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Benchmark Analysis of Criticality Experimentsin the TRIGA Mark II Using a Continuous EnergyMonte Carlo Code MCNPTetsuo MATSUMOTO aa Atomic Energy Research Laboratory , Musashi Institute of Technology , Ozenji,Asao-ku, Kawasaki , 215-0013Published online: 15 Mar 2012.

To cite this article: Tetsuo MATSUMOTO (1998) Benchmark Analysis of Criticality Experiments in the TRIGA Mark IIUsing a Continuous Energy Monte Carlo Code MCNP, Journal of Nuclear Science and Technology, 35:9, 662-670, DOI:10.1080/18811248.1998.9733922

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Journal of NUCLEAR SCIENCE and TECHNOLOGY, Vol. 35, No. 9: p. 662-670 (September 1998)

TECHNICAL REPORT

Benchmark Analysis of Criticality Experiments in the TRIGA Mark I1 Using a Continuous Energy

Monte Carlo Code MCNP

Tetsuo MATSUMOTOt

Atomic Energy Research Laboratory, Musashi Institute of Technology*

(Received March 11, 1998)

The criticality analysis of the TRIGA-I1 benchmark experiment at the Musashi Institute of Technology Research Reactor (MuITR, 100 kW) was performed by the three-dimensional continuous-energy Monte Carlo code (MCNP4A). To minimize errors due to an inexact geometry model, all fresh fuels and control rods as well as vicinity of the core were precisely modeled. Effective multiplication factors ( k e E ) in the initial core critical experiment and in the excess reactivity adjustment for the several fuel-loading patterns as well as the fuel element reactivity worth distributions were used in the validation process of the physical model and neutron cross section data from the ENDF/B-V evaluation. The calculated k,ff overestimated the experimental data by about l.O%Ak/k for both the initial core and the several fuel-loading arrangements (fuels or graphite elements were added only to the outer-ring), but the discrepancy increased to l.S%Ak/k for the some fuel- loading patterns (graphite elements were inserted into the inner-ring). The comparison result of the fuel element worth distribution showed above tendency. All in all, the agreement between the MCNP predictions and the experimentally determined values is good, which indicates that the Monte Carlo model is enough to simulate criticality of the TRIGA-I1 reactor.

KEYWORDS: TRIGA-11 reactor, continuous-energy Monte Carlo code MCNP, three- dimensional geometry, benchmark experiment, multiplication factor, excess reactivity, fuel element reactivity worth distribution

I. Introduction The Musashi Institute of Technology Research Reactor

(MuITR) is a 20% enriched TRIGA-type-fueled, 100 kW multipurpose research reactor that was designed to pro- vide both in-core and out-of-core irradiation facilities. The MuITR is shown in Figs. l ( a ) and (b), respec- tively, in vert,ical and horizontal cross sections, and in cutaway view in Fig. 2. The core is cooled by light water and is surrounded by a graphit.e reflector. The beam tubes provide beams of neutron and gamma ra- diation for a variety of experiments. The thermal col- umn had been used for treatment of a brain tumor by boron neutron capture therapy (BNCT) since 1976 af- ter the modifications to t*he original MuITR were com- pleted(’)(*). The MuITR had many different uses includ- ing BNCT projects, a wide range of neutron activation studies, an application of neutron radiography and other neutron beam experiments till the end of 1989 when un- fortunately water leaking trouble was occurred in the reactor tank. For installing a new tank and restarting the reactor an adequate design of a core and irradiation

* Ozenji, Asao-ku, Kawasaki 215-0013. Corresponding author, Tel. $81-44-966-6131, Fax. +81-4-955-6071, E-mail: mtetsuoQatom.musashi-tech.ac.jp

facilities is inevitable. We have many available exper- imental data, reactor operational data and the experi- ence of the investigators. Some of the reactor opera- tional data were analyzed by the diffusion theory model using CITATION code(3) and also Monte Carlo model us- ing KENO code with multigroup cross sections(4). How- ever, in some cases diffusion theory is simply not able to provide the results desired. The KENO code needs the process for collapsing multigroup cross sections for the reactor model. In order to get an exact informa- tion about, the core characteristics, both experimenters and reactor operators need more accurate calculations. Therefore, it is important to develop an accurate three- dimensional reactor physics model of the MuITR core. The MCNP Monte Carlo code (MCNP4A)(5) was chosen because of its general geometry modeling capability, cor- rect representation of transport effects and continuous- energy cross sections. The general geometry is essential and this permits easy modeling of any in-core or out-of- core experiment. Using continuous-energy cross sections is significant because this eliminates the need for collaps- ing multigroup cross sections.

