MU= O.~Rn& 6.=3SF-II ~.~01F-11 ~.~37E-ll ~.~IF-II ~.?~2F-tI I.~56:-11 5.11~F-17

FNFPGY AND ~NGLIL&o qFPCNnENT

&.qTF O 0 - - - 6 . ~ F 00 ~ .0 7 E O 0 - - - 4 . g ? F O0 ~.OTE O 0 - - - A = O 7 E O0 ?.46E O0---~,01F O0 2.~5E 0 0 - - - 2 . ~ 6 E O0 I.B3F O0---?.~E 90 1.1IE 00---|,~ O0 ~.50r-Ol---l.!lF O0 I.II¢-01---5.50E-0~ ~.35E-O~---t.11F-Ot 5.B3E-O4---~.3~E-O~ ~.OIE-O~---~.~F-04 2.90F-O~---I.OtE-O~ 1.0T~-O~---~.oOEoO~ 3.06~-0~---1.07F-0~ I.I?F-OA---~.O6E-O~ ~.14E-O?---I.12E-O~ 0~0 ---4.14~-07

!.00~ e . lO~

ENERGY GP~UP IMFV) I.?2F O~---l.~OW

: J ?;C,Zi,~j} ENFOGY ANP ANGUL%P DEPENDENT TRANSMISSION F&CTqRS NEUTRON D{3SE FQUIVALENT tO0 CM TSF CONCRETE SLAB NEUTRON C,~f)UPS (RFMS/IISOURC~ NFUTRON ) / ( C M * * ? ) ) )

(3

<)

sb

~b

(.J OO

AN~LF I &N~LE 2 MU= O , e ~ 9 ~ ~U= 0 . 9 ~ A 6 1.0~2F-12 ~.506E-13 6.700E-13 5.536E-!~ 8.~80Fol3 6.~0~r-13 7.326E-13 5.~63~-1~ 4o273E-13 3.586E-1~ !.Oe2F-t~ q,38qE-]4 ?.35qc-!4 2.171P-14 ~.361F-14 2.oOTE-l~ P~37E-l~ 5.q78F-i~ ~.PO~F-15 %272F-15 ?.0~6F-16 6.~g~F-16 ~.1~6P-I~ 2.055E-1~ 9.~62F-17 9 . Og1E-17 6.~18F-17 6,17~F-17 5.735F-17 5.52~E-lT ~.BSTr-17 ~.679F-17 ~.173F-IT ~.019E-! • 3.TI2E-I? 3.574E-17 3.250E-17 3.12RF-17 2.756E-17 2.650E-17 2.2~qF-17 2.151E-17 1.2~-17 !.210F-17

1

ANGLE 3 ANGLE ~ MU= 0 . 8 6 5 6 MU= 0 . 7 5 5 0 6,0~0E-13 3.q~OF-!3 ~,0~F-13 2.717F-13 4.805F-13 3.095F-!3 ~.330~-13 ?.~82F-13 2.676E-1~ 1.842E-13 ?.416E-1~ =.467F-1~ 1.286~-14 1.56~E-I~ 2,301F-14 1.722E-I~ 3.609r-14 1.q53F-l~ 2.STOE-~5 !.90?F-l~ 5.6~7E-16 ~.681F-16 ~.875F-!6 1.650F-16 8,4TIE-17 7.65~E-17 ~.7FOf-I7 5.21~F-17 5.16TE~I7 4.bqlF-17 &.37kF-17 3.qT?E-I? 3.757f-17 ~.~O~E-17 3.338E-17 3.025F-lT 2.91OF-l? 2.642f-17 2.469E-17 ?.22oE-17 2.002r-17 1.803E-17 1,143E-17 1.052F-17

ANGLE S MU= 0 . 6 1 7 0 2.4~o~-13 I.TT2E-13 1,Q2!E-~3 1,~3E-13 1,210E-13 3.855E-14 I=256E-I~ 1,2~qE-14 1.024~-]6 1.371F-1~ 3.761E-16 1,~05E-16 6.709E-17 4.ST6F-17 4.12qE-17 3.~gSE-17 2,qo6E-17 2.655£-17 2.314E-17 1.q~6E-!7 1.568F-17 o.~00F-18

ANGLE 6 MU= 0 . ~ 0 1.~36F-13 1,166f-13 1,207E-13 1.182E-1~ 7.83~E-14 2.6~aF-t~ q.857F-15 ~.qtqF-15 5.36~F-15 g.6e7c-16 2.~IE-16 1.157F-16 5.~8~E-17 3.880E-17 3,~OqF-17 ~.qTOE-17 2.542F-~7 2.2~OE-1T I,OFSE-17 1.636E-17 1.300~-lT 8.120E-18

ANGLE 7 MU= 0 . 2 8 1 6 q.T~F-t~ 7.869Fo1~ 7.8qqF-14 7.TBBE-14 5.0~6E-1~ I°784E-14 7.STtE-1~ 6.28gE-15 2,~?qF-15 6.T~lF-16 2.22gE-16 q.142E-17 4.312E-17 3.1~7E-17 2.851E-17 2,~12F-17 2.062E-17 I.RZOF-17 1.576r-17 1.310E-I? 1,037E-17 6.707~-1R

ANGLE 8 MU= 0 . 0 9 5 0 6.224E-1~ 5.314E-14 5.2TIE-I~ 5.19TE-14 3.272E-I~ 1.149E-1~ ~.$4~E-15 4.315E-15 1.4qOE-15 #.5~1E-16 1.591~-16 6.TOqE-IT 3.~72F-IT 2.366E-IT 2.144E-17 l. Bl3F-17 1.5~?F-l? 1.362E-IT t.lTFF-17 q.b~IE-18 7.502E-18 5.135E-18

CM TSF C O N C R E T E

SCALAR ADJOINT 2.805E-13 l.q56E-13 2.229E-13 2.05~E-13 1.292E-13 ~.833E-~ I,IT2E-14 1,2~0E-14 1,504E-1~ 1.36TE-15 ~,484E-16 1,271E-16 ~.0~9E-i7 ~.120E-17 3.TI4E-17 3,1~E-17 2.694E-17 2.38bE-IT 2.OTTE-IT 1.7~3F-17 l.~97E-17 ~.468E-18

SLA~

0.0

---4.1~F-07

?.gOE-05---l.O!~-O~ l,OTF-O~---~.~oF-O r 3.06F-O6---|.OT~-O~ t.12F-O6---~.O~F-O~

t.OlF-O~---5.~E-o~

ENERGY GROU~ I ~ V ) I.~TE O l - - - t . ~ O F 01 I.OOE ~ l - - - l , ? ? F O~ ~.]qE " , - - - 1 . 0 0 ~ O! 6.36F O0. . . . 8.1OE Oq ~ .g T F 0 0 - - - 6 . ~ 6 c 00 ~.O~F O 0 - - - ~ . ~ T E 00 ~ , 0 1 ~ O 0 - - - ~ . 0 7 F O0 ?.4~F 0 0 - - - ~ . O I E GO 2 . 3 5 F O 0 - - - 2 . & 6 F O0 l . ~ 3 F 0 0 - - - 2 . ~ 5 F O0 I . I ~ E 0 ~ - - - 1 . R 3 ~ O0 5 , 5 0 E - 0 1 - - - I . I I ~ O0 I.ItE-OI---5.SOF-OI 3.~SF-O3---1,11F-Ot ~U =

ANGL~ 1 o.qRq4 l.~q3F-t~ 1.044E-12 1.245F-1 ~ ~.0~7F-12 7.~38F-13 ~.5~F-13 l.?76F-t~ 2.320E-13 3.562F-13 1.~13~-13 R.479F-14 ~.165F-1~ 3.7~,~r-1~ 2.846E-l& 2,97~F-14 ?.83RF-14 2.728F-14 ~.b?~f-t~ ?.~63E-t~ 2.25~F-1~ l.q~Or-14 1.2~3E-l~

ANGLE 2 MU= 0 , q446 1.259E-I? 8.q4qE-13 1.04~F-12 o.280E-13 b.586F-13 3.23q~-13 1.686~-!3 2.1~3F-13 ~,102E-I~ 1.331E-13 R,llOF-I~ ~.qB2F-l~ 3.144E-|4 2,7~F-|4 2.88~F-]4 2.75~r-I~ 2.646E-14 2.545E-I~ 2.388E-14 ?.lqOF-14 Z.o20~-14 1.250E-14

LNGLF 3 NU = 0 . e656 o.5~6E-1~ 6.qS6F-13 7.qOTE-I3 7.152F-1] 5.272~-13 2.T66E-13 1.540F-l~ I.qOOE-13 2.~97E-13 1,201r-1~ 7.~q4F-l~ ~.66RF-I~ 2.gTof-14 2.~07E-1~ 2.727E-1~ 2.604P-1~ 2.50~F-1~ 2.~O~F-l~ 2.75~F-1~ 2,070C-I~ 1.819F-14 l.lq~F-14

ANGLF ~ ~U = 0 . 7 S ~ 0 b.~?SF-!3 5.088E-13 5.sSBF-13 5.158E-13 ~gT4F-13 ?.?84E-13 l.~5~E-13 1.610F-13 1.92~E-13 1.043~-13 ~.6q4E-l~ ~.~4~F-l~ 2.731F-16 2.~qRF-l~ 2.~IOE-I~ ?.~o8E-I~ 2.304~-16 2.214F-14 2.0T'/E-I~ I.o02E-14 1.665E-14 1.111~-I~

ANGLF 5 MU= O.6~Tg 4.~82~-1~ 3.633F-13 3,Q?2E-13 3.~llF-l~ 2 , S QS E -1 3 1.805F-13 1.1~2E-13 1.3206-13 I.~4TE-13 8,7Z4F-14 5.778F-14 ~.T38F-14 2.63TF-1~ 2.1~0E-I~ 2.2~3E-14 2.142F-14 2.058E-14 l,g?6F-l~ 1.851E-1~ 1.6q3E-14 l.~80F-l~ 1,0ORE-I~

AN GL E ~ qO = 0 . 4 5 8 0 3.134F-13 2=~g3r-13 2.635E-13 2.~?OE-I~ 2.073E-13 1.382E-13 q.~2qE-l~ 1.050E-Z~ 1.063r-1] 7. O Z T E - I ~ ~.800E-t~ 3,lbqE-14 2.09~E-1~ 1.8~2E-I~ 1.9~3E-t~ 1.8~S~-I~ l.T72E-I~ 1.700F-|~ 1.5~OF-I~ I,~50E-I~ 1.262F-I~ 8.8~6E-t~

ANGLE 7 wU= 0 . 2 8 ! 6 2.156E-13 1.857E-13 1.8;OE~I ~ 1.?~5F-13 1.46[F-13 l.Ol~F-]3 T.oT3£-I~ 8,0;7E-14 7.53~E-I~ 5.394F-l~ 3,?q4F-l~ 2.5~7F-14 1.726F-1~ l.~lZF-|~ 1.5~SE-l~ 1.5l/F-l~ I.~5~E-I~ l.~F-14 lo30O~-l~ I.ITqE-I~ 1.0|8F-14 7.~-|5

