Distribution of fission products in irradiated graphite materials of HTGR fuel assemblies: Third and fourth OGL-1 fuels

Distribution of fission products in irradiated graphite materials of HTGR fuel assemblies: Third and fourth OGL-1 fuels

Journal of Nuclear Materials North-Holland, Amsterdam 207 136 (1985) 207-217 DISTRIBUTION OF FISSION PRODUCTS IN IRRADIATED GRAPHITE HTGR FUEL ASSE...

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Journal of Nuclear Materials North-Holland, Amsterdam

207

136 (1985) 207-217

DISTRIBUTION OF FISSION PRODUCTS IN IRRADIATED GRAPHITE HTGR FUEL ASSEMBLIES: THIRD AND FOURTH OGL-1 FUELS K. HAYASHI, K. IWAMOTO

T. KIKUCHI,

F. KOBAYASHI,

K. MINATO,

K. FUKUDA,

Japan Atomic Energy Research Inslitute, Tokai murcr, Naka - gun, Iharaki - ken, 319 Received

11 January

1985; accepted

MATERIALS

K. IKAWA

OF

and

I I Japan

4 July 1985

Axial, circumferential and radial distributions of fission products in the graphite sleeve, inner-tube and block of irradiated high temperature gas-cooled reactor (HTGR) fuel assemblies were measured by gamma spectromerry, lathe sectioning and beta counting with ion-exchange separation. Some distinctive peaks of ‘@Ce and ‘*‘Sb in their axial profiles, together with the very high activity level of fission products are ascribed to the failure of coated fuel particles. The effective retention capability of the graphite sleeve was observed for %r, ‘06Ru, ‘25Sb, ‘“Ce and 15’Eu; whereas not for ‘j4Cs and ‘s’Cs. Silver-1lOm was detected in graphite materials of the fourth OGL-1 fuel assembly with an increased burnup of 1.96% fissions per initial metal atom (FIMA). Effective in-pile diffusion coefficients of 90Sr, ‘*‘Sb and ‘@Ce in the graphite sleeves have been estimated using the Fickian diffusion theory.

1. Introduction The fuel of a high temperature gas-cooled reactor (HTGR) consists of a carbon matrix and/or graphite materials as well as coated fuel particles. The diffusion and release behavior of key fission products (FP), such as cesium, strontium and silver, in carbon matrix and graphite materials has been extensively studied [l-4], because of its importance in the operational and safety aspects of HTGR. It is known that the diffusion and release kinetics are not only dependent on the temperature and other external conditions but also on the microstructural properties, which are initially relevant to the production process and are later affected by fast neutron irradiation and corrosion (4,5]. Further information is that the diffusion coefficients of metal fission products, especially alkali earth elements such as Sr and Ba, are strongly affected by their concentration in graphite [2,6]. This indicates the importance of studies on the in-pile behavior of fission products under realistic HTGR conditions including its very low concentration in graphite. In the design of the Multi-purpose Very High Temperature Gas-cooled Reactor (VHTR) at the Japan Atomic Energy Research Institute (JAERI), the fuel assembly consists of graphite sleeves, block and other graphite materials and of fuel compacts, which are

0022-3115/85/$03.30 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)

made through consolidation of coated fuel particles dispersed in a carbon matrix [7]. Some simulated VHTR fuel assemblies were irradiated in a high temperature in-pile gas loop OGL-1 [S], which is installed in the Japan Materials Testing Reactor (JMTR) of JAERI. The present paper deals with the distribution of the fission products measured in the graphite sleeves and blocks of the third and fourth OGL-1 fuel assemblies. A paper on the first and second assemblies, and a preliminary report of the distribution of activation products of 6oCo and 54Mn have been published elsewhere [9,101. A series of measurements has revealed that “OrnAg, “‘Ag, 13’1, ‘34Cs, ‘j6Cs, 13’Cs, 14’Ba and 14’La have been deposited on the surface of the components of the Loop OGL-1 [8,11]. These nuclides should have been produced in the fuel compacts, and thus released into the coolant channel. The fission products detected in the graphite sleeves and blocks were compared with the deposited nuclides mentioned above.

2. Experimental procedure A schematic diagram of the OGL-1 fuel assembly and the experimental procedure were presented in the previous paper [9].

B.V.

