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Study of Neutron Wave PropagationHideo HAYASAKA a & Seiiti TAKEDA aa Department of Nuclear Engineering, Faculty of Engineering ,Tohoku University , Aramaki-Aoba, SendaiPublished online: 15 Mar 2012.

To cite this article: Hideo HAYASAKA & Seiiti TAKEDA (1968) Study of Neutron Wave Propagation,Journal of Nuclear Science and Technology, 5:11, 564-571

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Journal of NUCLEAR SCIENCE and TECHNOLOGY, 5 (11], p. 564-571 (November 1968).

Study of Neutron Wave Propagation

Hideo HAY ASAKA * and Seiiti TAKEDA*

Received February 28, 1968

Revised May 1, 1968

Neutron wave propagation in both non·multiplying and multiplying media is treated on the basis of the monochromatic telegrapher's equation. This approach makes it possible to take account of the aspects related to wave characteristics.

Using the Green function of the telegrapher's equation, the transient behavior of neutron waves propagating in a finite homogeneous medium is investigated. It is found that wave pro­pagates in three different ways depending upon the size and nuclear properties of the medium. The asymptotic solutions of the telegraper's equation are next investigated. The dispersion re­lations of non-multiplying and multiplying media are derived.

I. INTRODUCTION

Particular interest has been centered in recent years around the neutron wave pro­pagation method0 ) -<•). Most of the analyses reported in this field are based upon the dif­fusion approximation as applied to the Boltz­mann equaion, with consideration given to energy dependent problems<ocs)CG)-Cs).

It is however an established fact that use of the diffusion equation for investigating neutron wave properties is not appropriate: When the diffusion equation is used, we tacitly concede that the wave propagates in the medium with infinite velocity causing no wave front or wake. On the other hand, while the most accurate treatment of wave pheno­mena is by rigorous application of the Boltz­mann equation, in many cases this is imprac­tically complex.

Use of the telegrapher's equation<•) -which

is equivalent to the P-1 approximation- for anal­yzing the neutron wave propagation provides a relatively easy means of representing the physical image of the wave, since its general solution depicts the phenomenon of retarda­tion, a well-defined wave front. In particular the Green function of the telegrapher's equa­tion, provides us with information on the transient behavior of the wave propagating through the medium.

The asymptotic solution of the telegra­pher's equation -which includes the retarda-

tion effect of waves- further yields data on the behavior of the time-decay. These results can be extended to cover multiplying media with the addition of slight modifications.

ll. USES OF TELEGRAPHER'S

EQUATION

The telegrapher's equation is derived from the monochromatic transport equation already described by other authors<lo)cul, and in its space and time dependent form in a non­multiplying medium, it is written

3D 1:.._"' (r t) + ( 1 + 3DZ a )-iL_"' (r t) V2 (jf2 'f'O ' V f}f 'f'O '

=DV2¢o(r,t) -2a¢0 (r,t) +(~I! gt +1)So(r,t),

( 1)

where ¢o(r,t) is the neutron flux at point r and at time t, So(r,t) the neutron source, D

the diffusion coefficient, 2 a the macroscopic absorption cross section, and v the neutron velocity.

1- Green Functions for Infinite or Unbounded Domain

A appropriate Green function for Eq. ( 1 )

should satisfy

V2G-a2 fJG_j_ ~~g_-b2G= -411:~ (r- ru)~(f-to) fJt c2 fJt2 '

( 2)

* Department of Nuclear Engineering, Faculty of En­gineering, Tohoku University, Aramaki-Aoba, Sen­dai.

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where a'= 1+3D.Z~ b'= .Za 1 _ 3 vD , D, C'-1)2.

We shall now develop the appropriate Green function g(R, r) for an infinite or un­bounded domain. Let

( 3)

where R=r-r0 , r=t-to.