AN GL E 8 MU= O.Oq 5 0 |,~0E-13 1.288~-13 1.2~q~-13 1.20~F-13 9.833F-!~ 6oqOOF-l~ 5.68~E-1~ 5.776F-1~ ~.9~6~-14 3.806F-14 2.7~E-|4 1.~94E-14 1.306F-14 l.l~f-|~ t.202E-14 l.l~7E-l~ I,OogE-I~ 1.050F-14 ~,Tb2E-15 ~.TgOE-l~ 7.~55E-15 5.801E-15

SCALAR ADJOINT ~.810E-13 3.TO2E-t3 #,029E-1~ 3.71~-I~ 2.8~8E-13 ;.~68E-13 1.05;E-13 1,210E-13 t,395E-[3 ~.f155E-14 5.174E-1~ 3.345E-14 2.188E-14 I.g20E-14 2.013E-t~ 1.922E-14 1.8~5E-14 1.771~-1~ 1.657E-1~ |.512E-1~ l.~lSE-la q, I l O E - I 5

z'"~)N~UTqON PLUS GAMMA-P~Y DDSE EQUIVALENT 150 CM TSF CONCRETE SLAB E'4FPGY AND ANGU[A~ D~PFNDFNT T~NSMISSION FACTorS NEUTRON C,ROUPS (REMS/((SOURCE NEUTRON ) / ( C M * * 2 | ) |

1.01F-O~---~.~3F-O~ 2.qOF-OS---1.O!~-O~ 1.07F-O~---2.eO~-O= ~.06F-O6---1.07E-O ~ 1.12F-O~---3.0~-O~ 4.14E-O7---1,1?F-OF 0.0 ---~.14F-07

EPZERGY ~ O U P (MEV| I.~2E OI---1.50E 01 l . OOE 0 1 - - - 1 . 2 2 E O1 ~ . ! q E O 0 - - - ! . O O E 01 6.36r 00~--~.l~F OO ~ . 9 7 E O0---6.36E O0 ~.OTE O 0 - - - ~ , ° T E 00 ~.OtE 00---~.07F 00 ? . ~ 6 F 0 0 - - - 3 . 0 1 c O0 ~.~5E O 0 - - - ? . ~ F 0o I.B3~ 0 0 - - - ~ . 3 5 F O0 I . I I E O 0 - - - I . P ~ F 00 5 . 5 0 F - O 1 - - - t . l I F O0 l.ltF-Ol---5.SOF-O1 3.~5~-0~---1,1~¢-0!

TABLE 7.6 NEUTRON G~OUP ~RANSM!S~ZON ~'AC']'O~.SFV}~ A 15C CM TSF CONCRETE SLAB •In ( 15o ;E i ,L,j) NEUTRON DOSE EQUIV6LENT ! 5 0 FNEPGY &Nr~ ANGULAP OFP~:NDENT T~ANSMISSIf~N FACTORS NEI~TRON C,R D U P S !REMS/IlSOU~CE NEUTRON I / ( [ . M * * 2 ) I I

h,J

.,.=

%

c~

c~

O0

5.50E-OI---I.IIE

ANGLE I MU= 0 . q 8 9 4 I.53bE-14 8,82bE-15 1.170E-14 9.ZbZE-15 ~.140E-15 6.039E-|6 I.O~OE-16 l.~20E-16 4.~IIE-16 q. IO3F-18 1.660F-18 5.133E-1~ 2.242E-19 1.521E-19 1.3~qE-19 i*lSlf=lq 9.Rq~F-20 8.TqqF-?O 7.70bF-20 6.534E-20 5.308E-20 2.qSBE-20

ANGLE 2 MU= 0 . 9 4 4 6 1.224E-14 7.154E-15 q. 243E-15 7.~5~F-15 3.402E-15 5,182E-16 g.569E-17 1.309E-16 3.111E-16 7.812E-18 1.577E-18 ~.870E-Ig ~.ISSE-i~ 1.463E-Iq l.30qE-lq I.IOqE-I~ q.528E-20 R.~72E-20 7°~16F-20 ~.Z83E-20 5.100E-~0 ?.flhTE-20

ANGLE 3 ANGLE 4 NU= 0 . 8 6 5 6 MU= 0 . 7 5 5 0 8.~33E-15 5.~01E-15 5oORbE-15 3,341E-15 6.2BgE-15 ~.90~E-15 5,22gE-15 3,356E-15 2.467F-15 1,645E-15 ~.027E-Ib 2.917E-16 8.307E-17 6.886E-17 1,032E-16 7.TOgE-17 1.752E-16 q.O43E-17 6.124E-18 4.538E-18 1.3~6E-18 I.IO?E-I~ 4°443E-Iq 3.911E-19 2.008E-Iq 1.814E-19 I.365E-19 1.236E-19 1.225E-1~ I.II~E-Iq I.037F-19 q.416E-20 8.907E-20 B.O79E-20 7.q14E-20 7.171~-20 6.q21E-20 6.263E-20 5.R55E-SC F.286E-20 4.746F-20 4~274E-20 2.709E-20 2.~g3E-20

ANGLE S ANGLE 6 MU= 0 . 6 1 7 9 MU= 0 . ~ 5 8 0 3.211E-15 I.q57E-15 2.138E-15 l.3q0E-15 2.345E-15 1.436E-15 2.07~E-15 1.289E-15 1.049E-15 6.60~E-16 2.023E-16 1.369E-16 5,526E-17 4.338E-IT 5.591E-17 3.990E-IT 4.567E-17 2.286E-17 3.261E-18 2.305E-18 ~.BEZE-19 6.931E-lq 3.331E-1~ 2.743E-lq 1.590E-19 1.3476-19 1.085E-19 9.1g6E-20 q.Tg6E-20 8.318E-20 ~.285E-20 7.039E-20 7.102Eo20 6.027E-20 6.295E-20 5.332E-20 5.487E-20 ~.635E-20 ~.615E-20 3,87qE-20 3.717E-20 3.104E-20 2.228E-20 l.q25F-20

ANGLE 7 MU= 0 . 2 8 1 6 1.225E-15 9,345E-16 q,255E-16 8,SgTE-16 4.185E-16 9.09gE-17 3.3~SE-IT 2.810E-17 1.138E-17 1.604E-18 5.254E-Iq 2.167E-19 t.Oq3E-Iq 7.~59E-20 6.75qE-20 5,717E-20 4.887E-2G 4.314E-20 3.737E-20 3.107E-20 2.458E-20 1.590E-20

ANGLE 8 MU= 0 . 0 9 5 0 7.701E-16 6.331E-I& 6.166E-16 5.458E-16 2.644E-16 5.80gE-!? 2.~48E-lT 1.926E-17 5.622E-18 1.074E-18 3.752E-19 1.590E-Ig 8.228E-20 5.607E-20 5.083E-20 4.297E-20 3.668E-20 3.230E-20 2.786E-20 ~.SqSE-20 1.778E-20 1.21TE-20

SCALAR ~DJOINT 3.823E-15 2.431E-15 2.858E-15 2.415E-15 I.159E-15 2.04~E-16 5.160E-17 5.560E-17 7.340E-17 3.256E-I8 8.205E-19 3.012E-19 1.433E-I? 9.766E-20 8.803E-20 7.452E-20 6.385E-20 5.657E-20 4.925E-20 4.133E-20 3.313E-20 2.OOTE-20

NffUTRON DOSE EQUIVALENT 2 0 0 CM TSF CONCRETE SLAB NEUTRON | I ( C M t t S ) I I

00---~.97E O0. . . . 4 . 0 7 7 09---3.01E OO..... / . ~ r

uu

O0 00

oo

00

O1 01 O!

~Fead 1.5 x LO1

1 . 1 ~ F £;0---1.83F DO 5 . ~ O F - O I - - - I . I I F OO 1,11E-OI---S.50E-O~ ),35E'-O~---l.I[E-O: ~.83F-O4---3~35E-O~ t.O1E-O~---5.B3E-0~ 2.gOF-OS---1.O1EoO& l.OTE-~---?.~OE-O5 3.06~-06---1.07~-0~ 1.12E-OA---?.OaE-06 4.16~-07---l.12E-Ob o,0 ---4.14~-07

4.07E 3.01E ?,46F 2.35E

ENFRGY GROUP (NEV! 1.22E 01---1.50E 1.00E 01---1.22F 8~!eF O0---t,OOE 6.36~ 00---8.Iq~ 2.267E-14

~.6bbF-!4

1.934E-1~ 1.377E-14 8.321E-15 5.200E-15 6.SqqE-15 R.q~OE-I5 ~.6qOF-!5 3.000E-15 1.8qSF-15 1.214E-15 1.074F-I~ 1.137E-15 1.087E-!5 1.069E-I~ 1.O!2E-!5 q.~25=-16 8.761E-16 7.701F-lb 5.0~3E-16

1.a69~-I~

2.Z41F-I~ 1.5~5E-1~ 8.q~gE-15 %4~5E-15 7 . 0 1 f l ~ ~5 ~,88RE-!~ 4.n~8¢-!5 3.130F-1¢ I,gb3P-~ ~ 1.?~2~-15 I.IO@E-I = 1.167E-15 ~.120E-!5 I.OPlF-15 1.0~3E-15 9.81gE-16 g.O33E-lb 7.q~IE-I6 5.~7~F-I~

?.771E*I~

2.2~4E-1~

ANGLc 2 ~U= 0 . 9 4 4 6

3.2~6E-14

ANGLF 1 NU= O . q B q 4

1.527c-1~ I,I~IE-I~ 7.36~E-15 4.7qSE-15 ~.g36F-I~ 7.~qqE-15 #.2~gE-15 2.781E-15 1.77n~-I5 1.147F-1~ I.01~E-15 1.072F-15 1.02q~-15 9.92OE-!6 9.57~E-I~ q.OOqE-l~ 8.287E-16 7.278F-16 ~.RISF-16

1.7~IF-14

I,ATAE-14

Z.t41E-14

ANGLE 3 NU= 0 . R 6 5 6

L.I4|¢-14 ~.qqOE-15 6.23qE-15 4.27qE-15 5,136E-15 ~.177E-15 3.740F-15 2.494E-15 1.61qE-15 1.056E-15 Q.3~TE-16 9.874E-16 9.47~E-16 9.1~5E-16 R.817E-16 B.~OE-,I6 7.617E-16 b.Ef17E-16 ~.4fl~F-16

1.281E-14

1.200E-14

1.563E-14

ANGLE ~ NU= 0 . 7 5 5 0

R.3~?F-15 6.86~E-15 5,093E-15 3.700E-15 &.294E-15 ~.~46E-16 3.i58F-I~ 2.161[-15 1,428E-15 9,427E-16 8.3~7F-16 ~.827E-16 8.~T~F-16 ~.173F-16 T.B74E-16 7.397E-16 6.786F-I~ 5.q~RE-Ib 4.073E-16

