Ann. nucl. Energy, Vol. 14, No. 12, pp. 643~551, 1987 0306-4549/87 $3.00+0.00 Printed in Great Britain. All rights reserved Copyright © 1987 Pergamon Journals Ltd

STUDY OF SPACE-DEPENDENT FAST-NEUTRON SPECTRA A N D TRITIUM BREEDING RATIO IN

DIFFERENT ASSEMBLIES OF 7Li, 6Li AND NATURAL Li

M. MALIK, F. AHMED and L. S. KOTHARI

Department of Physics and Astrophysics, University of Delhi, Delhi-110007, India

(Received 29 June 1987 ; in revised form 31 July 1987)

Abstract--Using diffusion theory and the eigenfunction expansion method, a detailed space-dependent study of fast neutron spectra has been carried out in 7Li, 6Li and natural Li assemblies of dimensions 100 x 60 x 60 cm 3 and 30 × 60 x 60 cm 3. Values of total (space-averaged) tritium breeding ratio (TBR) have been obtained for these assemblies. BARC-892, a 27-group data-set was used for these calculations.

The results of TBR for the smaller assembly have been compared with the corresponding experimental and calculated values of Takahashi et aL (1984). We find that the present values of TBR are in reasonably good agreement with the above experimental results.

INTRODUCTION crepancies between the measured and the calculated results were attributed to the uncertainties in the meas-

Because of the growing interest in the D-T fuel cycle uring techniques and in the nuclear data-files. in fusion reactors, study of spatial dependence of Using a simple model based on multigroup tritium production rate (TPR) and tritium breeding diffusion theory, eigenvalues and eigenfunctions ratio (TBR) in simulated lithium blanket assemblies approach, detailed studies of both space- and time- is becoming very important, dependent behaviour of fast neutron spectra in natu-

Measurements and calculations on neutron spectra ral uranium (Mohan et al., 1982a,b), enriched and and TBR have been made by several workers for depleted uranium (Mohan et al., 1985), thorium various blanket geometries. For a cylindrical lithium (Mohan et al., 1986), Th-U mixtures and iron assembly, Herzing et al. (1976) determined only TPR (Bhateja et al., 1985) have been made. The results whereas Kuijepers et al. (1977) and Profio et al. (1981) based on this simple model when compared with have made studies of neutron spectra as well. Experi- transport calculations were found to be quite accur- ment on a spherical assembly was made by Fritcher ate. Furthermore, earlier discrepancies in measured et al. (1978) to measure the radial dependence of and calculated results in natural and depleted U-sys- tritium production and Bachmann et al. (1978) carried terns were successfully resolved. Particularly, this out measurementsandcalculationsofangularspectra method has been found useful in studying the and TPR for the same assembly. These workers (with approach to equilibrium or pseudo-equilibrium of a the exception of Profio et al., who used the DLC-37 fast-neutron field in multiplying and non-multiplying (EPR) data file for calculations) have mainly used systems. We may also mention here that it requires the ENDF/B-III data-file, Monte-Carlo and discrete much less computation time and computer memory ordinates methods for their calculations. Recently, as compared to other calculational methods. In this experiments on cylindrical and spherical assemblies paper, using the above method, we report some of the of Li and Li 20 have been carried out at JAERI (Sugi- results of a detailed study of space-dependent fast- yama et al., 1984; Takahashi et al., 1985; Maekawa neutron spectra and of TBR in assemblies of natural et al., 1986) and TPR as well as neutron spectra were Li and its two isotopes (6Li and 7Li). The results have studied extensively. Takahashi et al. (1984) have also been obtained for two assembly sizes : 100 x 60 x 60 studied TPR and TBR in 7Li and 6Li for a slab cm 3 and 30 × 60 x 60 cm 3. The multigroup data used geometry. Here too, these workers have compared hereis a BARC-892 (1976) cross-section set evaluated their experimental results with calculations using from the ENDF/B-III library. The values of TBR group cross-sections derived from ENDF/B-IV and for the smaller assembly have been compared with JENDL-(3PR1; 3PR2) data-files. In all cases, dis- the corresponding measured and calculated values

643

644 M. MALIK et al.

reported by Takahashi et al. (1984). We find that ~ [ ~Z ( ~ the present values of TBR are in reasonably good agreement with the above experimental results. I

METHOD OF CALCULATIONS I

For the steady-state case, the transport equation in I • the diffusion approximation can be written as : I I

i - D(E)V 2¢p(r, E) + Z,(E)cp(r, E)