Substituting this expression into Eq. ( 2 ), we obtain a differential equation

( 1)d'r+ ,ar+b' +P'- 471: ~c) c4 ) C2 (ii2 a dr- r r- (271:)• u r '

where n(=1,2 or 3) corresponds to the num­ber of spatial dimensions involved. Particular paths of integration are chosen so that the required boundary conditions are satisfied:

g(R, r)= ~R71:J~ e'Pnr(P, r)pdp for n=3 t -~

for n=1,

( 5)

where·: g,(R,r)=- 2;Ra~[g,(R,r)). (6)

To determine r. we must first consider the solutions of the homogeneous form of Eq. ( 4 ) . These are e- ;w•T and e- ;w-7 , where

c:o+={-C -ia'c'+v 4(p'+b')c'-a'c4 ),

c:o-={(-ia'c'-v 4(p'+b')c'-a'c'). ( 7)

The proper linear combination satisfying the condition o (r) =0 for r <o is

( 8)

where u(r) =1 for r>O, and u(t) =0 for r<O. The integral determining gl becomes

g1 (R,r)=2c2iu(r)J~ e-;w•: -e -;w-7

·e'PRdp, (g) -~ co -co

where as a contour we take a line in the upper half plane of p parallel to the real axis of p. The branch line is chosen to run from p= ( + 1/2)-V a'c'-4b2 top= ( -1/2)-V a'c2 -4b2 along the real axis. Let us just consides the integral involving e-iw'T:

exp{i[PR-J p2-l(a4c2 -4b2)cr]} c~ )eH/2la'c'f. 4 dp

J p2-l(a4c2-4b2) 4

565

When R>cr:, the contour may be closed by a semi-circle in the upper plane. The integral is taken to be zero, since there are no singu­larites within the contour. When R<cr:, the contour is deformed so as to extend along the negative imaginary axis. We must then find an integral which is very similar to the inte­gral involved in the calculation of the Green function for the Klein-Gordon equation<''l. We obtain

-(~-)e(-l/Zla'c'TJo( -}v a'c"-4b2V R"-c"r']

·u(cr:-R).

The contibution coming from the integral involving e-;w-T is treated in a similar way, and gives

- ( ~ )ec -l/2la'c'T ]o ( {va'c'- 4b'V R"- c'i:" ]

·[1-u(R+cr)J.

Combining these to expressions yields

gJR,r) =2u/-l/2)a'c'7 Jo( {v a4c2 -4b0

·vR'-c'r:' ]uCcr:-IRi). (lo)

We obtain the three-dimensional g, from the differential equation ( 6):

(R ) _ c ( -1 /2)a2c'T{o ( _ R)+ 1 V a4c'-4b2 · R g, ,r --R-e cr: 2- -V R"=c'r'

·J~(lv a'c'-4b2V R"-c"r:']u(cr- RJ1 (11) 2 )•

Both terms in Eq. (11) vanish when R>cr:, as it should be expected whenever phenomena propagate with a finite velocity. The first term represents the initial pulse, modified however, by two factors. The first, 1/R, is the geometrical factor which already appeared in the solution of the simple wave equation. The second is the factor el- 112la'c'T which tells us that this part of the wave generated by the point source decays with time as it moves through the medium. The second term in Eq.(ll) constitutes the wake.

2. Green Function for Finite Domain

The proper G for bounded domain may be obtained by the method of eigenfunction. Let u. be a solution of the scalar Helmholtz equation in a region bounded by a surface S, upon which u. satisfies the homogeneous

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566

boundary condition. Then

and J u,umdV=o, ...

Since the functions u, form a complete set, we may expand G in terms of u,:

G(r, tiro, to)= 2 c. (t, to)u, (r)u, (ro) (12) n

Introducing this expansion into Eq. ( 4 ) satisfied by G and noting that ~u.(r)u,(ro)= o(r-ro), one obtains a second order different· ial equation for c.:

d'C, +a'c' dC"+c2(B'+b')C =4;rrc'i5(t-t) dt 2 dt n n °

(13)

To determine C., we first consider the solutions of the homogeneous form of Eq.(13). These are e-;w+T and e-;w-T, where

w+=i-C -ia'c'+-v' 4c'(B,i+b') -a•c•),

w-=tC -ia'c"--V 4c'(B,;+b') -a•c•).

The proper linear combination satisfying the condition c.(~) =0 for ~<o is

( -l/2)a2c'T C, (~) =4;rrc2ie

. {e( -l/2)i J4c2W,'+b') a4c4T -i +l/2)i J4c2 lB,2 +b2J -a4c4T}

-V 4c'Cm+b') -a'c'

·u(~). (14)

Now, we describe the physical image of Eq.(14).