9.1qlE-15

8.951E-15

I.I18E-14

ANGL[ 5 MU= 0 . 6 1 7 9

6.025E-15 5.12~E-15 4.007E-15 3,095E-15 3.~68E-15 3.~T3E-15 2.563E-15 1.801E-15 1.213E-15 8.12~Eo16 7.192E-16 7.614E-16 7.~0~E-16 7.0~6~-16 6.779F-16 ~.358F-16 5,817F-16 5.079E-16 3.~80E-Ib

~.602E-15

6.6#6E-15

7.990E-15

ANGLE 6 No= 0 , 4 f i 8 0

4.32qE-15 3.723E-15 3.008E-15 2.482E-15 2.6qRE-15 2.657E-15 1.977E-15 1.427E-15 9.795E-~6 6.678F-16 5.qOTE-16 6.2~E-16 6.003E-16 5.782E-16 5.557E-16 5.199E-16 ~.733E-16 4.100E-16 3.011E-16

4.7~5E-15

4.qOOE-15

5.700E-15

ANGLE 7 ~U= 0 . 2 8 1 6

2.981E-15 2.5~3E-15 2.068E-15 1.842E-15 1,~3qE-15 1.760E-15 1,399E-I~ 1.036E-15 7.~5~E-16 5.06!E-16 4.~71E-16 4.737E-16 4.543E-16 6.369E-16 4.190~-16 3.906E-16 3.529~-16 3.003E-16 2.348E-16

3.2qlE-15

3.460E-15

3.qOgE=15

ANGLE 8 MU= 0 . 0 9 5 0

8.307E-15 b.538E-15 4.620E-15 3.340E-15 3.8q~E-15 ~.~83E-15 Z.831E-15 1.932E-15 !.277E-15 8.~66E-16 7.492E-16 7.921E-Ib 7.600E-16 7.32gE-16 7.05T~-16 6.621E-Ib b.ObOE-16 5.288E-16 3.681E-16

9.377E-15

8.8~9E-15

I.I#OE-14

SCALAR ADJOI~T

ENERGY ~NO ANGUL&P OFPENDENT TRANSMISSION F~CTORS z ]~EUTRON PLUS GAmMA-RAY DOSE EOUIV~I_ENT 200 CM TSF CONCRETE SLAB NEUTRON GROUPS IRENSIIISOURCE NEUTRON ) I I C M * * S I I I

2.qOE'05---I.OIE-0~ 1.07E-OS"--?.qOE-05 3.06E-O6---I.OTE-OS 1.12E-O6---3.06E-O6 4,14E-O7---1.12E-06 0°0 ---4.14E-07

I.llE-OI---~.5OE-OI 3.35E-03---I.IIE-OI ~.83E-O4---3.35E-O~

01 01 01 O0 O0 00 O0 00 O0 00 00

ENERGY GROUP IMEV) 1.22E 0 1 - - - I . 5 0 E 1.OOE O I - - - I , 2 2 E 8.lqE O0~-I.OOF 6,36E 00---8.19E 4.q7E O0---6.~bE 4.0TE O0---a.g7E 3.ORE O 0 - - - ~ . 0 7 E 2.46E 00---3.01F 2.3~E 00---2.46E 1.83E 00---2.35F l . I t E O0---I.R~E

ENERGY AND ANGULAR DEPENOENT TRANSMISSION FACTORS NEUTRON GPGUPS ( R E M S I ( I S O U k C F

~n(2OO~l:i'~J)

TABLE ?. 7 NEUTRON GP£!_~ TFJ~NSMISSION FACTORS FOR A 20C CM ': ,~ ,. :,iC~,,ZTE SLAB

~o

~o

ANGLE 1 NU= O.qO94 1.397E-Oe 1.186E-09 9.B~0~-10 8.139E-10 b.603E-tO 5.312F-10 ~.389E-10 3,581E-10 2.BTBE-10 2.lB3E-lO |.562F-10 1.126E-IO 7.006E-11 3.788E-1I 2.05B~-11 6.727E-12 ~.5~6F-16 |.3qOE-18

ANGLE 2 NU= 0 , q 6 6 6 l.~05F-Oq l.193F-OR 9.936E-10 8.165E-10 6.606E-|0 5.296E-10 ~.357E-10 ~°5~5E-!0 2.B?~E-IO 2.12~E-10 1.506E-10 1.076E-lO 6.62qE-11 3.544F-11 I.90qF-[I 8.178E-!2 3.758r-1~ 1.00~F-18

~NGLE 3 MU= 0 . R656 |.6~|F-OQ 1.212E-09 1.007E-09 ~.228E-10 6.606E-|0 ~.2~6F-10 ~,273E-10 3°~25E-10 2.702E-10 I.qDBE-IO lo392F-lO OoTBOE-11 5.e2~--ll 3.~g'~-t| 1.651E-11 5.27~F-12 2.736E-1~ 5. S O B E - I q

ANGLE ~ MU= 0 . 7 5 5 0 1,673E-09 I.?41F-OQ I,021E-Oq B.244E-lO ~.512F-10 ~.07~E-10 ~,058E-tO 3.18#E-10 2,462E-10 1.77~F-I0 1.20~F-lO ~.??OF-I! ~.BR~E-|I 7.502~-11 1.310E-~I ~.lT6E-12 l.R66F-I~ ?,?~3E-lq

~,oor-o?---c.

OOr-O ~

FNCOGY GROUP (M~V) ~ .0 0 ~ 0 0 - - - 1 . 0 0 c Ol ~ .5 0 E 0 0 - - - ~ . 0 0 c O0 ~ . 0 0 ~ 0 0 - - - ~ . 5 0 F O0 ~,OOF O 0 - - - 5 . O O F O0 3.0OF O 0 - - - & . O O F O0 ?.SOF O O - - -~ .O O E O0 ? ° 0 0 c 9 0 - - - 2 , ~ 0 ~ O0 1 . 6 6 c 0 3 - - - ? . O O F OO l . ~ c 0 0 - - - ~ . ~ 6 c O0 1.00 r O0---I.~3F on n . O O = - O l - - - l . O 0 ~ O0 ~.OOV-Ol---~.O0:-O! 6oOOC-Ol---6.OOr-ql • ,OOC-Ol---#oOOF-Ot ?-O0¢-0!---~-OOr-Ol 3.|o~F-28

ANGLE I MU= OoqPG4 7.~36E-10 5,Q92F-lO ~.79~F-|0 ~.?l&c-lO ).~8lF-lO ?.O)qr-]O ]o~lqF-]O |.Oq?F-|O 7.T&Or-ll ~.~7~=o!] ?.90~r-!| I.~?IF-!I 7,~wlr-12 ?.5&~F-12 l-O]?r-~ ~ | . ~ 7 0 c->~

A N C LP ? ~U= 0 ° ~ 4 ~ 7.0~?F-10 5.~@~-10 ~.6¢7F-10 ~o5~F-lO ~.~6~c-13 l.q?Ec-]O lo~>~F-t3 l.OtqC-lO 7.lOqP-ll 4.~17c-11 2.E1~¢-11 1.~V-l! ~.~6~E-I~ ?.~7~c-I ~ q*770F-I ~ ~.~&7F-?~

ANGLE ~ MU= 0 . q6~6 6.77~F-10 5,557F-!0 ~,~l~-]O ~.~SqE-lO ?.~F-~O |,?[Rr-IO 1.~50ro|O q,T&SC-ll ~.~q~E--ll ~.6~lrI ?.07~r-ll l.l~r-ll ~ol30F-I ~ I.?P~-I? ~*?~C-l~ I,O|~F-~q

A N GL E 4 MU= 0 ° 7 ~ $ 0 6.1~=-I0 5.00l~-10 ~,~70E-|O 2.86Pr-10 2.o~o~-lO l°3eqF-|O ~.927~-]1 #.6~Sc-ll 6,~6¢-1| 2.612r-11 I.~27~-II 7,~o~r-l? T.r~?F-I? t.??~c-13 &-?Tl=-13

ANGLE & MU= 0 . 6 5 B 0 lo34qP-OR l,Oq0E-O0 8.617E-10 b,5~OE-tO ~.784E-lO ~.~37E-10 2.5~6F-10 1.971E-]O ).35TE-lO 9.IOIE-II ~.88oE-|| ?.932E-1l 2,2O9E-ll I.I?BF-II 6.330E-12 ?.271E-12 ~.OOIE-I~ 2.72~E-20

&.~qTF-*O

AN~L~ 5 MU= 0 ° 6 | ? 9 5.OllF-lO 3.qT~F-tO ?.qBOF-lO 2,125E-19 l,a~qF-lO q,~07c-II 6,&|SF-ll z |~7F-;| ?,727E-1! 1.569c-ll ~°&8?c-12 a.T~Or-17 7.186F-12 7.753F-1~ ~.I~F-13

?.7~Q;-lO

AN GL E 6 MU= 0 . 4 ~ 0 3.072F-|0 ~.~7F-10 I.&q3E-|O I.I~BF-IO 7,&OSE-IT 4.e4&F-tl 3°0q~-1| 2.O07F-I~ I.~I~F-Ii 7.779E-17 &o&?OE-12 ?.*OgE-12 1.26qF-I? 4.7~r-1~ 2.033~-13

SCALAR ~DJOINT 1.07~E-O9 B.qOIE-IO 7.158E-|0 5.e22E-lO 4.~16E-lO 3,27bE-10 2.573E-i0 |.9~qE-|O 1,~?3E-lO 1.092E-lO ?o~54E-|| ~.I?~E-II 3,111E-li 1.626E-l| B°TISE-I2 2.qsDE-12 ?,007E-16 2,013;-1g

],R~O¢-~O

ANGLE 7 NU = 0 . 2 8 1 6 9,3~DE-I| 7°~1TE-11 5.097E-l| 3°EeDE-ll 2.3~6E-11 t.%~E-1l I,II~F-|I 7.839E-12 5.~rOF-I2 ~.588F-17 2°??~E-I2 l.~05F-12 7.2~E-13 2.gOIE-13 |.SqTF-13

t°~t?F-~O

ANGLE 8 ~U= 0 ° 0 9 5 0 l.4blE-ll t.270F-11 1.05?E-II 8o~5~E-12 6.54bE-12 5.O0~E-12 3.~7E-t2 3.0~8E-12 2.~38C-12 1.6~SF-|? l.llZF-|2 7.~gF-13 ~.O~gE-I) l.7)8F-l~ B.051¢-14

?,~SBF-~9

SCAL~R ADJO[NT 3,519E-10 2,826E-10 2.165E-10 l,591E-lO I.ISIE-IO ?,&8BE-|1 5,~77E-|1 ~.762E-1| 2.550E-lI l,$~lE-ll 8.658E-12 ~,g52E-12 2.292E-12 8,212E-1~ ~.~BTE-13

30 CM TSF CONCRETE SLAB

ANGLE 8 MU= O.Oq~O l,~lOE-lO |.233E-tO 1,043E-[0 R.531E-|l &.830E-11 5°392E-|| ~.~ITE-II 3.567E-|1 2.B92E-XI 2.222E-11 1.672E-11 1.259F-11 8o283E-12 ~.682E-|2 ?,717E-12 1.143E-12 9.503E-15 1.137E-20