= dE 'Y~(E '~E)x4~(r ,E ' )+S(r ,E) (1) Y

where :

~b(r, E) = neutron flux at the position r per unit ~ . / _ ~ energy interval about E, b

'U S(r,E) = external source of neutrons at space / point r per unit energy interval about E, ×

D(E) = 1/[3Ztr(E)] ~ diffusion coefficient for Fig. 1. The rectangular assembly. neutrons of energy E,

Ztr(E ) = macroscopic transport cross-section for neutrons of energy E,

Zs(E' --* E) = macroscopic scattering cross-section Hence equation (1) for q~(z, E) for z > 0 becomes : for a neutron going from an initial energy E' to a unit energy interval _D(E)d2~k(z, E) + D(E)BZI (E)49(z,E) about E, dz 2

Et(E) = macroscopic total cross-section for r ~ neutrons of energy E. For Li this +Zt(E)dp(z,E) = J0 dE'~.s(E'~ E)(o(z,E') should consist of the following partial cross-sections : ~0~

•t = Zel"F ~inel"[- ~c-F'~n. 2,,-~- En.p~- ~'~TP + dE'Z~(E' --. E)dp(z, E')

(Here Ze~ and Zi,eL are the macroscopic Vcos {xBx(E')}" cos {yB~(E')) ] cross-sections for elastic and inelastic × E cos {xBx(E)}'~os{yBy(E)} -- 1J (3a) scatterings respectively. Ec is the macroscopic capture cross-section, where the transverse buckling B~(E) is defined as: E,,:, and E,,p correspond to macro-

Bx(E)+By(E), scopic cross-sections for (n, 2n) and B2(E) = 2 2 (n,p) reactions respectively while Zvp with is the macroscopic tritium production

cross-section). B2(E)=I[a+I.~22tr(E)]] 2 However in 7Li, Y~i.~l includes Y~TP besides the cross-

section for the (n, n'7) reaction. To calculate total tri- and tium breeding ratio in 7Li, we have taken Z~,o~ to be equal to ETp above 2.8 MeV which is the threshold B~(E) = I [ ~ 12 energy for tritium production in 7 Li. b+ 1.422,~(E)]

If we consider an assembly with dimensions a, b (We may mention here that B 2 (E) corresponds to the and c in x, y and z directions respectively, with a point source at the origin (Fig. 1), the flux ~b(r, E) can be fundamental spatial mode and higher spatial modes written in the form : have been neglected).

One observes that the second term on the right hand ~b(r, E) = cos [xBx(E)]" cos [yB~(E)]" dp(z, E). (2) side of equation (3a) is an oscillating term. We find

Study of space-dependent fast-neutron spectra 645

that for all values of E considered here and at all Since the eigenvalues of a triangular matrix are points in the xy plane, its value is smaller by some simply the diagonal elements, we have :

orders of magnitude than the contribution of the first k~ = ]~/D i (9) term (see also Ahmed et al., 1971 ; Kumar et al., 1973, 1978). We therefore neglect the second integral and where E~ = [{E~+Di(B'~)2}-Y~ ~i] is the removal write : cross-section for group i.

The eigenfunctions associated with these eigen- d2~b(z, E) values are :

--D(E) ~z 2 'y: + D(E)B ~ (E)~b(z, E) + Et(E)q~(z, E) E{'~Y"/D~

(~in j = l for i > n, (10a) = k, ~ - k ~

f: = dE'Zs(E' ~ E)~(z,E'). (3b) = constant, for i = n (10b)

This equation in the mult igroup form can be written = 0, for i < n (10c)

as The coefficient b. 's can be obtained in terms of a. 's by s using the extrapolated end-point boundary condit ion : d 2

- D' d~z2 ~b'(z) + [ZI + Di(B~) 21~b' (z) = ~ E j~q~(z) j=, qS'(?) = 0. (1 i)

(4) F rom equation (11) and (6), we have:

with b. = - a. e - 2ke. (12)

# (z ) = ~b(z, E) dE, (5a) Therefore with ~b~'s given by equation (10) the group , flux can be written as :

= --~ dE dE'E~(E' --, E)c~(z, E') 4)i(z) = a.c~. e - ~ : ( l - e ak.(e-~)), (13) 4~J~, .,'n " = '

(5b) where coefficient a, 's can be determined from the and initial condition :