(1) When B~>t(a'cL4b2)

sin_!_~~ C ( ) ( -lf2)a'c'T 2

" ~ cx.e ~

where ~2 =4c2 (B~+b2) -a'c',

Eq. (15) denotes vibrated damping effect.

C2) When m<-,tCa'c'-4b')

(15)

e( -1f',;)(a~c2 -t-' JT -e( -1/2)( a2c2+t;T

c, (~)ex. ~' ' (16)

where (~')'=a'c4 -4c'(B~+b').

In this case, C, (~) has the two decay constants

?.,== :D{ (1 +3D2,)

±-v' (1+3D2.)L 12(B,W2 + 2.)' }. (17)

(3) When 4c2 (B.i+b') -a4c4 converges to zero

J. Nucl. Sci. Techno!.,

(18a)

in which case, C,(~) has only one decay con· stant

3. Green Function for Multiplying System

(18b)

In a multiplying system, we must add the

neutron source term 2.kJK(r,r1)¢o(r1,t)dr'

to the right-hand side of Eq.(l ). When this multiplying system satisfies the first funda­mental theorem of reactor theory(7), stipulat· ing that the flux vanish at the boundary of the system,

2.kJ K(r, r 1)¢o(r1, t)dr1 =S.k%(B)¢0 (r, t) (19)

where k is the infinite multiplication factor, K an isotropic displacement kernel, and %(B) the Fourier transform of K(r) in the sense of Eq.(20):

J{(B) = J.oo K(r)4;rrrB-1 sin B·rdr (20)

By replacing b' in Eq.(2) by 2.(1-k%(B))/ D we can use the foregoing results under similar conditions .

4. Neutron Wave Propagation with Periodically Varying Source

3Dft+(3D2.+1 )a¢ v' at• v at

=DV''¢-2.¢+( 3vDiQ+ 1)s;e""'o(r-ro),

(21)

where s;ew'o(r-ro) is the external neutron source.

Using Eqs. (12) and (14), the Green function for Eq. (21) is

(22)

where a2= (1/2)a2c2, b2 =2./D(1 +k% (B)) for

multiplying system, and

w!·= +_!_-V 4c2 (B'+b2) -a'c' 2 n '

w~= -tv 4c'(B.;+b'J -a'c'.

The time part ¢ (t) in Eq. (22) is given by in­tegrating einto as the integral kernel G(t,to) :

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Vol. 5, No. 11 (Nov. 1968)

t+ ( 4n:c2i )(3D ) ¢(t)= J, S(fo)G(t,t0 )dto= (L);-(L), viQ+1 Sa

·dfo. (23)

The result is

¢ (t) = 2n:c' ( 3DiQ + 1)s· 1 (L); v 0 Q2 -(L)": 2-a'-2ia'Q

• C { (Q+(L); -ia2)e+iw:!"t

- (Q-(L); -ia')e -;w:!"1}e -a't_ 2(L):!"e'OtJ.

(24)

To describe in concrete terms the physical image of Eq. (24), we can classify Eq. (24) as follows: (1) When 4c2 (B,i+b2) -a'c'>O

Equation (24) denotes superposition of at­tenuated oscillating waves possessing a damp­ing coefficient a' and a period ±(L)::-.

(2) When 4c2 (B.7+b2) -a'c'<O

¢ Ctl = ~n:~' ( 3DiQ + 1)s; 1 !(L), v Q'+(L):!" 2-a4-2ia2Q

Equation (25) denotes the superposition of two damping waves with damping coefficients, i.e. decay constants (L):!"+a' and a'-(L)::-.

(3) When 4c'(B,i+b') -a'c'=O

Let (L); extend to zero. Then ¢ (t) is

¢(t) =4n:c'( 3DiQ + 1)s 1 v Q2 -a'-2ia2Q

(26)

Equation (26) has only one decay constant, which indicates that the decay form is not e-a'', but te-a''. Particular interest is attach­ed to this phenomenon, for the fact that the decay form is e-a't when we analyze the nentron wave propagation by the diffusion equation.