15 CM TSF CUNCRETE SLAfi

ANC4.F 7 MU= 0 . 2 8 1 6 8.305E-10 6,51qE-lO ~,8~qF-|O 3.4T8E-IG 2.4OqE-IO 1,658E-10 1.213E-10 B.TOIE-II 6.#80E-11 ~.5?OE-I| 3,11~L-11 2.21~E-1| 1.385E-1! 7.483E-12 6.200E-l~ 1.658E-I2 I,520E-l~ 1.590E-20

30 CM TSF CONCRFTc SLAR GAMMA-RAY DC~SE EQtJ[VALENT GAMM~-~AY|/.~CM**~)II

ANGLE 5 MU= 0 . 6 t 7 9 I.~BTF-Oq 1.238E-Oq t.OOlE-OO T,896E-lO 6,08|E-IO ~,571E-10 3.~53E-10 2,701E-10 2.026E-10 I.~07F-IO 9,257E-1| 6,205E-11 3o~REF-II ~.BOEE-ll q.~35E-12 3,II2F-12 I.?~SF-!~ 7.281E-20

TA~L~ 7 . 9 (';~,U'Ul~,-~A~ G~30¢) TRANSNISSI~N r'ACTr)qS F"JR A ~',,IERGY A'~O fiNGIIL~, o ~FPI:Ni'}~',IT T:tANSM|SS| ~ FACTORS ,~.'.I'4A-~AY GROUP'S [ R C M S # I ( S O | I ~ C

ENERGY GROUP (MEV| 8.OOE O 0 - - - I . O O E Ol 6 . 5 0 E O 0 - - - 8 . O O E O0 5.GOE 0 0 - - - 6 . 5 0 E O0 4 . 0 0 E O 0 - - - - 5 . 0 0 F O0 3 , 0 0 P O 0 - - - 4 o O O E O0 2 . 5 0 E O 0 - - - 3 , O O E O0 2.00F 00---2,50E O0 1 . 6 6 E O 0 - - - 2 . O O E O0 1 . 3 3E 0 0 - - - 1 . 6 6 ~ OG I.OOE G O - - - I . ~ F O0 8 , O O E - O I - - - I . O O E 90 6. OOE-OI---B°OOE-O| ~,OOE-O1---6,OOE-OI 3,O0~-OI---4.~OE-OI 2.00F-OI---3.OO~-OX t.OOE-OI~-2.0OE-01 5.00E-O2---I.OOE-OI 2.00E-O?---5.00E-02

TABLF 7.B GAMMA-RAY G~OUP TRANSMISSIOfJ FAC¢ORS FOR A 1F CN TSF CDNE~FTE SLAB ENERGY AND ANGULA~ DEPENDENT TRA~S~ISSIO~ FACTORS GAMMA-RAY DOSE FQUIVALFNT GAMMA-RAY GROUPS (REMS/I(SOURCF GAMMA-RAY|IICP=*?ll|

,.,a

,,,=

;b

--'.'_

L

ANGLF I aNGLI 2 uU= O.qB96 HU= 0,g~45 2.900E-I0 ~.712F-10 2.2o~F-I0 2,!3?~-I0 1.709E-10 1.57~E-,0 1.200E-lO 1.0q~c-iO 7.qO2E-11 7.OqOE-II 4.92qE-tl ~.350E-ll 3.172E-11 2.75qE-ll 1.~O~E-ll 1.630E-II 1.106~-ll q.3~TF-12 5.3~IE-12 4.43BF-12 2.232E°12 1.B~OE-12 q.~5BE-[3 7.701E-13 2,892E-13 2°35~E-13 5.782F-14 ~.65qE-14 1,384E-I~ 1.13BE-I~ IoI~OE-I5 q,q37E-15 1,537E-22 I,lbqF-2~ 1.422F-37 ~.6qSE-3R

ANGLF 3 ANGLE ~ MU= 0.95~6 ~U= 0°7~50 2.361F-10 1.82~F-IO I.B33F-IO ~.38T~-I0 l.~?qE-lo 9,76~E-11 q . O O B F - 1 1 6.~76E-11 5.687E-11 ~.9~7F-11 3.38~-11 2.102c-1! 2.090E-11 I.]07E-[I 1.201E-ll 7.251F-17 b.7!7~-12 3.953E-12 ~.115F-I~ t°TgSE-12 1.262F-12 7.228E-13 5.785E-13 3.07~E-13 1,633E-13 q,B67C-14 3,212E-1~ 1.972F-14 8.204F-15 5.425E-~5 7.o82F-I~ 6.112E-I~ ~.052~-2~ 5,~1F-23 9.14qF-39 2.g37E-3q

ANGLF 5 ~IJ= 0.6179 I.I2&F-IO B,?81~-|l 5.593E-11 3.~72E-11 1.~9~-~1 !.07BF-11 6.?36F-12 3.3~1E-12 I.~3¢=-12 8.~4tE-13 3.526F-1~ 1.592E-13 5.~47E-14 1.1~?E-14 3.432E-!5 ~.57~E-16 ?,767E-23 I=557E-3g

ANGLF 6 MU= 0.~5~0 4.372E-11 3.I20E-II 2.030E-II 1.216F-II 6.8A8¢-I? 3.693F-1? 2.181E-12 I°230F-12 7.O&~E-I~ 3,4R~E-13 1.SqlE-13 7.T47F-14 2,873E-1~ 6.508~-15 2.123;-15 3.38qE-16 7o976~-23 q,697t-@O

ENER GV GROUP (MEVI 8 . 0 0 E O 0 - - - I ° O O E Ol 8.50E O0---8°OOE O0 5.00E 0 0 - - - 6 . 5 0 E O0 4.00E O0---5.OOE O0 3.OOE O 0 - - - 4 . 0 0 E O0 2,SOE O0---3.00E O0 2. OOE 0 0 - - - 2 . 5 0 E O0 1.66E O0---2.OOE O0 1,33~ 00---1,66E O0 I.OOE 0 0 - - - 1 . 3 3 E O0 8,OOF-OI---t.OOF O0 6°OOE-OI---B.OOF-O! ~,OOE-OI---6,0OE-O1 ~,OOE-OI---&.OOF-O] 2.00~-01---3.00E-01 1.00E-OI---2.00F-O1 5.00E-O2---1.OOE-OI ~.OOF-O2---5°OOF-O?

ANGL~ ! MU= O°qBq~ 8.824E-1! 6.51OE-!I 4.382E-I~ 2.67qE-It 1.~R2E-1I 7.~5~E-I? 3.923~-12 I.~42E-12 8,29BE-13 2.BSqF-13 7.q~3E-14 2°760E-14 ~.14~E-15 3.935E-I~ 5.~97F-17 2.16qE-18 1.26~E-2B A.30~E-51

ANGLE ~ M,J= 0 ° q 4 4 8 7.816F-11 5.717E-II 3.TglE-1l ~.~75F-II 1.23~F-lI 6.0~7=-12 3.12TE-12 I.~3gE-I2 6,377E-13 ?.159F-l~ 5.8~IF-1~ I,685E-1~ 3,I62E-16 ~.975E-16 4.360~-I~ t.BBTE-lB g°5~BF-~q B.BgSE-52

ANGLE 3 ANGL~ 4 MU= 0 . 8 6 ~ 6 MU= P°T~SO 6o044E-1| 3.BOSE-ll 4,341E-11 ~o8563-II 2.807E-11 1.651~II 1.630E-II q.!lqE-12 8.507~-12 4.516F-12 ~.OOB~-I2 2.013E-I? 2 o 0 0 3 E - 1 2 ~.aqOE-13 O.ql6F-l~ &.IT~E-13 3.955E-13 1,780E-1~ |.280;-1? 5.971F-1~ 3.~2~F-I~ 1,61PE-1~ 1.006E-14 5.03~-15 2.002F-15 1,107~-15 1.881E-16 1.067F-16 3.020F-17 1.q~F=17 1.51~F-1 ~ 1.160~-18 6.606F-79 4.~BOF-?q ~.59~E-52 ~.TTTE-53

ANGLE ~ MU= ~ . 6 1 7 9 1.bqqE-II 1.13~E-II ~°592E-12 3.~90E-12 1.54~E-12 7.0!~P-I? =.3~5F-13 1.~6E-13 6.368F-14 ?.~OF-I~ 6.63~F-15 ?.~TqF-15 5.638C-1~. ¢.6q7~-17 1.1qOF-17 8.&86~-1~ ?.O~IE-2 ~ 3.742~-53

ANGLE 6 MU ff 0 . 4 5 R 0 6.147E-12 2.611E-12 1.517E-12 7.~5E-13 ~.80~E-13 1.707E-13 8.665E-14 4.095E-14 l,q6q~-14 7.@SgE-I ~ 2,585E-1~ q.q58E-l~ 2,71qF-t6 p.oq7~-17 7.140E-IP 6.436F-19 6.5~0~-7q 7.2q~E-=~

SLA~

ANGL~ 7 NOr 0 . 2 8 1 6 4.596E-13 3,Oq3E-13 ~.055E-13 !.~8E-I~ 6.q57E-14 3.b42F-l~ 2.075E-14 1.107E-14 5,878E-15 2.556E-1~ 1.004E-I = ~.~16E-16 1,261~-1~ 1.5~4F-17 ~.190~-18 4.776E-19 3.503F-29 1.53~E-53

ANg~ B MU= O o O Q ~ O -3.270E-14 3.617E-14 2.910E-14 2.085E-14 1.34qE-14 9,125E-15 5.126E-15 ~.035E-15 1,?bBF-15 B.673F-16 ~.944~-16 1.8~3~-16 5.669E-17 8.413E-IB 2.381E-18 3.370F-lQ 2.239E-2~ 1.121E-53

SCALAR ~DJOINT 2. l O G E - I 1 I.496E-11 9.57qF-12 5.513E-12 2°867E-12 1.35~E-12 6.819E-13 ?.076E-13 1,353E-13 6.60~E-1~ 1.273E-14 3.871E-15 8.020E-16 7.R~E-IT 1.370E-17 8.5~1E-19 ~.750E-29 2. I 0 3 E - 5 2

75 CM TSF CONCRETE SLAB

~NGLE 9 SCALAR MU= O.OgSO ADJOINT A.91SF-13 9°566E-II ~.7~0F-13 7,303E-11 ~.~05E-13 5.187E-li 3,771E-13 B.4~7E-II 2.99qE-13 2.127E-11 2.3~6E-13 1.2~6E-11 1.7~8F-13 7.6~8E-12 1.303E-13 ~.391E-12 q.133E-l~ 2.471E-12 5.SgbE-14 1,163E-12 3.lq2E-14 4.834E-|3 1.810E-IA 2.093E-lS 7.42~F-15 &,T~6E-14 2,102E-16 I.397E-I~ 7.64qE-16 3.794E-15 1°77~F-16 ~.4qBE-I6 2.728E-23 5.ROIE-23 @ . 6 3 0 E - 4 0 8.6lgE-3q