~bi(z = 0) = ~b'0. (14)

P I e' 'dEZt(E)c~(z , E), (5c) Equations (14) and (13) give: 1

~ = ~ j ~ , i - - I

where i , j= 1,2 . . . . . N ; N being the number o f q ~ ' 0 - ~ q ~ a . ( 1 - e - E k / ) groups. We seek a solution of equation (4) in the ,= a~ - (15) form: ~b;(l - e - 2kit)

N

#(z) = ~ ' e-*: q~.(a. + b . d : ) . (6) The total flux can now be calculated using the . = ~ relation :

Substituting for ~b~(z) from equation (6) in equation ~b(z) = ~ #(z) . (16) (4), we get i

N We may also define a space-dependent decay constant 2 ~ ~ ~ 2 ~ = Z s q~. for the total flux ~b(z) as : [ -Dk, ,+{Et+D(BI ) }]q~. ~. J~' j

j=l

d which can be rewritten as an eigenvalue equat ion: K(z) = -- dzz In q~(z). (17)

N 2 i k.~a. = ~ Pjid? j . (7) The TBR is defined as the number of T-atoms pro-

:= ~ duced in the blanket per neutron incident. It can be For a fast Li system in the absence of both fission and calculated from the expression : upscattering, the matrix Pj~ will be a triangular matrix :

P:~=-~_.{~/D ~ for j < i , (8a) f fZTp(E)4)(z,E) dEdz

= 0 for j > i , (8b) T B R = ' ~ ,

JJ i i t 2 i ~ i i = [ { E t + D ( B ) }--IE~ ]/D for j = i. (8c) S(z ,E)dEdz

ANE 14:12-8

646 M. MALIK et al.

where 57Tp(E ) is the macroscopic T-production cross- We note that for 7Li, the values ofk~ remain almost section for neutrons of energy E. constant (4.4 x 10- 3 to 4.8 x 10- 3 cm- 2) below about

For the present case, in the multigroup form we can 21.5 keV (group index i > 12). This is due to the fact write : that the absorption cross-section for 7Li is almost zero

in the entire energy region whereas the elastic cross- t )

~"/Z~-p~bi(z) dz section does not show any appreciable energy-depen- "7 d dence up to 21.5 keV. For energies higher than this,

TBR - (18) ~b~ one observes oscillations in the values of k 2 which are

i due to the resonances present in the total cross-section of 7Li in the energy region from ~ 0.2 to ~ 4 MeV. We also note that the minimum of k~ occurs at the ninth energy group (i.e. 0.1-0.2 MeV) and the cor-

R E S U L T S A N D D I S C U S S I O N responding eigenfunctions are positive definite for

Using the procedure outlined in the last section, the energy groups below this, as shown in Fig. 3. eigenvalue equation (7) has been solved in order The eigenvalues for 6Li show large variations [i.e. to calculate the fast neutron spectra and TBR in as- from 103 cm- 2 (last energy group) to 10- 3 cm- 2 (first semblies of 7Li, 6Li and natural Li. energy group)] in the energy range considered. The

maximum value occurs at the last energy group Space eiyenvalues (0.025-0.215 eV) due to the large absorption cross-

The space eigenvalues k~ would be given by the cor- section (~ 940 barn) in this energy range. As rr,, responding diagonal elements of the matrix Pji becomes smaller at higher energies, while the elastic [defined by equation (8)]. These eigenvalues for natu- cross-section remains constant, the values of k~ show ral Li and its two isotopes are shown as a function of a uniform fall from 0.215 eV to 0.1 MeV. Beyond this, energy in Fig. 2. it shows oscillations as observed in the case of 7Li.

1 0 4 - -

I

I I

1 0 3 - - J ~ 7 L i

I . . . . . . . . N a t u r a l L i t h i u m

I 6 L i

10 2 ~ - - I

I . . . . . . ° . . . . ~ ' - I

I

IE ~ "7

~ . _ : I 1 0 o - . . . . =._ _

I

I -.._ ~ I- 7

1 0 - 1 _ " " : ~ 1 I I I I

. . . . . . ~ , _ - I I

i .... ":.--=. " ~ ~ ~ . : . . . . ._1 1 10-2 _ . . . . . = . . . . : , . .

