531 LETTERS TO THE EDITORS
the D 2 0 ; ejected thoria redeposits on the s u r f a c e
of the p a r t i c l e s , trapping many of the f i s s i o n p r o ducts that had a b s o r b e d on the s u r f a c e 4 4) Our
i r r a d i a t e d s l u r r y had an o v e r p r e s s u r e of oxygen,
contained a palladium catalyst, and w a s in other
w a y s different f r o m the s l u r r y used by G a r d n e r .
H o w e v e r , our s l u r r y is m o r e representative of
that expected f r o m an aqueous homogeneous r e actor.
To date
ducts f r o m
been found
properties
prohibitive
no method f o r leaching of f i s s i o n p r o i r r a d i a t e d thoria o r urania s l u r r y has
which does not completely change the
of the s l u r r y solids o r d i s s o l v e a
fraction of the oxide.
Robert
H.
Rainey
Oak Ridge National Laboratory
Oak Ridge, Tennessee
Received April 11, 1963
Revised October 7, 1963
Comment on Doppler Broadened
Absorption
Since the p a p e r * ' A c c u r a t e Doppler Broadened
A b s o r p t i o n " 1 w a s printed in the June 1963 issue of
N u c l e a r Science and Engineering, D r . Joseph J.
Devaney of the L o s A l a m o s Scientific L a b o r a t o r y
has written to us about his extensive e a r l i e r
w o r k 2 " 8 on this subject. Using essentially the s a m e
expression f o r the Doppler broadening a s Eq. (7)
of the above p a p e r , Devaney and his c o l l a b o r a t o r s
have applied a coded digital computation to U 2 3 8 ,
Th, Pu 239 , Pu 240 , Mo, Hf, W .
W e r e g r e t our oversight in not having given
1G. W. HINMAN, G. F. KUNCIR, J. B. SAMPSON, and
G. B. WEST, Nucl. Sci. Eng. 16, 202 (1963).
2J. DEVANEY, M. GOLDSTEIN, and B. FAGAN, "Pu239
Cross Sections and Their Temperature Dependence," LA2127, Los Alamos Scientific Laboratory (1957).
3J. J. DEVANEY and B. G. FAGAN, U238 Cross Sections
and Their Temperature Dependence," LA-2144,
Los
Alamos Scientific Laboratory (1958).
4J. J. DEVANEY, M. A. DEVANEY, and D. COWARD,
"Tungsten Cross Sections and Their Temperature Dependence," LA-2289 Los Alamos Scientific Laboratory (1959).
5J. J. DEVANEY, D. COWARD, and R. E. ANDERSON,
"Molybdenum Cross Sections and Their Temperature Dependence," LA-2373, Los Alamos Scientific Laboratory
(1960).
®J. J. DEVANEY, L. O. BORDWELL, and R. E. ANDERSON, "Thorium Cross Sections and Their Temperature
Dependence," LA-2525, Los Alamos Scientific Laboratory
(1961).
7J. J. DEVANEY and L. BORDWELL,
"Plutonium 240
Cross Sections and Their Temperature Dependence," L A 2574, Los Alamos Scientific Laboratory (1961).
8J. J. DEVANEY, L. O. BORDWELL, and M. J. DEVANEY, "Hafnium Cross Sections and Their Temperature
Dependence," LA-2763, Los Alamos Scientific Laboratory
(1962).
credit to this v e r y useful w o r k . On the other hand,
these r e p o r t s have not compared the accurate
treatment with the m o r e approximate ^/-function
method, and, in this sense, our w o r k can be considered to supplement his.
John B. Sampson
George W. Hinman
General Atomic Division
of General Dynamics Corporation
San Diego, California
Received July 22, 1963
Effect of Neutron Spectrum on the
Branching Ratio of the Ni 5 8 (n,p)
Co 58 Reaction
The effect of branching ratio on the thermal
neutron absorption corrections f o r nickel a c t i v a tion measurements has been discussed fully by
Martin and C l a r e 1 . T h e s e authors show that an
e r r o r of ±10% in the branching ratio can produce
an e r r o r of ±5% in m e a s u r e d fast-neutron doses
using nickel activation monitors in a thermal neutron flux of ~ 1014 n . c m " 2 s e c . _ 1 and that the e r r o r
is g r e a t e r in higher thermal-neutron fluxes. It is,
t h e r e f o r e , important to know the effect of neutronspectrum variation on the branching ratio if nickel
is to be u s e d as an accurate fast - neutron dose
monitor in different r e a c t o r facilities.
The mean branching ratio k f o r a given neutron
spectrum is defined by Martin and C l a r e 1 in t e r m s
of the mean neutron activation c r o s s - s e c t i o n of the
Ni 5 8 (n,p) reaction,
The product k oa is the
c r o s s section f o r activation of Ni 5 8 to the ground
state Co 58 , and (1 - k) va is the c r o s s section f o r
activation of Ni 5 8 to the i s o m e r i c state Co 58 .