5. Asymptotic Solution of Telegrapher's Equation

( 1 ) Infinite Non-multiplying System We put the periodically varying neutron

source with an angular frequency (L) at the center of the system. We further assume the medium to be uniform, and that S=O outside the region where neutrons are still being

567

thermalized by moderation, so that the ther­mal neutron flux throughout the medium will have the same time dependence as the source, with consideration given to the retardation effect. The neutron flux will then satisfy the equation

3D ft+_l(l+3Dl' ).!Jrt=DV'"--l'"' (27) V 2 at' v a at 'I' a'f'

of which the approximate solution is

¢(r,t)~+ exp {w+i(L)( t--;) }. (28)

Substituting Eq. (28) into Eq. (27), the dis­persion relation becomes

i(L) (1+3Dl'.)- 3f(L) 2 - (DJ.'-l'.) =0, (29) v v

where ?.=fi-i{JJ_=~+iTJ-i{JJ_ v v

K:'=e-(7J-{JJ_)' = l'. -~ v D v2

8=-;-( ~ +3l'.), p=2~( 7}--;-) -(K:'+p')1/2 ~---

2

7J-{JJ_=(p'-K:')1/2 v 2 .

From these quantities, we have:

Attenuation length

aw=~-1 =( K:'! p'YI' Wave length

lw=2n:(7J--;-r =2n:C,~f(;,r, Propagation velocity

( 2 )1/2 Vw==-OJ -,-, p -K

(30)

(31)

(32)

From these quantities, by measuring the phase lag at the position r and deriving 2n:/lw,

we can obtain the group velocity v/v3 from the formula,

(33)

that is, by plotting a as function of (L) 2, the

group velocity is given from the slope. And also, if the line is extended to zero (L) 2

, we obtain l'./D. On the other hand,

(34)

so that, by plotting {3 as function of (L), with v determined as above, we have (1/D+3l'.)

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568

from the slope. From 2./D and (1/D+32.) thus derived, we can obtain 2. and D.

C 2 ) Correspondence to the Pulsed Neutron Method in Finite System

Let us consider the relation with the pulsed neutron method, in a spherical system of radius R. In the pulsed neutron method, by letting ¢(r,t)~rp(r)e-Xnt and substituting this value which satisfies the Helmholtz equation into Eq. (27), we obtain the second order equa­tion for A.:

3fA~-l(1+3D2.)A.+DB;+2.=0 (35) v v

From above equation we obtain the follow­ing results : (i) When o<m<b, where 6=(1/12)(1/D-32.) 2

(A. is real and positive): When B,; is smaller than 1, An has two eigenvalues.

_ :z Dv 2 3D3v B'+ A,. 1-v a+ 1-32aDB.+ (l-32aD) 3 " ······,

(36a)

d A _ v Dv B~ 3D 3v D4 an ·•--3Jj- l-32aD ,.- (l-32.D)' ,.-· ..

(36b)

(ii) When 1>B~>b CA. is a complex number):

A~.==f(32.+ 1) -'--~B {1-~_L_.§~_L ...... }i (37) - .Y 3 " 2 B.1 8 B:

(iii) When B~=b, there is only one decay constant:

(38)

C 3) Propagation in Multiplying System As mentioned in Sec. I-3, the delayed neu­

trons are neglected. If we neglect also the time during which the neutrons are " fast ", the telegrapher's equation becomes

.!~+l..(1+3D2.)~t v2 at• v at

=DV'2¢-2.¢+k,2 • .7t(B)¢. (39)

The approximate solution considering the re­tardation effect is

¢(r,t)~+ exp {iBr+icv( t-% )}. (40)

In a large system, the diffusion kernel is used in so far as possible, e.g. %(B) ~ 1-B2r.

Inserting Eq. (40) into Eq. (39) the dispersion

J. Nucl. Sci Technol.,

relation becomes

(k.r+L")BL Zcv L2B+1-k. 2cv2 U

v v2

. ( 3L') +teo lo+ v•to =0 (41)

where

K. is the multiplying coefficient due to prompt neutrons.

From Eq. (41), the material buckling

B=-4[ 2cv L2± (a+i/3)] 2M. v •

where a=± J2. ( -p+.Y p'+~>•)- 1 .'2

(3= ±)-:/ -p+.Yp•+K2)1/2

p=.ifJl:..L'-4Mi(1-k.-~v) v2 v2

~>= -4Micv(to+]_~2 ) v·lo '

and where a and (3 take the same sign.