I

10 -3 l I l I I I I l I 2 . 5 x i 0 -2 1 0 -1 10 ° 101 1 0 2 10 3 1 0 4 1 0 5 1 0 6 1 0 7 2 x t 0 8

E n e r g y ( e V )

Fig. 2. Group decay constants k7 (eigenvalues) as a function of energy.

Study of space-dependent fast-neutron spectra 647

1ol I- ~ and have been plotted as a function of energy in Fig. 3.

/ / - \ . , , , For natural Li, at lower energies (0.025 eV-0.1 10 ° / / / f - J MeV) the behaviour of k2 is similar to that of 6Li;

1°-1 // showing a uniform decrease in the eigenvalues with ~ / 1 1 / increase in energy. Beyond 0.2 MeV (i < 8) the energy-

dependence of k,? is similar to that in the case of 7Li. 1°-a: " ~ ' - Here the min imum eigenvalue occurs at the tenth

._ 10-3~ "~'. . / - - - - - ?Li energy group (46.5 keV-0.2 MeV). Hence as shown -e- Li in Fig. 3, the eigenfunctions corresponding to this

1 0 - 4 ~ / "~°"~/( ------6Li eigenvalue are positive and non-zero f or group /> 10. 1 0 ~ ' ~ / ' ~ " . Space-dependent spectra

t / ' " ~-6 / Neutron spectra [~(z,E)= 4;(z)/dE ~] at various

/ \ distances inside the larger assembly (100 x 60 x 60 cr[l 3) / I J t I I I\ I I of 7Li, 6Li and natural Li are shown in Figs 4-6

10° 101 102 103 t04 t05 106 107 respectively. In all cases (Figs 4-6) we find that at Energy (eVl distances close to the source plane, there is a peak

Fig. 3. Lowest mode eigenfunction as a function of energy, around source energy which disappears as one moves away from the source. The peak near the source energy is due to neutrons which have undergone only

Here, the lowest eigenvalue occurs at the first energy elastic scattering and are later on removed by inelastic group which corresponds to the energy of the source scattering from higher levels and various reactions neutrons. The eigenfunctions corresponding to this like (n,p), (n, 2n), (n, ~) etc. The other common feature eigenvalue are positive and non-zero for all energies in the spectra is that there is a pile-up of neutrons at an

10 .6 _

I o - ~ - / lO Z:.,

5o ... '-_.~-.~ I 60~ . . -r" ~ ' ~ ./ '~5 \ ... " P " - / , 2 0

_ _ . ~ ~ " 8 0 ~ . - ' - - - - ~ \ x / . . - . . ~ / . • ~ .o" °% . .

I o -8 - _ - ~ ~ r , ~ . . / . . -...

:: \ , "'.. .. 50

10-9 " ~ . ~ .

i0 -~ 1 I I I I 10 3 10 4 10 5 10 6 10 7 10 8

E n e r g y ( e V )

Fig. 4. Spatial variations of neutron spectra for the larger assembly of 7Li. Numbers by the curves indicate the distance (in cm) from the source plane.

648 lO -7 _

2O 10 .8

," / ' ' ~ " " " 5O '~"7" . \ ." ' - . .."

/ . . . . . \'#'\ X'~, 6o ~0-~ - / " 4 \. "

80 ~ - ~ J / / , lOO lOO /~,

N~ 10-11 --

-e.

10 -12 _

!

10-I~

10-14

I /it/ I I I [ I I I 10 ° 101 10 2 10 3 10 4 10 5 10 6 10 7

E n e r g y ( e V )

Fig. 5. Spatial variations of neutron spectra for the larger assembly of 6Li. Numbers by the curves indicate the distance (in cm) from the source plane.

IO ~ _

,10 -7 - . ~. 10

20

10 ....--- °'. o. ~o~ 2o / ~ 3 - r . ~ - ~ - x Y \ ~ . - ; - F lO9 I ° ~ Z ~""\"~ =o

~ 1 0 0 = / W - ' ° ° ,,,.,oo

10-11 /

i0-1z

10-13

I I I I I I I 10 ° 101 10 z 103 104 105 106 107 108

E n e r g y ( e V )

Fig. 6. Spatial variations of neutron spectra for the larger assembly of natural Li. Numbers by the curves indicate the distance (in cm) from the source plane.