208

K. Hayasht

et ul. /

Distribution

of fission products

and irradiation

Number of fuel rod Coated fuel particle Fuel compact ‘) Graphite sleeve ‘) Graphite block” Graphite Irradiation Irradiation

inner tubed’ period time ‘)

(h) (s) Maximum burnup (S FIMA)d’ (MWD/T) Maximum fast neutron fIuence(m-2 s-‘) (E z 0.18 MeV) Maximum outlet He Gas temperature(K) ‘) s) ‘I ‘r

condition

gruphrte

muterruls

profile by lathe sectioning followed by gamma spectrometry of the turned-off graphite powder sample and by beta counting with ion-exchange separation. The circumferential distribution of activity was measured using a short cylindrical sample of the graphite sleeve cut to 10 or 40 mm in length. Gamma particles through a lead collimator slit with 5 mm width, whose path is perpendicular to the sample cylinder axis. were analyzed by the gamma spectrometer as the sample was rotated on its axis. The measured count rate has been converted into the activity per unit weight of graphite i.e. Bq/kg-graphite by making use of standard activity sources.

The specification of the third and fourth fuel assemblies is listed in table 1. For the third assembly the graphite block has only one fuel rod with an inner tube in the central hole of the fuel compacts, whereas there are three fuel rods for the fourth assembly. The graphite material is a purified fine-grained petroleum coke IG-110 with a density of 1.78 MS/~. The structure of the fourth assembly is very similar to those of the first and second assemblies [9]; the physical and chemical properties including impurity content are essentially identical for the second, third and fourth assemblies. Irradiation conditions and the calculated temperature distribution are given in table 1 and fig. 1, respectively. The maximum temperatures are 1410 and 1330 K for the third and the fourth assembly sleeves, respectively; and 1080 K for the third assembly graphite block. After being cooled for about three and two years for the third and fourth assemblies, respectively, the irradiated graphite materials were analyzed by gamma spectrometry with a high-purity germanium detector. The axial profile of fission products was measured by gamma spectrometry with a lead collimator slit, and the radial

Table 1 Specification

tn Irradiated

3. Results and discussion 3.1. FP distribution in the sleeve and inner-tube of the third assembly A typical gamma spectrum for the third fuel sleeve is given in fig. 2. Fission products detected in the sleeve are lo6Ru, lz5Sb, ‘34Cs, 13’Cs, IaCe, lUPr, and 155Eu; other photoelectric peaks come from activation prod-

of the fuel assemblies 3rd fuels

4th fuels

one 12% enriched U UO, Kernel TRISO Coating 18m~36O~x36~ 36.2’o ~46~~ x IX’501D x800D x 780L

three 19.98 enriched U UO, Kernel TRISO Coating 8’“~24o~x36~ 24.21D x 300D x 790 L 800D x 785’. 32.61D x 3 holes ‘)

131D x 17.80D ~730~ March 1979-July

1979

Nov. 1979-June

976 3.51 x loh

1872 6.74 x lo6

0.45 4.14x

1.96 1.37 x lo4

lo3

0.7 x 10 24

2.5 x 1O24

1200

1200

Dimension in mm. Each hole is 32.6 mm in diameter (3 fuel rods). Effective full power time. Percentage of fissions per initial metallic atoms

1980

209

K. Hayashi et al. / Distribution of fission products in irradiated graphite materrals

3rd OGL-1

1600 c

3rd OGL-1 Sleeve (390-400mm)

(inner surface)

0

500

1000

1500

Channel 0

100

200

300

400

500

600

(Top)

700 780 (Bottom)

Axial

distance

2coo

2500

3cm

number

Fig. 2. Gamma spectrum measured for the sleeve of the third OGL-1 fuel assembly.