The main requirement for the reliable use of a particle transport computer code is its validation on a benchmark experiment. There are two main objectives of such veri- fication. The first is to check the consistency of physical

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models and data used in a transport code, and the second is to determine systematic errors made by approximate simulation of the experiment. The accuracy of both the neutron transport physics as represented in MCNP and the user-defined model must be assessed. Even though MCNP has been proven to simulate the physical interac- tions correctly(G), it does not necessarily follow that the MCNP model of the MuITR core will provide accurate solutions. Therefore, t o put full confidence in the model, we decided to compare MCNP calculated values to pre- viously obt.ained experimental data. These data were obtained in 1985, after replacing the old fuel elements of aluminum cladding with new ones of shinless-steel cladding to keep a more safe operatlion(7).

This paper describes the model development and the comparison to existing experimental data and the typ-

663

ical uncertainties involved in the calculations. The ex- perimental data used are as follows:

(1) Initial core crit,icality measurement, (2)

(3)

Excess reactivity of the core for several fuel- loading pattern crit.icality measurements, and Fuel element reactivity worth distribut,ions.

11. MCNP Model The MuITR core was modeled using the three-

dimensional detail to reduce possible systematic errors due to inexact geometry simulation. Therefore, t.he fuel elements were explicitly modeled to eliminate any ho- mogenization effects. Figure 3 is a cross-sectional view of an MCNP model of a single fuel element. A fuel el- ement consists of meat, graphite reflectors and stainless steel end fixt.ures. The meat. is a solid, homogenized

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Irradiation tubes

// Control rods Thermalidng

Fig. 2 Cutaway view of the MuITR reactor

mixture of U and ZrH1.6 containing 8.45% U enriched to 20% 235U. The fuel element is 3.75cm in diameter with a total length of 76 cm, and is clad in 0.05 cm thick stainless steel canning. The t,apered end fixtures of the stainless steel axe shown by the dotted line. The effect of neglecting these end fixtures will be discussed later.

Figure 4 is a cross-sectional view of t,he MuITR core as modeled. The reactor core and the reflector assem- bly form a cylinder 106 cm in diameter and 56 cm high. The reactor core consists of a lattice of fuel elements, graphite dummy elements, control rods and irradiation tubes. These components are located at ninety holes

0.79 ......... t ...... ......... .... I'

6.5

38.1

0.08 ;-::::d;;: 9.45

Fuel Element

- EndFixture

t=0.05 Upper Reflector - (Graphite) sus

c Clad(SUS)

- Rod(Zr) 4 + 0.58

k- 3.64

(Unit: cm)

Fig. 3 Model of a single TRIGA fuel

reserved for them on the grid plate, distributed in five circular rings (B to F ring) as shown in Fig. 5. The reflect,or is a ring-shaped graphit.e block rising slightly

Irradiation pit Irradiation pit

( unit:cm ) I Fuel

Fig. 4 Model of core and reflector arrangements used for the MCNP criticality calculations

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Fig. 5 Grid plate with ninety holes distributed in five circular rings (B to F) including two irradiation tube positions (C.T. (A) and Pn (F24)) and three control rod positions (Safety (C5), Shim (C9) and Regulating (El))

higher than 55 cm, with an inside diameter of 45 cm and radially surrounding the core t,o a thickness of 30 cm. Provision for the isotope production facility (irradiat,ion pit.) is made in the form of ring-shaped well (25 cm in deep and 8cm in thickness) in the graphite that is open toward the tank top.

The control rods (safety, shim and regulating rods) were made of boron carbide powder (B4C). The safet,y and shim rods are 3.0 cm in diameter and the regulating rod 2.0cm in diameter, respectively, which are clad in 0.2 cm thick aluminum. The active lengths of the control rods are 48 cm that extend well above the core in the fully inserted position. The control rods were also explicitly modeled along the active length with the exception of the drive mechanisms.