Study of space-dependent fast-neutron spectra 649

energy group cor responding to the inelastic threshold 10 -7 t00 x 60 x 60 cm / (i.e. i = 7 for 7Li and na tura l Li ; i = 6 for 6Li). This - - - 30 x 60 x 60 cm ~ - - / " t r a p p i n g " of neu t rons is due to the fact tha t once the 1o -0 / / "~" IO¢m neut rons a t ta in energies below the inelastic threshold, ,/,/ ~ / S ~ ] fur ther energy loss is due to the slower process of t 0-9 elastic scatte ring. We may also no t e t h at for 7Li and 7fl Z ' / ~ na tura l Li, this peak gets sharper as one moves far ther 10-1° f rom the source plane (Figs 4 and 6) whereas it is quite ,7, b road even at the free end b o u n d a r y for the case of N" IO-11 '/:tl//¢//// ~ O e m

6Li (Fig. 5). This difference in the behav iour of 6Li "e- f['////I and 7Li (and na tura l Li) can be a t t r ibuted to the 1°-~z V Y--/// relatively small value of the elastic scat ter ing cross- ¢/7 / section in 7Li for the 7th energy group, compared to 10--13 ~ f ! the cross-section values for groups bo th above and below it. The dip at the 8th energy group (0.24).4 10-14

MeV) is due to the resonance in elastic scattering 10-15 ~ ~ I I I cross-sections at 0.3 MeV in bo th 7Li and 6Li. Fur- 100 to I 1o 2 103 1o 4 1o 5 I06 1o 7 thermore , it is observed tha t the spectra in no case Energy (eV)

show a 1/E behav iour in the lower energy region Fig. 8. Space-dependent spectra in 6Li for the two assembly (below 1 keV). In this energy region, one finds tha t in sizes. Numbers on the right hand side of the curves indicate all cases the flux at any distance falls with a decrease the distance in cm from the source plane. The results at 20 in energy. Also, one may note tha t this decrease is and 30 cm have been shown by shifting one and two cycles

respectively for ~b(z, El.

~0_ 6 more in 6Li and na tura l Li than in 7Li. This is due to the a lmost negligible absorp t ion cross-section of 7Li.

- - I 00x60 x 60 cm - - - - - - 30 x60 x6Ocm (It may be ment ioned here tha t the fluxes have been

lo-r plot ted up to 1 keV for the case of 7Li (Fig. 4) since

~ ~ ~ J 1Oem they remain a lmost cons tan t at energies below this.) Neu t ron spectra at var ious distances inside the

10 -8 smaller assembly are shown in Figs 7-9 for 7Li, 6Li /

/ / 10- 7 /

/ 100 x60 x 60cm ~ ]

20cm

I~ 10 -10 / 10-9 ~ / _

-0- / / 10-t0 /

/ / ,10-12 / 30crn ~ - , / /

. " I k ~ .," ,o-o ,-" , o - + / # # __-

+o-1, / / l / / l / 1/ /

10-14 I I I I I I1 I I / 10 3 10 4 10 5 10 6 10 7 10 8 10-t~ It ~11 I I I I I I I

10 0 10 2 10 3 10 4 10 5 10 6 10 7 10 °

Energy ( e V ) Energy (eVI

Fig. 7. Space-dependent spectra in 7Li for two assembly sizes. Fig. 9. Space-dependent spectra in natural Li for the two Numbers in the right hand side of the curves indicate the assembly sizes. Numbers on the right hand side of the curves distance in cm from the source plane. The results at 20 and indicate the distance in cm from the source plane. The results 30 cm have been shown by shifting two and four cycles at 20 and 30 cm have been shown by shifting two and four

respectively for q~(z, El. cycles respectively for ~b(z, El.

650 M. MAL1K et al.

1o ° (solid curves) ~b(z) varies exponentially in the distance range 40q50 cm for 7Li; 40-55 cm for 6Li and for natural Li an exponential decay is observed in the

10-1 6Li " - . ~ , - ' , L , ~ range 48-65 cm. From Fig. 11 one may note that in ~ - . . . . . ~ _ _ _ _ _ . . _ the above distance ranges, K(z) varies only slightly

-o-lo_Z ~ ~ , (solid curves). The average values of decay constants in these distance ranges come out to be 0.048 cm ~,

6L~l Li 0.061 cm and 0.052 cm for the three cases. The 1 1

to~% ~ol 2ol 3oi 4oJ 5ol sol 7ol 8ol 9ol ~oo'~ corresponding average fast neutron diffusion lengths Z (cm) will be given by 20.8, 16.1 and 19.2 cm for 7Li, 6Li and

natural Li respectively. No such exponential decay is Fig. 10. Variations of total flux with distance for 7Li, 6Li seen for the smaller assembly (dashed curves in Figs and natural Li. Solid curves are for the larger assembly (100x60x60 cm 3) and dashed curves are for the smaller 10 and 11). Therefore, one can conclude that in fast assembly (30 × 60 × 60 cm3). The region between the pairs of Li systems of dimensions of about (1 m) 3 or larger,

arrows shows exponential decay, pseudoequilibrium conditions can be observed in cer- tain distance ranges.