(42)

In Eq. (42), B is represented by the real part B, and the imaginary part B,; that is, B,= (20JL'/v± I ai)/2Mi, B,= (±I f31)/2Mi.

we obtain the attenuation length a.,, the wave length lOJ and the propagation velocity ii.,:

Attenuation length

ii - n-1- 2M:-- .y·sMi (43) .,- t - 1/31 V -p+.y' p2 +-K'

Wave length

[.,=2~r/(-;--n,)=4~rMi{2;k,r:;: ./z" 1 }-1 . (44)

.Y-p+vp•+""

Propagation velocity

- - /(OJ B)-2M 2 f20Jk - K v.,-OJ ·~;-- r - pOJ\. v pr+ .Y2

1 }-1 . (45) V -p+.y' p•+K2

From Eq. (41), if cv converges to zero,

BJ(O) (46)

This material buckling corresponds to the usual critical equation

B• _ k-1 _k-1 Mo- r+L'- M".

At this point, we call attention to the change from r+L' to rk,+V. From the diffusion

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Vol. 5, No. 11 (Nov. 1968)

equation<•J we have;

Attenuaion length

aw=v2M{((k.-1)2+(~zo)'t'- (kp-1) r 2

Wave length

Propagation velocity

Vw=V-2 M;li {[(kp-1)'+( ;7i lo)"r' + (k.-1) f' 12_

There exist some basic differences between the results from the telegrapher's equation and from the diffusion equation. For example, iiw. Tw. and iiw are dependent on the phase lag of OJ/v, that is, the retardation effect. And if OJ diverges to infinity, vw also diverges to infinity in the order vw, while vw converges to the finite value vMi/k,r:. Also if OJ con­verges to zero, vw also converges to zero, while vw converges to a fiinite value 2Mp(1-k.)· (lo+ (3L'/v 2lo) + (2kpr:/v) V1- k.)-1=1=0.

lli. DISCUSSIONS

The Green functions of the telegrapher's equation were obtained for the cases of non­multiplying and multiplying systems. Also, using these Green functions, we have derived solutions describing the time behavior of the neutron wave occasioned by an external neu­tron source varying periodically with an an­gular frequency of OJ.

In a finite system, these solutions are classified into three cases according to the relative value of the geometrical buckling Bn in reference to the nuclear properties of the system as follows: oscillating decay, super­position of two decay forms and singular decay form. These are presented in Eqs. (15), (17), (18b), (24), (25) and (26).

In order to describe wave phenomena pre­cisely, we have followed the view that the telegrapher's equation should be used rather than the diffusion equation in expressing wave propagation.

Denoting by rCB') the ratio between the first and second terms of the left-hand side of Eq. (1 ), as a function of the geometrical buckling B 2

, and assuming the decay form ¢>(r,t) to be approximately <p(r)e-a,',

569

rCB') =/lf2fl_/ j /l(l +3DS.) a¢> 1

v2 at• v at _ 3Da(B 2)

v(l+3DS.)-

The values of rCB') for H,O, D,O and gra­phite, determined on the basis of experiment­al values given by Kiichle<13

', Starr & Price 0 'J and Kussmaul & Meister<'') for H,O, graphite and D,O, respectively are presented in Table 1.

Table 1 r (B') as function of the geomet­rical buckling B' of media

Medium rCB')

H,O 0.02(0.14) 0.04(0.42) 0.06(0. 73)

D,O 0.04 (0.017) 0.09(0.046) -~ --··~- -------

Graphite I 0.012(0.005) 0.024 (0.012)

We can state from Table 1 that: (1) r is nearly constant irrespective of medium if the size of the medium is of normal order; (2) r is larger, the smaller the size of medium. This means that when the system or neutron group velocity is smaller, wave phenomena become predominant, increasing the validity of analyses based on the telegrapher's equa­tion.

Let us compare the decay constant besed on the asymptotic solution of the telegrapher's equation with the experimental value.

The smallest spherical dimensions of sys­tems possessing discrete eigenvalues''6

l is determined from Eq. (38). The radii thus obtained are listed in Table 2.

Table 2 Smallest radii of systems pos­sessing discrete eigenvalues

Medium 0 R(cm) Ao(cm- 1)

H,O 4.08 1.6 2.6X10'

Graphite 0.102 9.9 4.6Xl05

Be 0.169 7.7 5.3Xl04

D,O 0.130 8.7 4.6X104

A comparison of the decay constants calcu­lated with Eqs. (36a) and (36b) with experi­mental values is shown in Table 3.