Three of the beam tubes (A, B and C) are oriented radially with respect to the center of the core, and the fourth tube (D) is tangential to the outer edge of the core as shown in Fig. l(b). Two of the radial tubes (B and C) terminates at the outer edge of the reflector assembly; one (C) is aligned with a cylindrical void in the reflec- tor graphite. The third radial tube (A) penetrates into the graphite reflector and terminates at the inner sur- face of the reflector assembly, just a t the outer edge of t,he core as shown in Fig. 4. Their horizontal centerlines

are located 7cm below the centerline of the core. The inner diameter of two beam tubes penetrating through the reflector graphite is 15 cm.

The MCNP model was extended to 20cm beyond the end of the graphite reflector and approximately 20cm above the core, which were more than sufficient to ac- count for the neutron returning from the HzO coolant. The primary coolant was non-pressurized and the cool- ing was natural convection. Coolant water occupied about one-third of the core volume. The coolant tem- perature was 28 f 1°C throughout the criticality experi- ments which carried out at zero power (maximum 1W). Based on these operating conditions, all of the cross- sections used in the MCNP model were 300K evalua- tions, usually from the ENDF/B-V cross-section data (other evaluations were from Los Alamos National Lab- oratory (LANL) and Lawrence Livermore National Lab- oratory (LLNL))@)(S). The slow neutron scattering law S(a, ,f3) used to account for the molecular binding effects of the light water, graphite, and hydrogen and zirconium in ZrH were also evaluated at 300 K. These thermal scat- tering data are essential to model accurately the neutron interactions at energies below -1 eV.

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111. Criticality Calculations The calculat.ions of the effective multiplication factor

( k e ~ ) in the eigenvalue problem were performed with the MCNP4A code. The initial source distribution for the k e ~ calculations was given on the fuel meat points. There was 1 source point (1 cm part for radial direction from the meat center) in each of the fuel element in this model. The calculations were performed for the core both with and without control rods. The control rods in the for- mer were in the critical positions and in the latter were completely withdrawn like an excess reactivity measure- ment. The estimated statistical error (la) was reduced below 0.1% upon 300 cycles of it.erat.ion on a nominal source size of 3,000 particles per cycle. The approximate CPU time for the eigenvalue problem in MCNP4A was about 360min on a typical SUN-workstation. Table 1 summarizes the composition of materials used in various regions for tmhe MCNP model.

1. Initial-Core Calculation The first comparison to t.he experimental dat8a was

done for the fresh-core multiplication factor. An MCNP pictorial representation of the init,ial fuel loading is pre- sented in Fig. 6(a). The core configuration is the fol- lowing:

(1) Number of fuel elements: 66 (2) Number of dummy elements (graphite elements

clad in aluminum): 0 (3) Crit.ica1 mass: 2,500 g 235U (4) Coiit,rol rod positions: Safety rod (up), shim rod

(79% withdrawn), and regulating rod (up). The comparison of k,ff between the experimental value

and the MCMP calculated one is shown in Table 2. The calculated value overestimated about l % A k / k for both all control rod withdrawn and the control rod crit.ica1 positions.

Table 2 also includes a comparison of three effective multiplication fact.ors: t.he MCNP predicted value, the KENO predicted value(*) and the CITATION predicted value(3) for the initial critical experiments in condition of all cont,rol rods withdrawn. This result is very encourag- ing and seems to indicate that the MCNP model of the MuITR core is correct. Even though the MCNP calcu-

Table 1 Composition of materials used for the MCNP calculation

Material Density density (atoms/cm3) (g/cm3)

Atomic number Nuclide

Fuel Meat 2.556 x 10’’ 5.95 2 3 5 u

(U-ZrH) 238U 1.026 x loz1 Zr 3.532 x 10” H 5.651 x 10’’

Clad Cr 1.760 x 10” 7.93 Ni 7.596 x loz1 C 3.021 x 10’’ Mn 1.754 x 10’’ c o 1.214 X 10’’ Si 1.715 x lo’’ Fe 5.924 x 10’’