Using equation (18) of the last section, the total and natural Li respectively. In each case we have also breeding ratios have been calculated for the two given the spectra corresponding to the larger assembly assemblies considered. The values of TBR for the at the same distances. One may note that the spectra larger assembly have been found to be 0.409, 0.056 for 7Li and natural Li in larger assemblies are "softer" and 0.465 for 7Li, 6Li and natural Li. than those for the smaller assembly whereas in 6Li, due to its very large absorption cross-section, the two Comparison with the experiment

spectra have similar shapes at all distances. The values of TBR for the smaller assembly are The spatial variations of total flux ~b(z) inside the given in Table 1 for 7Li, 6Li and natural Li. Also given

two assemblies of 7Li, 6El and natural Li are shown in Table 1 are the experimental and calculated values in Fig. 10. In Fig. 11 the corresponding variations of reported by Takahashi et al. (1984) for 7Li and 6Li. K(z) are shown. We find that for the larger assembly We find that the presently calculated value for 6Li is

r 0.20 I I

6Li 0.18 I

I

0,16 / / 6Li

0.14

v 0.12

0,10 / /

O,OE / i / 7Li /11 ii/ ,/7El 1

O.OE / / / / /

0.0'~ ~ ~ I I I I I J I I I I 0 t0 20 30 40 50 60 70 80 90 100

Z (cm)

Fig. l 1. Spatial variations of K(z) (which is constant between pairs of small arrows) for natural Li and its two isotopes. Solid curves are for the larger assembly (100 × 60 x 60 c m 3) and dashed curves are for the

smaller assembly (30 × 60 × 60 cm3).

Study of space-dependent fast-neutron spectra 651

Table I. TBR in an assembly of dimensions : 30 × 60 × 60 c m 3

Results of Takahashi et ak (1984) Present Calculations r e su l t s Experiment NITRAN + ENDF/B-IV NITRAN + JENDL-3PR 1

T7 ~ 0.334 0.305 +0.018 0.3963 0.3401 T6 0.047 0.0457 + 0.004 0.0410 0.0363 Tt 0.381 0.351 _+ 0.02 l 0.4373 0.3764

a T7 ' T6 and T, are the TBRs for 7Li, 6Li and natural Li respectively ; T, = T 7 + T6.

in reasonably good agreement with their experimental Bhatcja P. et al. (1985) Nucl. Sci. Engng 89, 366. result. However, the value of TBR for 7Li is slightly Fritcher U. et al. (1978) Nucl. Inst. and Methods 153, 564.

Herzing R. et aL (1976) Nucl. Sci. Engng 60, 169. higher than the experimental value. This is partly due Kuijpers L. et al. (1977) Nucl. Inst. and Methods 144, 215. to the fact that we have taken Zi,e~ to be equal to Exp Kumar A. et al. (1973) J. Nucl. Energy 27, 485. above 2.8 MeV in calculating TBR for 7Li. Kumar A. et aL (1978) NucL Sci. Engng 67, 120.

Maekawa H. et al. (1986) Report JAERI-M86-182. Mohan P. et al. (1986) Ann. nucl. Energy 13, 307. Mohan R. et al. (1982a) J. Phys. D15, 411.

REFERENCES Mohan R. et al. (1982b) Nucl. Sci. Engng 81,532. Mohan R. et al. (1985) Nucl. Sci. Engng 90, 111.

Ahmed F. et al. (1971) Nucl. Sci. Engng 46, 203. Profio A. et al. (1981) Nucl. Sci. Engng 78, 178. Bachmann H. et al. (1978) Nuel. Sci. Engng 67, 74. Sugiyama K. et al. (1984) OKTAVIAN Report C-84-04. BARC-892 (1976) (Evaluated by S. B. Garg). BARC, Takahashi A. et al. (1984) Proc. 13th SOFT, Italy.

Bombay. Takahashi A. et al. (1985) OKTAVIAN Report C-85-02.