(mm)

Fig. 1. Calculated temperature distribution in the third OGL-1 fuel assembly.

ucts of 54Mn, 6oCo, and from other gamma emitters. The axial distribution of fission products in the sleeve is depicted in fig. 3. Many peaks of l”Ce and ‘*‘Sb are observed in the figure, and some of the peak positions correspond to each other, whereas the profiles of 134Cs and ‘37Cs are relatively smooth. The activity level of lo6Ru, ‘37Cs and l”Ce is higher by two and one order of magnitude than in the second and the fourth assembly sleeves, respectively. Fig. 4 shows a typical circumferential distribution of fission products in the sleeve. It should be noted that the peak at &r is an imaginary one which comes from the true peak located at the opposite side of the cylindrical sample: $r. Distinctive peaks of lUCe and ‘25Sb are also observed in the graphite inner-tube (fig. 5). A failure fraction of 8 x 10m4 has been obtained by an acid leaching technique for three compact samples of the third assembly [12]. This value is a factor of 20 higher than the highest leaching fraction of three compacts measured for the second assembly [13]. Some of

the failed fuel particles were visually detected at the inner- and outer-surfaces of fuel compacts [12]. They should have resulted in the activity peaks observed in the graphite sleeve and inner-tube through the direct recoil and evaporation of fission products. The typical radial distributions of fission products in the sleeve are depicted in figs. 6a and 6b for different axial positions. Strontium-90, ‘06Ru, and “‘Eu were detected only in the vicinity of the inner surface of the sleeve. It should be emphasized here that the graphite sleeve has effectively blocked release of these nuclides together with lz5Sb and l”Ce, into the coolant channel, although the failure fraction of coated fuel particles was relatively higher for this assembly. Cesium-137 has a much shallower slope in its radial profile than other nuclides. The flat profiles in the radial, axial and circumferential directions are ascribed to its high diffusivity at high temperatures. 3.2. FP. distribution in third assembly block Figs. 7 and 8 show axial and radial profiles of fission and activation products. Ruthenium-106, “‘Sb, l”Ce and ‘55Eu were not detected in the block in contrast to

K. ficyashr

210

et a/. / Durrihurion

of fission

products

in rrradinted

graphite

3rd

3rd

Axial

500

distance

600

:

r--

.I-

‘-T.

700 775 (Bottom)

100 lo30 (Top)

(mm)

Fig. 3. Axial profile of fission products assembly sleeve. ,

Inner Sleeve

1

I

I

300 400

100 200

(Top)

r

OGL-1

OGL- I Sleeve

I

0

matrriul,s

j

in the third OGL-1 fuel

.

‘__._,_

_

,_.___

?

3rd OGL-1 Sleeve (160-160mm)

14?.e q

200 Axial

300

400

distance

500

600

700 (Bottom)

(mm 1

Fig. 5. Axial profile of fission products in the inner-tube of the third OGL-1 fuel assembly. Activity of IaCe and ‘*‘Sb has been reduced by a factor of 10 in the figure.

their existence in the sleeve. These nuclides have not been observed during plate-out measurement over the OGL-1 cooiant channel, either 1111. The facts indicate that they have almost completely been retained within the sleeve and fuel compacts, as stated above. 3.3 FP distribution assembly

in the sleeve and block of the fourth

Axial and radial profiles of fission products in the fourth OGL-1 sleeve (rod B) are depicted in figs. 9 and 10, respectively. 0.1 c

0

i

+l

l-r

Angle

$i-T

2l-r

______I._-~_..._ Fig. 4. Typical circumferential distribution of fission products in the third OGL-1 fuel assembly sleeve at an axial position of 160-180 mm from the top.

211

K. Hayashi et al. / Distribution off &ion products rn Irradiated graphite materials 1

I

I

3rd OGL-1

Sleeve

I

4

a. (40-50mm) lo*

-I

Distance from the inner surface (mm) I

0

I

I

I

200

400

I

I

I

(Bottom)

( Top) Axial b. (370-380mm)

distance

Fig. 7. Axial profile of fission products

GO

600 (mm) in the graphite

block of

the third OGL-1 fuel assembly.

Strontium-90, ‘25Sb and lMCe have been retained in the sleeve, and the total features of fission product distribution are similar to that for the second assembly except that “‘“‘Ag has been detected in this case. Silver-1lOm together with a small amount of “‘Sb has also been detected in the graphite (fig. 11) outside of the sleeve. 3.4. Fractional

release

of FP from fuel compact

to sleeve

The axial profiles of the fractional release of fission products are depicted in figs. 12 and 13. The fractional release is defined here as amount of fission product within a certain axial width (10 mm) of the sleeve,

Distance

from the inner surface (mm)

Fig. 6. Radial profile of fission products in the third OGL-1 fuel assembly sleeve at axial positions of (a) 40-50 mm and (b) 370-380 mm from the top.