~0 CM TSF CONCRETE

ANGLE 7 MU= 0.2816 7.$55E-12 5.671E-12 3.q6~E-12 2.597E-12 1.~25F-12 9.86BE-13 6.478E-13 6.03~E-13 2.537E-~3 1.3qOE-13 7.099E-16 3.7~6E-1~ 1.~77~-14 3,710E-15 1.292F-[5 ?.4q~E-16 4°26qE-23 6°366E-60

TAELE 7.11 GAMMA-RAY G~gUP TPANSMISSIflN ~ACTnnS FOR ~ 75 CM TSF CONCRETF SLAB G MMA-OA~ OOSF EQUIVALFNT ENERGY AND ANGULAR DEPENOFNT T~ANSMISSI3N FACTOP$ G&MMA-R~Y GPOUOS IREMSIIISOU~rp GAMMA-RAY)/(CM**2ll)

ENERGY GROUP (MEV| B.OOE O0---I.OOE 01 6.50E O 0 - - - 8 . 0 0 F O0 5.00F O 0 - - - b , SOE O0 #.OOF O0---5.OOE O0 3.OOE O 0 - - - ~ . O O E O0 2 . 5 0 E O 0 - - - 3 . 0 0 E O0 2.00E 00---2.50E O0 l . 6 6 E O 0 - - - 2 . 0 0 E O0 1.33E 00---1.66E O0 I.OOE 0 0 - - - 1 . 3 3 E O0 8.00F-OI---1.OOE O0 6.00E-OI---B.OOE-01 ~,OOE-O1---B°OOE-01 3,00F-OI---~°GOE-01 2.00E-OI---3.OOE-O! I.OOE-OI---2.00~-OI 5,00E-O?---I,OOE-OI 2.OOE-OS---5.OOE-02

TA~LF 7 . 1 0 GA~IMA-R&V G'-)UP TRANSMIr,SIt)~ fACTORS FqR A ~0 CM TSF c,r)NCRETF ~LAE FNrc'q6.~'~:'~vS','L~ o ?>EPFN~ENT TRANSMIS.~L3N ~ACTC)RS CAWMA-RAY F~OSF FOUIVALrNT GA ~MA-RAY GPOUPS (RE~SIIISOdPCE GAMMA-RAY|/'ICM**?|))

h

c~

R

~b

=b

~o (3

ANGLE 2 ANGLE 3 MU= O.g4~B MU= 0 . 8 6 ~ 6 ~,178E-11 1,500E-!I 1.671E-11 9,BBtE-12 B,722F-12 5,669E-1? 4.4Q~P-|2 2.800E-12 2,023~-12 1,20SF-12 7.867E-13 4.451F-17 3.293E-1~ 1.796E-13 1.170E-13 6.15SE-14 3,9qBF-14 2,062F-I~ @,6~RE-15 4 . 9 5 3 F - I ~ 1.6O2E-1~ B.651F-16 ~,~76~-16 1,814E-16 3.~E-17 ~.3~0E-17 I,722E-IR 1,032F-19 1,55~F-lq 1,056E-19 3.557E-21 2.85~-2! ?,6~6F-3~ 5,31~F-~5 ~ , O A B F - 6 ~ Io048F-65

ANGLE 4 NU= 0 , 7 6 5 0 7,761F-1~ 4,926F-12 2,Bq3E-l~ 1.?~4E-1P ~,O86E-I ~ 1.767E-1~ 6.890F-1~ ~.~O~F-!~ 7, Tb3E-I ~ 1,925E-15 ~.~14E-16 ~,lS?E-17 1.760~-17 S,5~qE-Iq 6,bb4E-?O P. I87E-21 ~,610F-35 6,8~9F-66

&NGLF 5 ANGLF S MU= 0 , 6 1 7 g M3= 0 , 4 5 8 0 2.528E-12 3,91qE-13 1.53~E-12 2.367E-13 7,qFTF-1) 1.244E-13 ~.505E-13 5.66°E-14 I,~65E-13 2,341E-14 4.611F~:4 8.6?4E-!~ I.B~qE-I~ 3.737E-15 6.~2~¢-I = 1.463E-15 2,274E-IK 5,876F-!6 6,15~F-16 1,780E-Ib ~.758E-!6 ~.~16E-17 3°342E-17 I,B26E-17 ~.132~-1~ ?.801=-18 2 , R O B E - 1 9 1,38~E-19 4,039E-20 P.381F-20 1.637E-21 1.2~E-21 2,~9~E-3~ ~,416E-35 2,700F-6~ I,65~E-66

ANGLE 7 AN GL E B MU= 0 . 2 8 1 6 MU= 0 ~ 0 9 5 0 3,053E-I~ ~,4~1E-15 2.157E-1~ 3,~47E-15 1.344E-14 2,222E-15 7 o 3 3 2 E- 1 F 1.2)]E-IS 3,5~4E-15 6,~07E-16 1.52qF-l~ " ~62F-16 7,420E-16 1.4~4E-16 3.287E-16 7.293F-17 I,~60E-16 3,591F-17 5,001F-17 1,433~-17 1.480E-17 5.184E-18 5,263F-IR ~,OBIE-18 1~21~-18 5.07~E-19 6,q?OF-?O 3,~gBE-~O 1.3aBE-20 7.579F-71 B . g O A E - 2 ? ~.351E-22 2,874E-35 1,831~-35 Io10~F-66 R,IIIE-67

SCALAR ADJOINT 4,909E-12 3.228E-12 1.85~E-12 9.203E-13 4,004E-13 1.~06E-13 ~.193E-1~ 2,173E-14 7,~38E-15 I,B?TE-15 3.286E-16 7,026E-17 9,~74E-18 4,23~c-19 6,7~5F-20 1.blOC-21 ~,BTOE-35 1,527E-65

3.00F-01---4o00~-01 ~.OOE-OI---3.0OE-OI I.OOF-OI---?.OOE-OI 5.00E-O~---1.OOE-O: ?.OOF-OS---5oOOF-O?

ENERGY GROUP (MEVI 8.00E O 0 - - - I , O O E Ol 6 . 50 E O 0 - - - O . O O E O0 5 .0 0 E 0 0 - - - 6 , 5 0 F O0 4 , 0 0 E O 0 - - - 5 . 0 0 E O0 3 . 0 0 E O 0 - - - 4 . 0 0 E O0 2,SOE O 0 - - - 3 , 0 0 E O0 2,OOE 00---2.50E O0 1 , 6 6 F O 0 - - - 2 . 0 0 E O0 I,33E 00---1,66E O0 l,O0~ O 0 - - - l , ~ E OO 8 , 0 0 E - O I - - - I , O O E O0 6.00E-OI---8.0OF-OI 7.~57E-73 ?.~7F-74 l.~63c-26 ~.~72{-~7 O.O

6.123~-23 loB?qF-?6 ~.273E-76 ~.07~E-~7 O.O

ANGLE | &NGLE 2 ~U= 0.9BOA MU= 0o9~4b 2.14bE-l? 1.592E-12 1.?AgF-12 O.087F-13 6.024E-13 4o271E-13 2.3~4E-13 1.602~-13 7.4Q1E-14 4,968¢-| & 1.~6F-14 1.~88E-14 5o277r-15 ~.266c-15 ].13bF-15 ~,B~SF-I6 2.34~F-16 1,3q5~-16 ?,~19F-17 1,747E-17 2,11~L-IB 1,250F-IP log~7~-Ig I.?IBE-IO 2.gO~F-Z~ |.225r-24 1.022~-~6 ~.~07F-47 0.0

AN GL E 3 MU= 0,8656 8.702F-|~ 4,794E-13 2.15~F-13 7.b35E-14 2.23qF-]~ 4.DqTE-1~ 1. ~3F-15 ?.~TPF-16 5.G~&F-~7 7,164E-16 5,15~F-lq ~.730F-?0 l,~7~F-73 7.636F-2~ 7.~25P-27 :,3B~F-~7 0,0

A N GL E 4 MU= 0.7550 3,Q85E-13 1.618~-13 6.RS]E-14 2,76~'-14 ~,250F-15 1.301r-1~ ~.~qq~-lh 5,B47E-|7 I.~85E-17 ?.176c-1H ~,~7=F-I o 2.2=2F-90

6.qBTF-24 4.570r-p~ 5.o~71:-27 1.~H~-47 0.0

ANGLE 5 MJ= 0.6179 5.67~F-14 ?.q407-16 1.153E-14 ?.6~8F-1~ 1,016~-1~ ? I?TF-?' ~o900E-17 1,31RE-17 3.~P-I~ ~,~r-l~g ~,~BoF-?O 7.q~OF-?l

~.l~ar-?4 2,~=4F-25 4.~0F-27 3,(10E-47 0.0

1.~r-?~ 1.4q6~-?~ ~,I~7r-~7 I.~13F-47 o.0

ANGLF 6 ANGLE T MU= O.45BO MU= 0.2816 4.16~F-15 4.97~F-16 ?.IB~F-I~ 2.798F-16 go634F-16 1.304E-16 ~.~IF-I~ 4.31QF-17 1.123F-l~ 1,174P-I7 2.~?0~-17 ?.477c-18 q.O~?C-|~ 7.6~E-19 P,~oqc-la ?,~aF-|9 6.TI~F-lO 9.33lF-?0 1,2?OF-~q 2,~IOF-20 I,~63~-20 ~,6qOE-?l P.bqAE-21 q.~SF-? 9

h.t72E-25 P.Oq4~-pb ?.272F-27 1,21~F-47 3.0

AN GL E S MU= 0.0950 1.tq4E-16 4.77qF-lV t,IA6E-17 -~.526E-19 -t.9~SF-]B -7.27~E-lq -2.2O?E-lq -?.SOLE-20 3,9~E-21 ~.lllE-21 1,003F-21 ~.?08F-72

1.177E-73 ~.~66F-25 ~,760F-77 2.~4F-~7 0.0

SC&LA~ ADJ9INI 2.B~OE-13 1.6lOE-13 7.380E-1~ 2,702E-14 8.P08~-15 1.921E-15 5,251F-lb 1,09B£-16 2.27~E-17 ?,q~O~-I8 2,157E-19 2.~01P-20

TABLE 7 . 1 3 GAMqA-RAY GROUP TRANSMISSION FACTORS FOR A ! 5 0 CM TSF CONCRETE SLAB GAMMA-RAY D~SF FQUIVALFNT 150 CM TSF CONCRFTE SLAB ENERGY AND ANGULBR DEPENDENT IQANSMISSION cACTORS GANMA-RAY GROdPS (RFMSII|SOUPCE GAMMA-RAY|/(CM=*2)I)

ANGLE ! MU=- O. q B q ~ ?,607E-ll I,785E-~1 1°078f-ll 5.684F-12 2,626~-12 1.052F-17 4.507F-~ 1.6~0~-1 = 5,700E-l~ 1,3~8F-14 2.~80F-15 4,BTOF-16 5.~03=-1~ 2,3~2F-]R 1.9OBE-lq 4.0~qE-?l I.OI2F-~ ?,~Or-O?---=.OOF-O? ~.69~E-6&