It is seen from Table 3 that An, is about 10~50 times larger that Ant- This can be ex-

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570 J. Nucl. Sci. Techno!.,

Table 3 Comparison between calculated decay constants and experimental values

Medium I B.(cm-2) I Decay constant (sec-1

) I Experimental value I Author

0.14 I

8.4 X 103 (il.,)

5.1 X 105 (il.2)

H.o

I 0.44

1.8 X 104 (il.,)

5.0 X 105 (il.2)

0.01 I

1.8 X 103 (il.,)

8. 9 X 104 (il.2)

0.027 I

5.0 X 103 (il.1) n.o 8. 7 X 10' CA •• )

0.045 I

8.6X10'(il.,) 8.1 X 104 (il.2)

0.005 I

1.1 X 103 (A.,)

8.1 X 104 (il •• ) Graphite

I 2.5 X 103 (il.,)

0.012 7.9 X 104 (il •• )

plained by the fact that the terms due to il.2

decay faster than those related to il.,, so that only the phenomena governed by the latter terms would be observed in the experiment.

Generally speaking, it is more accurate to treat wave phenomena by the P. approxima­tion (N>2). With this method, an (N+1)th order differential equation would be solved, which would determine N+ 1 decay constants. But, it is difficult to obtain the Green func­tion for an (N+ 1) th order differential equa­tion, and to present a direct physical image of these decay constants.

IV. CoNCLUSIONS

Making use of the telegrapher's equation the propagation of neutron wave has been studied, neglecting the energy dependent aspects.

The following results have been obtained: When a neutron beam is projected into the system, the result can be classified into three cases depending on which the system would either have only one decay constant, two decay constants or else an oscillating decay constant. The neutron wave propagation velocity depends on the angular frequency of the external source and tends to a finite

I 1 X104

I

Kiichle

2X10'

I 2X104

I 5X103

Kussmaul

& Meister

I 8X103

I 1X103

Starr ..

I & Price

2X103

velocity as m--+0 or m--+=. With diffusion ap­proximation, such a result is not obtained, that is, the system has usually only one decay constant, and the propagation velocity tends to zero as m--+0, and diverges to the infinity as m--+=.

Applying our proposed method to the multi­plying system, the critical equation becomes B'ito = (kp -1) I Mi,. where we call Mi,. the pseudo­migration area, which equals r:kp + V. At just critical condition there occurs a peculiar phenomenon, which is that the propagation velocity v., tends to zero as m--+0. On the other hand, analyses based on the diffusion approximation postulates that vw tend to zero as w--+0 independently of kp.

--REFERENCEs--

(1) PEREZ, R.B., UHRIG, R.E.: Nucl. Sci. Eng., 17, 90 (1963).

(2) "Symposium on Neutron Noise, Waves, and Pulse Propagation", (1966), Univ. of Florida, Gainesville, Florida.

(3) MULLER, K.H.: Nukleonik, 4, 218 (1966). (4) MOORE, M.N.: Nucl. Sci. Eng., 26, 354 (1966). (5) UTSURO, M., et al.: Tech. Rept. Kyoto Univ.,

KURRI-TR-26, (1966). (6) OHANIAN, M.J, BOOTH, R.S., PEREZ, R.B.: Nucl.

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Vol. 5, No. 11 (Nov. 1968)

Sci. Eng., 30, 95 (1967). (7) WEINBERG, A.M., WIGNER, E.P.: "The Physical

Theory of Neutron Chain Reactors", (1958), Univ. of Chicago Press, Chicago.

(8) RAIEVSK!, V., HOROWITZ,].: Int. Conf on Peace­ful Uses of Atomic Energy, Geneva, V. 42, (1955).

(9) WEINBERG, A.M., NODERER, L.C.: AECD-3471, (1951).

(10) AsH, M.: "Nuclear Reactor Kinetics", (1965), McGraw-Hill Co. Inc.

571

an BECKURTS, K.H., WIRTZ, K.: "Neutron Physics", (1964), Springer-Verlag.

a~ MORSE, P.M., FESHBACH, H.: "Methods of Theo­retical Physics", Part 1, (1953), McGraw-Hill Co. Inc.