I

I

I

I

I

1

I

4th OGL-1 Sleeve (8)

10’

L

3rd OGL-1 Graphite Block (385-390mm)

t

Y 2

? i ;

,o~____~

Background

(

holes for Hastelloy X tierods

L’

L..-.

0

II-L10

5

0

lj 15

Distance from the inner surface (mm) Fig. 8. Radial profile of fission products in the third assembly block at an axial position of 385-390 mm from the top.

divided

by

the

total

the nuclide in the fuel compact with the same has been calculated by a [14], which calculates radion the basis of the ORIGEN

inventory

(

,

1

,

,

1002003004005006007007 (Bottom)

(Top)

Axial

distance

(mm)

Fig. 9. Axial profile of fission products in the fourth OGL-1 fuel assembly sleeve (rod B). The activity of 54Mn and “OrnAg has been increased and decreased. respectively, by a factor of 10 in the figure. 4th

OGL-1

Sleeve

(rod B)

of

corresponding part of the axial width. The inventory computer code ORIGEN-JR ation sources of spent fuel code 1151. Fig. 13 indicates that the fractional releases of ‘34Cs, ‘j’Cs and l”Ce are of the order of lo-’ for the fourth assembly sleeve. The very low value suggests that these nuclides were mainly produced from original uranium contamination in the compact matrix [9,16,17]. By contrast, the fractional releases into the third assembly sleeve are much higher, and reach the order of 1O-5-1O-4, reflecting the higher failure fraction of coated fuel particles.

Fig. 10. Radial profile of fission products in the fourth OGL-1 assembly sleeve (rod B) at axial position of (a) 570480 mm and (b) 590-600 mm from the top.

Distance

from the inner surface (mm)

K. Hayashi et al. / ~jstrjbuti#n

offission

213

products in jrradjatgd graphite materials

3rd

OGL-1 Sleeve

( Bottal$

( Top) Axial (Top)

(Bottom)

Axial

distance

(rnrn~

Fig. 11. Axial profile of fission products in the graphite block of the fourth OGL-1 fuel assembly. The activity of ‘37Cs and ‘34Cs has been increased by a factor of 10 in the figure.

distance

Fig. 12. Fractional release of fission products into the sleeve of the third OGL-1 fuel assembly. The release profile of ‘&Ce has been depicted in reduced scale by a factor of IO.

cient obtained from fig. 14. The least squares fitting for calculated temperatures between 1150 K and 1410 K gives the following equation for ‘*‘Sb: D = lo-* exp( - 1.8 X 105/RT),

diffusion coefficients of fission products in the graphite sleeve are estimated from the radial profile data obtained above. It is assumed that transport behavior is described by Fickian diffusion with phenomenal diffusion coefficients. Fig. 14 summarizes the radial profiles of ‘*‘Sb measured at different axial positions, together with calculated profiles for the best fitted diffusion coefficients. The calculation method has been published elsewhere [ 181. The boundary condition at the inner surface is that the surface concentration increases in proportion to the irradiation time. Fig. 15 is the Arrhenius plot of the diffusion coeffiEffective

(mm)

(I)

where D is the diffusion coefficient in the graphite sleeve (m*/s), R is the gas constant (8.31 J/mol. K) and T is the absolute temperature (IQ. The diffusion coefficients of ?S.r and l”Ce are simply estimated by the following relationship for onedimensional diffusion: D - 1’/6T,

where I is the diffusion sion time (s). The diffusion length, radial profiles of these both for “Sr and i”Ce.

(2) length (m) and T is the diffuwhich is determined from the nuclides, is typically - 1 mm Thus the diffusion coefficients

K. Haymht

214

et al. / Dismributronof fission products m wruduted

graphite murerruk

3rd

OGL-1 Sleeve

4th OGL-1 Sleeve (rod

9)

0 I

3 i

E

ltisc

I loo

I ml

I

I

I

300

400

500

I 600

(TOP)

I

_

700

780

(Bottom)

Axial distance (mrr$ Fig. 13. Fractional the fourth OGL-1

release of fission products

into the sleeve of

Distance from the inner surface (mm) Fig. 14. Comparison between the measured and the calculated radial profiles of lzsSb at different axial positions of the third OGL-1 fuel assembly.

fuel assembly (rod B).