FNERGY GROUP (MEV) B,OOF O0---l,OOE Ol 6 . 5 0 F O 0 - - - 8 . O O E O0 ~,OOF 0 3 - - - 6 , 5 0 P oo 4 . 0 0 E O 0 - - - K . O O E O0 3,00F O0---~,OOF oo 2 . 5 o E O 0 - - - 3 , O O F O0 2 . 0 0 F O 0 - - - ? . 5 0 F O0 1 , 6 6 F O 0 - - - ? . O O F O0 1,33E 0 0 - - - 1 , 6 ~ c O0 I,OOF O 0 - - - I , ~ ? E C~ 8.00F-OI---1.00F on 6,00r-O~---R,OOE-O| ~oOOE-OI---6.0OF-OI ~,OOF-.OI---&,OOE-O! ? ,O O E - O I . . . . 3.OOF-Ol I.OOE-OI---?.OOE-0! S,OOF-OT---I,oOF-OI

TABLE 7.12 GAMMA-RAY GROUP TPANSM[SSION FACTORS FOQ A I 0 0 CM TSF CONCRETE SLAB ENERGY AND ANGULAR DEPENDENT IRANSMISSION FACTORS GAMMA-RAY DOSE EQUIVALFNT tO0 CM TSF CONCRETE SLAB GAMMA-RAY GROUPS (REMS/(ISOURCE GAMMA-RAYI/(CM=$SI)|

'..,J

,,,

:::o

2

FNFRGY GROUP IMFV) ~.OOF O 0 - - - 1 . 0 0 E O! ~.SOF O 0 - - - P , O O F OO ~nF O 0 - - - 6 . F O P 00 ~,OOF O~...... % 0 0 E O0 ~.GOF O 0 - - - ~ . O O F O0 ~.~OF O 0 - - - 3 . 0 0 E O0 2°00~ O O - - - ? . 5 0 E O0 | . ~ 6 ¢ O 0 - - - ? , O O E O0 1.~F O0---|.6~F O0 I°OOr 00---1.33E O0 8.00E-OI---I.OOE O0 ~,OOE-Ot---8°OOE-01 4.OOF-Ot---~.OOF-O~ 3.OOE-O1---~.OUE-01 ~.00F~O~---=.OOE-O! t°OOE-O1---?.OOF-O! KoOOE-O~---].O0~-O| ~.OOE-O2---¢.OOF-02

~N~L c ! MU= O,Qg~4 l.bTOF-l~ P.250£-~4 ~.~62F-l~ R.a~E-t~ I.QOIF-15 3.0=4F-1~ ~.~3F-17 7,15~E-19 o.B?IF-|O 5.5o7F-20 |.~32E-21 7.103F-2~ 1,208F-2~ ~,133F-27 ?.73FF-2~ ~.?Bl~-~ 4.FBB=-~ 0.0

~NGL~ ~ MI.I= 0 . q ~ 4 6 1.107E-[3 %~0BF-14 1.972F-14 ~.~5?E-tS 1.tqOC-|5 1.662¢-t5 3.0?4E-t7 ~°BqBF-|q &.~6~-lq ~.02~E-~O ~,633P-2Z 4.187~-~? 8.387E-25 I.~2F-27 ~.OR~E-? a 4.~q3F-~ 3.~P?E-~q 0.0

~NGLF ~ MU= 0 ° P 6 5 6 4,B28E-14 2,21~-!4 7.Tq~F-[~ 1,~7Rr-1~ 4.007£-16 ~,~ZIF-17 9.~1~-lR |,|[~F-~B t.~3~-l~ I.O?~P-?O ~.086¢-72 1.~4S~-~ &,~I7F-25 7.q~K¢-?R ~,~IF-?O ~.~F~F-~? 2.~OOE-~O 0.0

ANGLF ~ ~U = O. TSSO l,Ig~E-14 ~.156E-15 1.701F-15 ~.O02F-|~ 7°711E-17 q.601F-18 l.BB3F-tB ?.050E-lq ~.O[1E-20 2,939E-7l 8.574E-23 6,76tE-24 2,457E-25 ~,Q4~F-?8 8.~35E-?0 ?.82AE-~? 1,~2~¢-~o 0.0

ANGLF 5 MIJ= 0 , 6 1 7 q 1.303E-15 ~,~45E-16 1.780E-l~ &.~7~F-|7 B.8OOE-I~ 1.136E-l~ 2.278E-tg 3,236E-20 ~.582E-21 ~,t~E-?2 2.113E-23 2.174E-24 1,I~BE-25 1.8)0F-28 5,148F-30 2.11~E-32 l,12~F-sq 0.0

ANGLE 6 ~U = O°&5~O 6.503E-|7 3,498E-17 1.~60E-17 5.0QBE-]B 1.372E-18 2.205E-lq ~.819E-20 7.238~-21 1.215E-21 1.220F-27 ~,205E-24 6.~37E-2S A,q78E-26 7, POBE-29 2.qT~E-~O I,56bE-32 2.3qOE-Sq 0.0

AN GL E 7 MU= 0 . 2 8 1 6 8.553E-18 B.49|E-19 -1.175E-18 -8.696E-lq -3.465E-lq -6,SqbE-20 -1.366E-20 -1,54iE-21 -7.OTOF-23 |°5~7E-2~ 1.0636-24 1.997F-25 2,032E-2b ~.238E-2q 1.667E-30 1°150E-32 1.281E-Sq 0.0

ANGLE 8 MU= O.OgSO -9.452E-XB -6,086E-18 -3.143E-18 -1.0~8E-18 -~.qBOE-|9 -4.495E-20 -9,113E-21 -1,066E-21 -~.056~-22 -~,~23E-25 1,786E-25 6.001E-26 7,B77E-27 [,317E-29 8.950E-31 8.201E-33 8.176E-60 0.0

SCALAR ~OJOINT 1.774E-16 8,380E-t5 3.06~-15 8,~;~E-[8 1.7;-3F-16 2.501E-17 4.55~E-[8 5.~18~-19 7.08[E-20 ~.OqTE-Z| |,42~E-22 7.616E-2~ I°923E-25 3.20~E-28 6.188E-30 2.079E-32 !.735E-59 0,0

TABLE 7 , 1 4 GAMMA-RAY GROUP TRANSMISS|~N FACTORS FOg A ?00 CM TS~ CONCRETE SLAB ~ GBMM~-RAy DOSE EQUIVALSNT 200 CM TSF CONCRETE SL~B ENFRGY AND AN~LAR PFPFK'DFNT T~A~SMISSI3N ~ACTnRS GAM~A-RBY Gq~UPS IRF~S/iISOURCE GAMMA-RAY)/ICM*~2)))

rb

(3

R. W. Rottssin, F.A.R. Schmidt, Neutron .dttd gamma.ray tran.~port t/trough cotwrele .~lah~

I

i ]"'lii~

T

~--

] l~----I

i i il ~;

i0-7

,°' I ~o~

335

m

SOURCESAT NEARLY NORMAL INCIDENCE

i

i

I0-8

Ocfa

!

E

10-9

¢/I

,5

/

i

l"d

t0 z

30

t0-40 o

~0 ~ 10-tt

o

o CO Z

~0 °

o

t0-~2

I.-LL

o o

LU

Z

~0-~

o

t0-~3

lad

-

¢-,,1

~00

I---

tO-Z

10-t4 _.1

10-~3 t 10-2

0

tI~t_LLLLLL

10-~ 100 INCIDENT NEUTRON ENERGY (MeV)

t0 I

'"

W

i0_45 EC

o W

10 -16 Fig. 1. Ratio of tissue dose (rems) due to secondary gamma rays to tissue dose (rems) due to neutrons a:~ a function of incident neutron energy lbr various col,crete ~iab thicknesses and nearly normal incidence.

=~

150

~,

i0-q7

iO-q8

anaounts to integratingS(E,/a) over each energy group and angular interval of interest. As mentioned earlier, the energy group structure which was used in the calculations, and into which we must partition a source, is given in tables ! and 2. The cosines and cosine intervals widths (weights) for which the r(T; E i, lai) are specified are listed in table 4. These correspond to Gattss-Legendre quadrature of order 16 to approximate the integration over the angular variable in the discrete ordinates equation. Hence S(E, In) can merely be evaluated at ~ul and multiplied by the corresponding weight to represent the number in/-th cosine interval. An example of the use of transmission factors is shown in tables 7.1 through 7.14. The last column on

I L~!lL I d10-49 10-: ~

IO-4 ~00 404 'NCIDENT NEUTRON ENERG Y (Me~l)

FiF. 2. Tissue dose equivalent ( r e m s ) d u e Io n e u t r o n , ,~ a function of incident neutron energy f o r vari~uts cont rclc , , b b thicknesses and nearly normal incidence.

the right of these tables is titled "Scalar adjohu". For a i-th source group, this value.A [T;Ei) is I b e dose equivalent transmitted through the slab d u e ~, :~ plane isotropic source of particles in lhat grot~p ]],c

R. I#. Roussin, F.A.R. Schmidt, Neutron and gamma-ray transport through concrete slabs

336

t0-7

10-7 •

'

i0-8

AT NEARLY NORMAL INCIDENCE

o

I1

II

I

SOURCES

~ ' ~

I I IIlIIl[ I I 1 li~it I I l PLANE ISOTROPIC NEUTRON SOURCES

~l

10 - 8 L

:}

,IO-9

,_._~IO- 9 (%1

E

ill

b-X:~.~

TO 15 MeV SOURCE

~2.2

\

!

!

E

~. 1o-'2 cr F-

45 cm " ~ " t 0 - IO EfJ

30

i0_4 q

50

_ I:: ;

z I ° - ~ ~O F-LO

XI

t

t o ~4 i:

:1 I

t.12 TO 5.06eV • SOURCE. . . . . . . .

~o-15

g

o

29 TO t01eV SOURCE

O tuu~ t O - ~ 6 k-O

ca !O-~7

I-

ro'~ u'~

t

100 t0 -14

I-Z

LI.I _.1

~0 i0-~5 LU

I!-

ku 03

~0-20 0

t0-13

O htlJ

tO-~8 I:-7 I0-~9

75

O ne I--

;

:t

THERMAL SOURCE

E . O3".t0-42

i

'

i

!