M KDCHLE, M.: Nukleonik, 2, 131 (1960). a~ STARR,E., PRICE,G.: BNL-719, 1034 (1962). a~ KUSSMAUL, G., MEISTER, H.: J. Nucl. Energy,

AB 17, 411 (1963). Q6) CORN GOLD, N.: Nucl. Sci. Eng., 19, 80 (1964).

Nuclear Science Abstracts of Japan, and

English Translation Series of Japanese Papers

in the Nuclear Field

The Nuclear Science Abstracts of Japan, and English translations of certain papers abstracted in the NSAJ are offered free.

(1) Translation in Process

(To be added to the last in Vol.5, No.9, p. 484) (NSJ- Tr 144) Abstr. NSAJ 05221

Fundamental Studies on the Ion Exchange Separa­tion of Isotopes. (9). Separation factor of Uranium (3). Kozo GONDA, et al. (Atomic Fuel Corp.), Hide­take KAKIHANA (Tokyo Inst. of Techno!.)

OS: J. At. Energy Soc. Japan, 9(7), 376~381 (July 1967).

(2) Translations Completed

(To be added to the last in Vol.5, No.9, p. 484) (NSJ- Tr 133) Abstr. NSAJ 04926

Radiation Induced Terpolymerization of Sulfer Dioxide, Acrylonitrils, and Octene-1. Masayuki ITO, Zen-ichiro KURI (Nagoya Univ.) 8 p. (Sept. 1968).

OS: J. Chem. Soc. Japan, Ind. Chern. Sect., 70(6), 1011~1012 (June 1967).

(NSJ- Tr 134) 05480

Measurement of the Ash Content m Coal, Using Two Radiation Sources (1 37Cs.241 Am). Hiromu FUSHIMI (Waseda Univ.) 16 p. (Sept. 1968).

OS: Nucl. Eng. (Tokyo), 13(6), 47~51 (June 1967).

(NSJ- Tr 135) 05430

Development of In-core Void Meter. l\1asahiro SA­TOM!, et al. (Hetachi Ltd.), Takeo UGA, et al. (Japan Atomic Energy Res. Inst.) 16 p. (Sept. 1968).

OS: Trans. Soc. lnstr. Control Engrs. (Tokyo), 3(3), 229~235 (Sept. 1967).

Inquiries should be addressed to the Division of Technical Information, Japan Atomic En­ergy Research Institute, Tokai-mura, Japan.

(NSJ- Tr 136) 05761

An Application of Ultra High Speed Alpha-Autoradio­graphy in the Detection of 239Pu Skin Surface Con­tamination. Osamu MATSUOKA, Kikuo YoSHIKAWA, et al. (Nat. Inst. Radio!. Scis., Chiba) 11 p. (Sept. 1968).

OS: J. Japan Health Phys. Soc., 2 (3), 121~ 127 (Sept. 1967).

(NSJ-Tr 137) 05681-2

Energy Absorption Stectrum-Radiation Dose Opera­tor. Principle and the Automation of Operation. Ichiro MIY ANAGA, Shigeru MORIUCHI (Japan At. Energy Res. Inst.) 24 p. (Sept. 1968).

OS: J. At. Energy Soc. 9 (8), 440~446 (Aug. 1967); 9(9), 518~523 (Sept. 1967).

(NSJ- Tr 138) 05468

On the Polymorphic Transformation of Zirconium Dioxide Associated with the Breakaway During High Temperature Oxidation of Zr and Some Zr Alloys. Tadayuki NAKAYAMA, Tatsuya KOIZUMI (Waseda Univ.) 16 p. (Sept. 1968)

OS: J. Japan lnst. Metals, 31(7), 839~845 (July 1967.

(NSJ-Tr 139) 05133 '·

Studies on the Effects of Iaa, Tiba ar.d X-Ray Irra­diation on the Appearance of Abnormal Spikelets in a Special Variety of Paddy Rice "AKAHO ". Masaharu SHIMIZU, Katsuji KUNO (Nagoya Univ.). 13 p. (Sept. 1968)

OS: Proc. Crop Sci. Soc. Japan, 35(3, 4), 257~

263 (Dec. 1966).

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