B a r r y 2 m e a s u r e d the activation c r o s s - s e c t i o n f o r
the Ni 5 8 ( n , p ) reaction as a function of neutron
e n e r g y E , and obtained a value of oa = (111 ± 12)mb
by averaging the results over a ' f i s s i o n spectrum'.
This result is in good agreement with the value
obtained by W r i g h t (private communication) of 107
mb r e l a t i v e to 65 mb f o r the S 32 ( n , p ) reaction by
comparison of nickel and sulphur monitors in a
hollow f u e l element in P L U T O .
C r o s s 3 has determined the branching ratio as a
*W. H. MARTIN and D. M. CLARE, Determination of
fast neutron dose by nickel activation. Nucl. Sci. Eng., this
issue.
2 J. F. BARRY, The cross-section of the Ni58 (n,p) Co58
reaction for neutrons in the energy range 1.6 to 14.7 MeV.
Reactor Sci. & Technology, Vol. 16, pp. 467-472 (1962).
3 W. G. CROSS, Isomeric ratios in the reactions Ni58
(n,p) Co58 and Co59 (n, 2n) Co58. Bull. Amer. Phys. Soc. II,
8, No. 4 p. 368 (1963).
532
LETTERS TO THE EDITORS
function of neutron energy by following the b u i l d up of the 810 keV y - r a d i a t i o n that f o l l o w s /3-decay
f r o m the i s o m e r i c to the ground state of Co 58 .
The mean branching ratio has been calculated
f o r five different spectra, listed in T a b l e I, using
the r e s u l t s of B a r r y 2 and C r o s s 3 . The s p e c t r a f o r
the fuel-channel w a l l and X - h o l e in a C a l d e r Hall
reactor 4 and the P L U T O M a t e r i a l s Testing R e a c tor hollow f u e l element facilities 5 have been c a l c u lated by Wright 6 using the Monte C a r l o method.
The spectrum at the C a l d e r H a l l p r e s s u r e v e s s e l 4
w a s calculated by J. Butler (A. E . R . E . , H a r w e l l private communication) and the ' f i s s i o n neutron
spectrum' is that determined by C r a n b e r g 7 .
It is clear f r o m the results given in T a b l e I,
considering the wide variation in s p e c t r a investigated, that the mean branching ratio may be cons i d e r e d to be independent of spectrum variations.
This independence of spectrum variations results
f r o m most of the activation being by neutrons h a v ing energies in the range 2 - 6 M e V . In this range
the branching ratio v a r i e s f r o m 0.82 to 0.71 with a
mean value of 0.76.
Hogg et al* m e a s u r e d the branching ratio in
E T R to be 0.66, P a s s e l l and Heath 9 give two
4 R. V. MOORE, and B. L. GOODLET, Symposium on
Calder Works Nuclear Power Plant, British Nuclear
Energy Conf. (1957).
5Nuclear
Engineering, (April, 1958).
6 S. B. WRIGHT, Calculation of high
energy neutron
spectra in heterogeneous reactor systems. A.E.R.E.-R.
4080 (1962).
7 L. CRANBERG, G.FRYE, N.NERESON, and L.ROSEN,
Fission neutron spectrum of U235 Phys. Rev., 103, 662
(1956).
8 C. H., HOGG, L. D. WEBER, E. C. YATES, Thermal
neutron cross-sections of the Co58 isomers and the effect
on fast flux measurements using nickel. IDO-16744 (1962).
9 T. O. PASSELL and R. L. HEATH, Cross-sections of
threshold reactions for fission neutrons: nickel as a fast
flux monitor. Nucl. Sci. Eng. Vol. IV, pp. 308-15 (1961).
TABLE I
Mean Branching Ratio for Different Neutron Spectra
Mean
branching
Neutron spectrum position
ratio, k
Calder fuel-channel wall
0.76o
Calder X-hole
0.76o
Calder pressure vessel - reactor mid-plane
0.755
PLUTO - hollow fuel element
0.75s
Fission neutron spectrum
0.765
values, 0.68 and 0.71, corresponding to two d i f f e r ent positions in E B R - 1 , while M e l l i s h et al10
obtained a value of 0.71 in the c o r e s of B E P O and
DIDO. T h e s e determinations give mean values of
the branching ratio f o r the neutron spectrum
present in each investigation. This difference in
m e a s u r e d and calculated values of k is u n s a t i s f a c t o r y and could lead to an e r r o r of 15% in m e a s u r e d nickel doses in a t h e r m a l - neutron flux of
~ 1 0 1 4 n . c m " 2 s e c " 1 using k = 0.66 if the value of
0.76 is c o r r e c t . The e r r o r would be g r e a t e r in
higher thermal-neutron f l u x e s .
W. H.
Martin
United Kingdom Atomic Energy Authority,
Reactor Materials Laboratory,
Wigshaw Lane, Culcheth,
Warrington, Lanes., England.
Received December 23, 1963
10 C. E. MELLISH, J. A. PAYNE and R. L. OTLET, Flux
and cross-section measurements with fast fission neutrons
in BEPO and DIDO. A.E.R.E. I/R 2630 (1958).