1

75 1OO !25 SLAB THICKNESS (cm)

150

'175

200

i

25

50

I.ig. 3. Tissue dose equivalent (reins) due to n e u t r o n s as a function o f concrete slab thickness for n e u t r o n sources at n c a r b normal incidence.

values a~e normalized to one particle per cm 2 entering the slab .and were calculated from the sum

o IO_i 6 lid O') I--

150 i0-t7

~O-18

8

A ( T: k' i) = ~ /=1

( 1 ) ~) rl T: Ei, ~;) ,

t ° - 2 ° t 0 ~- 2

where we have assumed a plane ~3otropic source. "Io ob[am the dose equivalent "..lue to neutrons from a plane is,_mopic energy-dependent neutron source, we would lake 22

22

D(z 1 ~ = ~ S ( k i) ,al:~ A (T; EiJ = ~ i=I

200

iO-19

1 l I 111111 J 11 ! t I[11111 t0-i t0 o INCIDENT NEUTRON ENERGY (MeV)

I0 t

Fig. 4. Tissue dose equivalent (reins) due to n e u t r o n s as a f u n c t i o n o f incident n e u t r o n energy of plane isotropic sources for various concrete ,'.;lab t)" .ucknesses.

8

~ S(Ei) 2rEi w~ r,,(T; E i, ta/) ,

i=1 /=1

(8)

R. I4I. Roussin, F.A.R. Schmidt, Neutron and gamma-ra), transport through concrete ~ta/,s

~0-7 tO-8

=

I

%,,.

I I T'-"

[

1

=_---

I

PLANEISOTROPICNEUTRONSOURCES

\ ~o- 9

10-7

I 1

t - - - -

-

3 ~7

:

-2

LI

TO]AL NEUTRON

tO-e

0

E

l

! --i

z

-

4

"~.e°t0-'I0

-t tO-9

E

=

m ~0-t~: z

--2-

0 ne

K

r&-n .s,)

I

12.2 TOISMeV SOURCE 10"t°

4

I

._~ ~0-~3 Z

--

E ID

,., t O - ~ 4 I'--

,'-, t0-~ k-2' uJ .J

--

~',0 "~5 N.

=

I

I

~ I0-16

THERMAL SOUR(:[

bJ CO

l,,d 03 0

o Q ~ i0-17 I-

t

tO-IZ

FISSION SPECTRUM SOURCE

10-¢3

i0-~8

I0-19 ~tO -~4

i0-20

.i

0

25

I

50

I

I.

1

,

75 1OO 125 150 SLAB THICKNESS (cm)

I

17L

...J

200

Fig. S. Tissue dose equivalent (rems) due to neutrons as a function of concrete slab thickness for plane isotropic neutron

tO-~S

I

0

1

50 100 SLAB T H I C K N E S S

l

~50

__

200

(era)

s o u r c e s .

where S(E) is the spectrum of the source neutrons with S(Ei) (efined as some average value in AE i. Some result, will be given later for the case o f a plane isotropic fission source. The user should be aware that some inaccuracy will result due to the fact that eaergy group representation of the source is necessary. Better results are obtained if the S(Ei) are chosen b y weighting with a suitable function. The ideal weighting function would be ~0+(.T; z o, E, #). However, if this were known, we weuld have no need for using the group transmission factors. A comparison o f forward and adjoint results (see table 6) indicates that source weighting is less

Fig. 6. Total and neutron dose equivalent (reins) as a function of concrete slab thickness for 12.2 to ! 5 McV and lission neutron sources at nearly normal incidence. important if the source energy distribution of interesl spans a large range of energy {such as a fission sourcc I. In using the m, nsmission factor tables, two uthm areas of apparent inaccuracy should be noted. ] h e ft,-st can be seen by a comparison of total and neutr,'n dose equivalent for the 15 cm ddck slab (table 7, I ). For source groups between 0.5 and 5 MeV, it wi[l be noted that in some cases, the neutron dose equals or exceeds the total dose for a given source group. This results, in all probability, from the use of the

338

R. I¢. Roz~ssin, F.A.R. Sch midt, Neutron and gamma.ra;, transport through concrete slabs

10-8

I

~O-e

I

oTHIS WORK ~=MOMENTS METHOD TRUBEY AND EMMETT

~0-9

,o-~!,N

o THIS WORK,t2.2 TO]5IdeVSOURCEI II SPIELBERG MONTE CARLO, 14 MeV SOURCE

% u

co

,o-,o

J

I0 -12

5

-i

-

4

':--____"

i

_J >

3ONCRETE SLAB tO-~

I

5

SOIL HALFSPACE

8, C3 t'r IO-qZ I "

-----/ --.

Z 0 (r

t0-43

(.9 >rr <[ r'~ Z O

u~ D IO "t4 , -

z

_i

_._

O taJ taJ

~.__

0f-~

\

l-

-

(2Y tJ

t

I

\\ -

EID

__J

I

~

--

,o, iO-14

I0 -15 pi

t0-~6,

o

~00

200 500 400 CONCRETE THICKNESS (g/cm 2)

500

lO-4S

o

.J 50

I ~oo

I q5o

200

DISTANCE (era)

Fig. 7. Comparison of adjoint discrete ordinates and moments mcthod [81 calculations of neutron dose equivalent (rcms) from a plane isotropic fission source as a function of concrete thickness, source normalized to one neutron in forward direction.

Fig. 8. Comparison of adjoint discrete ordinates and Monte Carlo [91 calculations of secondary gamma-ray dose as a function o f concrete or soil thickness for neutron sources near 14, MeV and normal incidence.

differently weighted cross sections for the two sets. In any case the two numbers agree within three significant figures and, for practical purposes, the difference between the two is negligible for this small slab thickness. The other area of inaccuracy occurs for source gamma-ray groups for slab thicknesses 75 cm or greater for the two most grazing source angles, /z7 = 0.2816 and #8 = 0.095. The table entries are, in some cases, negative numbers. The cour.terpart o f this result is the occasional negative angular fluxes obtained by forward discrete ordinates calculations. For

gamma-ray group~, values found in tables 7.11 through 7 . 1 4 t o r t h e s e slab t h i c k n e s s e s are s e e n to d e c r e a s e

rather rapidly with decreasing/z and, in general, the contribution for these directions is very small. It is

possible ~o plot the transmission factors as a function o f # and e~;timate, by extrapolation, the values for the last two cosines. Fig. 1 gives the ratio of tissue dose* due to secondary gamma rays to tissue dose equivalent due to * The quality factor for converting gamma-ray dose (rads) to gamma-ray dose equivalent (rcms) is taken as unity.

R. h,t Roussin, F.A.R. Schmidt, Neutron and gamma.ray transport throttgh com'rete slabs

40-8 _ _ _

i0-9

10 0

I

o THIS ¢¢0RK,6.56 TO 0 . t 8 MeV SOURCE II SPIELBERG MONTE CARLO, 8 MeV SOURCE --~

b- - - - T -

T- . O

~t=1.0

it ;

IO-!

U

8

_,

I0"2

g,

\

~

o\

. r

-

.r

DOGGEr- AND B~AN, MONTE CARLO,N.25 MeV

.'ok o

,4

E

~¢= 0.9894

o i0.3 $Z

SLAB _1

.

THiS WOIRK i.OO TO I ~5 Ve',' ,~

• ii

8Q

10-t!

>

n.-

/..%=

t0-4

0 uJ

\

tl.I

SOIL HALFSPAC

~) 10 - ~ '

0

),,. ,¢I n-

,u.B=0.095C

10-5

9

,i

,q ¢

tO_l 3

=--

10-6

i.9 > ee

Z 0

NO-7

w

0

I 0

50

....

L,,

100 DISTANCE ( c m )

I 150

ZOO

Fig. 9. Comparison of adjoint discrete ordinates and Monte Carlo [91 calculations of secondary gamma-ray dose as a function of concrete or soil thickness for neutron sources near 8 Me'V and normal incidence.

neutrons as a function of incident neutron energy for various TSF concrete slab thicknesses and nearly normal incidence. The values plotted are r(T; Ei, Pl ), the ratio of gamma-ray to neutron dose due to source neutrons in the i-th energy group and at nearly normal incidence. They are computed from

r(T; Ei, ~ I ) = lrt(T;

Er tal)

- 1"n(T; Er/al)] / [~'n(T;

El' P l ) ]

'

where subscript t or n refers to total or neutron dose transmission factors, respectively. The transmission

50

100 150 200 CONCRETE THICKNESS (g/cm2)

250

Fig. 10. Comparison of Monte Carlo [ 10i and adjoint discrete ordinates calculations of gamma-ray dose trar, mission probability as a !'a:action of concrete slab thicL aes~ for gamma-ray source e,mrgy near 1.25 MeV and vafio'Js angle~ of incidence.

factors used are found in the first column of tables 7.1 through 7.7. The pronounced dip in the taiio at 2.4 MeV is due to the valley in the oxygen cross section near that energy. The proportion o f the total dose attributed to gamma rays increases with increasing slab thickness and decreasing source neutron energy. The gamma-ray dose exceeds the neutron d~)~,e equivalent for all combinations of slab thicknesses greater than 50 cm and neutron source energies le.':s than 1 MeV. For the 200 cm thick slab, the gammaray dose exceeds the neutron dose equivalent tbr all source neutron energies. For the 15 cm thick slab, ~he total equals the neutron dose equivalent to within about 0.2% for source neutron energies betweetl I and 4 MeV. The variation with incident neutron energy of

340

R. W. Roussin, F.A.R. Schmidt, Neutron and gamma.ray transport through concrete slabs

transmitted tissue dose equivalent due to neutrons for nearly normally incident, rn(T; El, 0-1), and plane isotropic,An(T, Ei), sources is shown in figs. 2 and 4, respectively. For neutron source energies above 0.1 MeV, tile transmitted tissue dose equivalent increases rather significantly with increasing enmgy and slab thickness. The valley in total cross section near 2.4 MeV causes the peak in the curves at that energy, Below 0.1 MeV th,: variation of transmitted tissue dose equivalent with neutron source energy is less pronounced. Figs. 3 and 5 show rn(T; El, ktl) and An(T: Ei), respectively, as a function of concrete slab thickness. The curves show this slaw variation with source energy, especially between 20 eV and 1 i 1 KeV. In general, the An(T: El) vary less rapidly with source energy than tile rn(T; El, ~ 1 )" For example, the peaks in the curves near 2.4 MeV are not as hi#l. Also, tile A n ( T;/r:'i) a r e smaller than the r n (T; E i, t.t l ) for a given Ei and T. Fig. 6 shows the comparative attenuation of 12.2 to 15 MeV and fission sources as a functior, of concrete slab thickness. The f r a c t i o n , i" fission source neutrons in each group is shown in table 5. We see that the gamma-ray c o m p o n e n t increases more rapidly for the fission source than for the higherenergy 1.2 to 15 MeV source.