Graphite C 8.624 x 10’’ 1.72

Zr-rod Zr 4.068 x 10’’ 6.52

Mo-ring Mo 6.403 x 10’’ 10.2

Reflector Graphite C 8.624 X 10’’ 1.72

Grid plate Aluminum Si 2.315 x 10’’ 2.7 Fe 2.037 X lo’’ Mn 4.438 x 10’’

Cr 4.689 X lo1’ A1 5.883 x 10”

Mg 5.349 x lozo

Control rod B4C 1°B 1.09 x lo2’ 1.25 l lB 4.37 x 10’’ (1/2 T.D.) C 1.36 x 10’’

Coolant Water H 6.686 x 10” 1.0 0 3.343 x lo2’

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- (a) Initial core loading (Step 0)

(c) Step 12

v (b) Step 10

(d) Step 19

0 : Fuel, 0: Water, A: Graphite rod, +: Control rod

Fig. 6 Typical core configurations used for the comparison

Table 2 Comparison of the MCNP criticality calculations to the experiment for the initial core

Initial core Multiplication factor ( k e ~ ) Control rods positions (66 elements) Calculation Experiment

MCNP 1.0086 * 0.0010 1.00 Critical positions 1.0124 f 0.0009 1.0018 Up (withdrawn)

KENO 1.0169 * 0.0011 1.0018 Up (withdrawn) CITATION 1.0609 1.0018 Up (withdrawn)

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lated value is very close to the experimental one, some possible explanations for the discrepancy have been ex- plored. The foremost reason for a discrepancy could be an error in the model (ie., physical representation of the reactor). Since the dimensions of the reactor were taken from the blueprints available, it is assumed that the model is correct. The dimensions for the fuel elements were also taken from the blueprints. Another uncertainty that has already been mentioned is the tapering of the end fixture, which was not modeled. This effect was esti- mated less than -0.06%Ak/k from the calculation tak- ing into consideration of the end fixture. This value was below the stat,istical error estimate (O.O9%Ak/k). Fur- thermore, the coolant temperature distribution is also uncertainty in this model. The temperature of the HzO coolant and the fuel were assumed to be 300K. All nu- clear data library including scattering law S(a , p) given in MCNP were treated explicitly.

2. Effect of Fuel-loading Pattern After the initial critical, the excess reactivity adjust-

ment was performed because we needed an addit,ional reactivity for the actual reactor operation. There were some requirements for the fuel addition and the excess reactivity adjustment. The first limitation was for reac- tivity losses (excess reactivity of the MuITR core should be less than l.s%Ak/k). The second was storage capac- ity of t,he fuel elements. The storage racks were capable to store only 12 elements. The third requirement was to increase neutron intensity at the irradiation field for the medical use.

The fuel or graphite dummy element was simply added

to the initial critical core with 66 elements. Table 3 gives all procedures consisting of 19 steps of fuel load- ing pattern and the multiplication factors measured at each step. The measurement of excess reactivity was exe- cuted by using the period method. The effective delayed neutron fraction ( p , ~ ) of 0.008 was used throughout the paper to convert the unit of experimentally determined value from (dollar or cent) to (Ak/l~)(4)(~) .

Figures 6(a)-(d) show 4 typical core configurations in- cluding the initial core.

The first comparison to the experimental data was the fuel-loading pattern from 1 to 10 steps. Here the additional fuel or graphite dummy element was added only to the F-ring in the initial core. A desirable value of excess reactivity which was as close as possible to l.6%Ak/k was achieved at step 10. The MCNP cal- culated values are compared with the experimental data in Fig. 7. The excess reactivity increased gradually ev- ery step. The values indicated in black symbol mark (0 ) are fitted by a least squares technique. The val- ues indicated in white symbol mark (0) should become 1.0 since those are obtained at the critical condition. The MCNP calculated values overestimated the experimental ones by about l.O%Ak/k. This comparison shows that a fuel-loading arrangement at F-ring could be modeled in MCNP without many approximations.