are estimated

to be

(10-‘4-10-‘3)

m2s

for the graphite sleeve at (1300 f 100) K. The coefficient of ‘%r obtained here is a little lower than those reviewed by Myers and Bell [2]. 3.6. In-pile behavior of i34Cs and “7Cs in the sleeve and block

Radial profiles of ‘37Cs in the third assembly sleeve are summarized in fig. 16; they are substantially straight lines except at 735-745 mm from the top. This suggests that the diffusion of ‘37Cs has eventually attained the steady state condition. The Fickian diffusion analysis gives an effective diffusion coefficient larger than 2 X lo-l2 m’/s for these straight lines. By contrast, the radial profile of 13’Cs at 735-745 mm corresponds to a non-steady state diffusion; the diffusion coefficient is - 1 x lo-‘* m*/s for a calculated temperature of 1150

K. These diffusion coefficient values for IG-110 graphite are nearly of the same order of magnitude as those reviewed by Myers and Bell for different graphite materials [ 11. The radial profiles of 134Cs and 137Cs are compared in figs. 17a and 17b for the graphite sleeve and block of the third assembly. Obviously the concentration of ‘“Cs is nearly constant inside the block, and almost at the same level as in the sleeve. By contrast, considerable gradients are noticeable for 137Cs in the sleeve, and its activity level is 2-3 orders of magnitude higher in the sleeve than in the block. The nuclide has also been detected at every measured point of the OGL-1 loop components [f&11). These facts indicate that 13’Cs has released partly into the coolant channel and partly into the graphite block. The flat profile of 134Cs all over the graphite material suggests two possible causes. One is that it has been produced by activation of 133Cs (natural abundance 100%) contained in the graphite material as an impurity which had uniformly distributed before irradiation. In

215

K. Hayashi et al. / Distribution of fission products in irradiated graphite materials

Temperature 1000 I

I

(“C 1 900 I

8.26

800 lj

I

a(40

GGL-1 Sleeves

I

3rd OGL-1 Sleeve

3rd 844th

:)\. ,

I

_

- 50mm)

@(180-190mm) @ (370- 38Omm)

0

1

2

Q&570-

58Omm)

@(735-

745mmj

3

4

. !I

4.9

Distance from the inner surface (mm)

i$g 7

8

9x1o-4

Fig. 16. Summary of normalized radial profiles of r3’Cs at different axial positions of the third OGL-1 fuel assembly sleeve.

Ret i procal absolute temperature

( 1 IK)

Fig. 15. Relationship between the measured diffusion coefficient of 125Sb and the temperature of the sleeves of the third and fourth OGL-1 fuel assemblies.

this case an impurity weight fraction of - 1 X lo-*’ is expected under a thermal neutron flux of 4.5 X 10” ,-2 s-1 and an absorption cross section of 3 X 10m2’ m2 (30 barn). Such an extremely low content would be conceivable for the high purification process of the graphite material utilized here. The other possibility is the precursors of 134Cs, namely ‘33I (half life 20.8 h) and ‘33Xe (5.25 day), have very rapidly diffused as gaseous species through the graphite sleeve and block. An activation analysis with long-term irradiation together with release model calculation could provide us with advanced knowledge of the release mechanism. 3.7. Generation

and release behavior of “OrnAg

There are two possible generation processes of “OrnAg; one is activation of losAg contained in the

graphite materials as impurity, and the other is activation of ‘09Ag which is produced as a fission product. In the case of the impurity activation process, its amount will increase roughly in proportion to the neutron fluence. Impossible detection of rromAg at any position of the third assembly sleeve in contrast to the considerable existence in the fourth cannot be explained by the difference of neutron fluence: approximately 1 :3 (table l), even though radioactive decay of “OrnAg (251 day) is taken into account. On the other hand, in the case of the fission product process, “OrnAg is generated through the two step neutron reaction of fission and subsequent activation of the fission-induced ‘09Ag. Thus “‘“‘Ag will be produced approximately in proportion to the square of neutron fluence through 235U fission. Actually ‘romAg is expected to increase more rapidly, because 239Pu, having a much larger fission yield of ro9Ag, will accumulate in proportion to the fluence. The observed much higher activity of “OrnAg for the fourth assembly is more reasonably ascribed to the fission-induced process than to the impurity activation process. This estimation is supported by the observed radial