5. Comparisons with other calculations To test the reliability of the adjoint calculations, several 40-group forward, i.e., eq. ( 1 ), calculations were performed using the ANISN cose. These were for 12.2 to 15 MeV sources at nearly normal incidence and the neutron and total doses eq:~ivalcnts were computed m the rightmost in~,erval. The 40.group cross sections used in the forward calculations were generated by collapsing the 122 -group structt re by ~cighlmg with fluxes c o m p u t e d in a 75 cm thick slab ~ltl~ a nearly normally incident soarce in the 12.2 to 15 Me V group. The comparison of forward and adjoint resul~s are shown in fable 6. The neutron a d j o i n l result is about 10% lower than the forward result fo~ the 200 cm thick slab. For all other cases, the results agree within 4% or ross. We feel that the comparatively close agreement between forward and adjomt results over the entire range of slab thicknesses

100

Id

•

~

--~t, " ~

o THI~, WORK, ~ t = 0 . 9 8 9 4

- - - - DOGGETT AND BRYAN,

-~ tO-t

z il

IO-2 I

g ,~

~o'~i

g

iO-4

t.r.

k

9 I,-o:

iO-5 0

200 300 400 CONCRETETHICKNESS ~g/cm z)

t00

SO0

Fig. ll. Compaxiso~_of Monte Carlo [ 10] and adjoint discrete ordinates calculations of gamma-ray dose transmission probability as a function of concrete slab thickness for nearly normally indicent gamma-ray sources with energies near 10 and 0.66 MeV. is substantial verification that the adjoint method produces reliable resalts. Some results are also compared for fission source calculations. Some forward runs were with the forward weighted cross sections mentioned above (12.2 to 15 MeV source) and some with fissionsource-forward weighted cross sections. Differences between the forward-forward and forward-adjoint comparisons can most probably be attributed more to tile use of differently weighted cross sections rather than defects in the adjoint calculations. The fission source S(Ei) &I:"i given in table 5 and the transmission factors ';n(T; E i, 0.1) were used in eq. (8) to calculate the neutron dose equivalent transmitted through slabs of various thicknesses. This is compared to m o m e n t s m e t h o d results of Trubey and E m m e t t [8] in fig. 7. Their results were doubled so that the comparison could be on the basis of 1 source neutron per cm 2 in tile forward direciion. Since the m o m e n t s m e t h o d results are for an infinite

R. W. Roussin, F.A.R. Schmidt, Neutron and gamma.ray tran,~port through concrete s'labs medium, we expect them to be higher than slab results due to increased scattering contributions at a given point. The attenuation characteristics are seen to be quite similar in the 200- to 400-g/cm 2-thickness region. The concrete composition used for the moments method calculation is given in table 3 under the heading type 3 concrete. To compare secondary gamma-ray results we refer to some recent Monte Carlo calculations by Spielberg [9] ,using the UCN-SAM-2 [10] Monte Carlo computer code. The results are given as a function of depth in a halfspace of soil with unit density and a water content of 10% by weight. The composition is give~, in table 3 for the soil with density 1.0 g]cm 3 and for a similar soil with density 2.3 g/cm 3 . Figs. 8 and 9 show comparisons of secondary gamma-ray do-e as a function of concrete or soil thickness for nearly normally incident neutron sources with energies near 14 and 8 MeV, respectively. For both source energies Spielberg's results are higher for distances near the interface in which the corresponding slab is thin. Thin slabs reduce the volume where gamma-ray production and scattering take place in comparison to the halfspace. In addition, the soil has a greater water content (10% as compared to 6%) which should shorten the distance for slowing neutrons down and thus increase the production of capture gamma rays near the surface. The attenuation beyond 150 cm appears to be quite similar for both soil and concrete. Some comparisons of attenuation of primary gamma-ray sources were also made. Doggett and Bryan [ 11 ] recently published tables of calculated dose transmission factors to: gamma rays incident on concrete barriers. The data reported is based on Monte Carlo calculations by Berger, Eisenhauer, and Morris. Fig. 10 shows a compa,ison of the gamma-ray dose transmission probability, PT" as a function of concrete slab thickness for gamma-ray source energy near 1.25 MeV and various incidence directions. The gamma-ray dose transmissim, probability for a gammaray source in the g-th energy group and/-th direction is given by

(r; g, ,g s%, ?

or

PT(IZg'la/) =

w,.

~o(T ; zo , Eg, la/) AEg W/ F(E g) '

6. Notation ~;(T; z, E,/a)

= differential particle fluence with energy E and directi~m p. per unit energy and cosine interval al h>cation z in a 5lab ~lthickness T ") (pamcles/cm--!vleV-cosine~ = slab thickness {,:ml -- detector reading al I,wali~lJ -Crems) = detector response fttllCl]olt at energy E (rems)/(particle/cm 2 .p = source, the differential time integrated currep.' of p,:r~ icles x~.ill energ.~ E and dirccl i~m/a, per uml •

T

D(z)

s(f,u) (9')

la/ rye.T; E , ~i) F(Eg)

where ,ul is the incidence direction cosine, f'(t-.g) the gamma-ray tlaence-to.dose conversion factor ;, u the g-th energy group and r.r(T; Eg, a,/)is |h~ tra.tsmission factor (tables 7.8 through 7.14} fo~ a slab ~>l thickness T due to a gamma-ray source m .,]w ~,,-lhe energy group and j-th direction. In fig. 10 we used data for the !.00 to 1.33 MeV gamma-~ay gr~mp. and values o f o / = 0.9894.0.458. and 0.005, ~,nd a v a l u e F ( k i ) = 6 . 2 5 X 10 10rads/(y, cm.t. The Doggett and Bryan data plotted are for a ~,,u~c~ energy of 1.25 MeV and incidence direcUon c,~sm<,, ,t = 1.0, 0.5.0.4, and 0.1. The l)ogge~t-Bryan data :~Ee tbr slab thicknesses from 0 to 70 g/cm 2 {about 4 mean-free-path-lengths) and the results of this st udy for slab thicknesses from 35 to 460 g/cm 2 . Agreemem is seen to be very good in the region of comnron thicknesses. Fig. 11 shows more comparisons be*wem~ this work and that of Doggett and Bryan. Again. the transmission probability, P r . is shown as a tonction of concrete thickness. The Dogget-Bryan values are for normally incident gamma.rays of energy 0.66 awl 10 MeV. They are compared with resuhs of *.his study for # = 0.9894 and energy groups 0.6 to 0.8 MeV and 8 to 10 MeV. Again, very reasonable agreemen~ is noted.

F(E)

Pr(Eg,uj)

341

342

energy and cosine interval, incident on a slab surface (particles/cm 2MeV.cosine) = detector reading integrated over a volume V (rem-cm 3) = energy representing the i-th group

R E.

R. W. Roussin, F.A.R. Schmidt, Neutron and gamma-ray transport through concrete slabs

l

(MeV)

= width o f i-th energy group (MeV) AE i = cosine representing the ]-th direction = weight or cosine interval associated V~~. I with ].th direction = source effectiveness distribution o f ,;+1 T; z o , E i, bt/) particles in the i-th energy group and/-th direction incident on the surface of a slab of thickness T (rem-cm 3)/(particle/cm2) = dose equivalent transmission factor r~T:Ei, P/) for particles in the i.th energy group and ]-th direction incident on the surface o f a slab o f thickness T (rems)/(particle/cm 2) = dose equivalent transmitted A ( T : E i) through a slab o f thickness T due to a plane isotropic source incident in the i.th energy group (rems)/ (particle/era 2) = used as a subscript for ~p+, r, or A and refers to total dose equivalent (from neutrons plus secondary gamma rays) due to neutron sources -- used as a subscript for ~p+, r, o r A and refers to neutron dose equivalent due to neutron sources = used as a subscript for ¢+, r, or A and refers to gamma-ray dose equivalent due to gamma-ray sources = spectrum o f fission neutrons .f ( /: ) (n/MeV) = ratio o f secondary gamma-ray to r(T:/:,'i, # I ) neutron tissue dose equivalent transmitted through a slab o f thickness T due to one neutron incident in the i-th interval and first direction P1• = gamma-ray dose transmission probability.

Acknowledgements The authors gratefully acknowledge the assistance of many members of the Neutron Physics Division o f the Oak Ridge National Laboratoryl In particular, the following people should be singled out: D.C.lrving, R.E.Maerker, S.K.Penny, E.Solomito, V.R.Cain, E.A.Straker and K.J.Yost. Also, to N.M.Greene, W.E.Ford, III, M.L.Gritzner, W.W.Engle, Jr., F.R.Mynatt, all of the Mathematics Division at Oak Ridge National Laboratory, go many thanks for their valuable assistance in producing the •group cross sections and in running the ANISN computer program. The authors wish especially to thank D.K.Trubey, Manager of the Radiation Shielding Information Center, for his many helpful suggestions and continuous support. The authors also appreciate the efforts o f Mrs. Margaret Elmore in typing the manuscript. One o f us remains in deep debt for the stimulating and fruitful hospitality he experienced during his stay at Oak Ridge National Laboratory.

References [ 1] F.A.R.Schmidt, The attenuation properties of concrete for shielding from neutrons with energies up to 15 MeV. ORNL-RSIC 26, Oak Ridge National Laboratory (1970). [2] W.W.Engle, Jr., A users manual for ANISN, K-1693 Union Carbide Corporation Computing Technology Center, Oak Ridge, Tennessee (1967). [3] G.E.Hansen and H.A.Sandmeier, Neutron penetration factors obtained by using adjoint transport calculations, Nucl. Sci. Eng. 22 (1965) 315. [4] E.A.Straker, Time dependent neutron and secondary gamma-ray transport in air-over-ground geometry, ORNL-4289, Vol. 1I (1968), Oak Ridge National Laboratory; and Trans. Am. Nucl. Soc. 11 (1) (1968) 410. 151 W.N.Snyder and J.Neufeid, Calculated depth dose curves in tissue for broad beams of fast neutrons, BriL J. Radiol. 28(1955) 342. 16] tt.C.C.Claiborne and D.K.Trubey, Gamma-lay dose rates in a slab phantom, Trans. Am. Nucl. Soc. 12 (I) (1969) 383, ORNL-TM-2574, and Nucl. Am. Tech. 8 (5l (1970) 450. [71 F.R.Mynatt and W.W.Engle, Jr., Group averaging of cross sections for multigroup adjoint dir,crete ordnates calculations, Neutron Phys. Dw. Ann. Progr. Rept. May 3 !, 1967, ORNL-4134, Oak Ridge National Laboratory (1967) p. 78.

R. W. Roussin, I,:A.tL Schmidt, Neutron attd gamma-ray transport through concrete slahs [8] D.K.Trubey and M.B.Emmett, 5ome calculations of the fast neutron distribution in ordinary concrete from point and plane isotropic fission sources, ORNL-RSIC-4, Oak Ridge National Laboratory (1965). [9] D.Spielberg, Shielding by soil against neutrons and secondary gamma rays, to be published in: Engineering Compendium on Radiation Shielding, Vol. 1I, Shielding Materials and Design, eds. R.lt.Jaeger et al. (SpringerVerlag, New York).

~43

[ 101 i-.S.Troubetzkoy, UNC-SAM-Z: A I OR1 R,',,N \lor.~,. Carlo Program Treating I mlc-Dci~cndcnt Ncutr~n :rod Photon Transport Through Matttr. I?N(-5157, United Nuclear Corp. t 1966). [ ! i ] W.O.Doggelt and I .A.Bryan, Jr.. I h,~,~rctical d t ~ lr:~,mis.,ion and reflection probabilities lot ~.2 10.~ MeV photons obliquely inciden~ on finttc concrete barter r~, Nucl. Sci. Eng. 39 (1970} 92.