However, other problems of fuel elements storage, neu- tron intensity at the irradiation facility and rod worth were still unsolved. To extend the core volume, a new trial was attempted from step 11 to step 19. Both the fuel elements of B2 and B6 were exchanged with the graphite dummy elements. As a result, the value of excess reac-

Table 3 History of the excess reactivity adjustments consisting of 19 steps

Fuel elements Multiplication Step Subject matter (units) factor (k,~)

0 1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19

Initial critical Fuel (F14) Fuel (F15) Graphite (F4) Graphite (F3) Graphite (F2) Graphite (Fl) Graphite (F30) Graphite (F29) Graphite (F28) Graphite (F26, F27) Unload fuel (BG) Graphite (B6) Fuel (F17) Unload fuel (B2), Graphite (B2) Fuel (F18, F19) Unload fuel (B4), Graphite (B4), Fuel (F20) Fuel (F21) Fuel (F22) Fuel (F23, F25)

66 67 68 68 68 68 68 68 68 68 68 67 67 68 67 69 69 70 71 73

1.0018 1.0062 1.0096 1.0099 1.0106 1.0114 1.0120 1.0126 1.0131 1.0134 1.0143 1.0033 1.0064 1.0095 1.0006 1.0055

Sub critical 1.0016 1.0042 1.0095

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1.03

1.01

t 0 withcontrolrods I i

Fig. 7

'1 1.01 Measured ken

Comparison of the MCNP prediction values to the experimental data from step 1 to step 10 under the conditions of all rod-withdrawn (symbol 0 )

The MCNP prediction values under the condition of critical rod positions are shown in symbol 0 at each step. Step number is denoted in numerical. Statistical error estimates are shown in bar for only rod-withdrawn condition.

tivity was drastically forced down in step 14. The opera- tions were continued to the full core except F16 and F24, which were used for sample irradiation tubes. The sub- stitution of fuel and graphite at B4 resulted in subcritical in step 16. The additional fuel loading to F-ring in step 19 was found to hold excess reactivity of 0.95%Ak/k.

The effective multiplication factors are compared in Fig. 8 for both the experimental data and the MCNP calculated values for the condition of control rods with- drawn. The discrepancy between the measured values and the MCNP calculated ones seems to be enlarged in comparison with the data obtained at the F-ring alone (step 1-10, Fig. 7). The separation of the data into three groups depending on the number of graphite element in- serted into B-ring was attempted, which indicating three lines fitted by a least squares technique, respectively. It can be seen that the discrepancy between the calculated values and experimental ones increases with the number of graphite element. There might be a certain problem related to the central region of the core, though the iiicre- ment of discrepancy was totally less than l%Ak/k when comparing with the discrepancy obtained at the F-ring. In general, it is difficult to obtain the detail information of the experimental data enough to analyze by as-built Monte Carlo simulation. The main difference between F- ring and B-ring was that the measured values at B-ring were larger than those a t F-ring. That is, the reactivity change observed in the B-ring was greater than that in the F-ring. Moreover, the neutron flux distribution in the core would be extremely changed in the B-ring. This

1.03

1.01

Fig. 8

0 Graphi te 1 1 1 1 Graphi te 2

A Graph i te 3 I I

1.01 1 ' 1

Measured ken

Comparison of the MCNP prediction values to the experimental data from step 11 to step 19

Step number is denoted in numerical. Symbol 0: and A show the values obtained in the condition

where one, two and three graphite elements were: respectively, inserted into B-ring (B2 or B4 or B6) instead of the fuel element.

effect is discussed in detail on the next.

3. Fuel Element Reactivity Worth Distribution The fuel element reactivity worth (substitution reac-

tivity of fuel and water) distributions were calculated and compared with the experimental data. The fuel was sim- ply replaced to the water at B4, C7, D11, El5 and F19 positions in the final adjusting configuration. Table 4 shows the comparison between the MCNP calculated val- ues and the experimental data. It is generally recognized that the closer an insertion reactivity of fuel gets to the center of a core, the larger it becomes. The proportion is also influenced by the surrounding environment near the inserted position. However, the discrepancy between the calculation value and the experimental data gradually increased as the insert position was closer to the center of core. The C-ring data was more than the limit of un- certainty estimate. Generally, a fuel element worth for a well-thermalized, small, compact and uniform core is approximately proportional to the square of the thermal neutron flux, integrated over the entire fissile volume of the fuel element(lO). For this reason, to implicitly com- pare the thermal neutron flux distribution to the fuel el- ement worth distribution, the MCNP calculation of the neutron flux was carried out. Table 4 includes the esti- mated fuel element reactivity worth for the experimental data where the reactivity of F19 was used as a normalized value. The estimated fuel element reactivity worth was obtained by multiplying square of the thermal neutron flux at each element which was also shown in Table 4.