K. Hayashi et al. / Distribution of jisslon products in irrudiafed graphite maferials

216

I

3rd

I

OGL-1

Graphite

Block

Graphite Sleeve

I

I

I

Radial

distance

from

the compact

3rd

(mm)

OGL-1

Graphite

lo6

outer-surface

Block

z I % F lo5 $ B

t

>, lo4 ._ > z Y lo3

5

5 I E

2 8

v

1o*y 0









’ 5

7

/ 12

Radial distance from the compact outer-surface

/ 17 (mm)

Fig. 17. Radial profiles of (a) 134Cs and (b) ‘)‘Cs in the sleeve and block of the third OGL-1 fuel assembly. approximately @ top; @ a quarter, @) half and @ three quarters of the full length from the top, and @ bottom

profiles of “OrnAg in the fourth assembly sleeves (fig. 10). The concentration is higher at the inner-surface than inside, which corresponds to a diffusional transport from the fuel compact to the coolant channel.

Axial levels are of the assembly.

4. Conclusions The distribution of fission products in the graphite sleeve, inner-tube and block of the third and fourth

K. Hayashi et al. / Distribution of fission products in irradiated graphite materials

OGL-1 fuel assemblies has been obtained. (1) Some distinctive peaks of l”Ce and izsSb have been observed in their axial profiles in the graphite sleeve and inner-tube of the third assembly. The peaks are ascribed to the failure of coated fuel particles. (2) Radial profiles in the graphite sleeve of the third and fourth assemblies indicate that the sleeve has an effective retention capability for %Sr, io6Ru, “‘Sb, ‘&Ce and ‘s5Eu; whereas not for ‘34Cs and ‘3’cs. An appreciable activity of “OrnAg was detected in (3) the fourth assembly sleeve, which was irradiated up to an increased burnup of 1.96% FIMA. This nuclide should have been produced through a fission process. was observed for ‘34Cs and (41 Different distribution 13’Cs in the graphite sleeve and block. (51 The Arrhenius equation of the diffusion coefficient of ‘25Sb has been obtained for the postulated Fickian diffusion process; the coefficients of WSr and l”Ce have roughly been estimated from the measured profiles.

Acknowledgements The authors are grateful to the members of JAERI who helped them so kindly with the present work, especially the staffs of the Department of the JMTR Project, and Hot Laboratory of Tokai Research Establishment of JAERI. Thanks are also due to Dr. J. Shimokawa, the previous Director of the Department of Fuels and Materials Research of JAERI for his encouragement.

217

References PI B.F. Myers

and W.E. Bell, General Atomic Company Report GA-A 13990 (1979). PI B.F. Myers and W.E. Bell, GA-A 13168 (1974). Report HMI-B372 131 B.F. Myers, Hahn-Meitner-Institut (1983) 56.

141 E. Hoi&is,

Hahn-Meitner-Institut Report HMI-B372 (1983) 77. [51 H. Gaus, W. Hensel, E. Hoi&is and D. Stritzke, HMI-B315 (1979). [61 F.J. Sandalls and M.R. Walford, J. Nucl. Mater. 62 (1976) 265. [71 JAERI, Present Status of Research and Development on Multi-purpose VHTR (1984). 181 H. Itami, H. Nakata, I. Tanaka, K. Aoyama and K. Ikawa, JAERI-M 83-104 (1983) p. 3. [91 K. Hayashi et al., J. Nucl. Mater. 116 (1983) 233. VOI K. Hayashi et al., JAERI-M 84-088 (1984). [ill N. Tsuyuzaki, private communication. WI K. Fukuda et al., J. At. Energy Sot. Japan (in Japanese) 26 (1984) 57. u31 K. Ikawa et al., JAERI-M 83-012 (in Japanese) (1983) 151. 1141 K. Koyama, N. Yamano and S. Miyasaka, JAERI-M 8229 (1979). WI M.J. Bell, ORNL-4628 (1973). K. Minato, K. Ikawa, T. Itoh and H. U61 K. Fukuda, Matsushima, J. Nucl. Sci. Technol. (Japan) 18 (1981) 887. P71 K. Ikawa et al., JAERI-M 83-012 (in Japanese) (1983) 143. [181 K. Hayashi and K. Ikawa, JAERI-M 82-109 (in Japanese) (1982).