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Table 4 Comparison of the MCNP calculations to the experimental data for the fuel element reactivity worth distributions

The estimated fuel element reactivity worth for the experimental data is indicated with the calculated thermal neutron flux.

Fuel insert position B4 c7 D11 E l5 F19

Reactivity (%Ak/k ) Experiment 1.20 0.91 0.72 0.48 0.28 Calculation 0.95f0.12 0.76f0.11 0.62f0.12 0.45f0.11 0.30fO.11

~

Estimated experimental 0.95 f 0.01 0.76 f 0.01 0.60 & 0.01 0.39 f 0.01 0.28 f 0.01 reactivity ( % d k / k )

Thermal neutron flux 1.51 f 0.01 1.35 f 0.01 1.20 f 0.01 0.97 f 0.01 0.82 f 0.01 (arbitrary unit)

The estimated values were in good agreement with the MCNP calculated values for all ring within the uncer- tainty estimate. This indicates that the neutron flux in the calculation is adequately represented. This also sug- gests that the experimental error should be considered in the referred benchmark data which is not estimated(’). The inconsistency between the MCNP calculated value and the experimental ones for the B- and C-rings could be settled by the assumption of the experimental error about 10%.

IV. Conclusion The simulation of the TRIGA-I1 benchmark exper-

iment at the Musashi Institute of Technology Re- search Reactor (MuITR, 100 kW) was performed by the three-dimensional continuous-energy Monte Carlo code (MCNP4A). Effective multiplication factors in the ini- tial core critical experiment and in the excess reactivity adjustment for the several fuel-loading patterns as well as the fuel element reactivity worth distributions were used in the validation process of the physical model and neutron cross section data from the ENDF/B-V evalua- tion.

The MCNP calculated values of the multiplication fac- tor are consistent with the experimental data for the ini- tial critical experiment and for t,he simple core of several fuel-loading arrangements, although the calculated val- ues are about l.O%Ak/k overestimated the experimental values. This is finding that a small, compact and uniform core could be easily modeled in MCNP without many approximations. However, another uncertainty incre- ment (l%Ak/k) are observed for the complex core of the some fuel-loading patterns where the graphite dummy el-

ements are positioned in the inner-ring of the core. As to the fuel element worth distribution, the MCNP cal- culated values agree well with the measured ones within uncertainties except for the inner-ring which underesti- mated the experimental data. All in all, it can be con- cluded that our model of the TRIGA-I1 core is precise enough to reproduce criticality experiment, excess reac- tivity and fuel element reactivity worth distribution.

ACKNOWLEDGMENT

The author thanks to Dr. H. Kadotani of CRC Re- search Institute, Inc. for his useful comments and careful reading of this paper.

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( 3 ) Takami, M., et al.: Bull. At . Energy Res. Lab., Musashi Inst. Technol. MITR-862, p. 152 (1986), [in Japanese].

( 4 ) Aizawa, 0.: “Reactor Physics and Reactor Computa- tion”, Ben-Gurion Univ. of Negev Press, p. 215 (1994).

( 5 ) Briesmeister, J. F., ed.: MCNP-A general Monte Carlo code for neutron and photon transport, LA-7396-M, Rev. 2, (1986).

(1989).

( 6 ) Jeraj, R., et al.: Nucl. Technol., 120, 179 (1997). ( 7 ) Horiuchi, N., et al.: Proc. l o th European TRIGA

User’s Conf., p. 7-24 (1993). ( 8 ) MCNPDAT: MCNP, version 4, Standard neutron cross

section data library based in part on ENDF/B-V, RSIC-DLC-105, (1994).

( 9 ) Howerton, R. J., et al.: The LLL evaluated nuclear data library (ENDL), UCRL-50400, Vol. 15, part A (1975).

(10) Lamarsh, J . R.: “Introduction to Nuclear Reactor The- ory)’, Addison-Wesley Publ., (1976).

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