Resonance Absorption in Nuclear Reactors

136 Pages·1960·4.271 MB·English

by  Lawrence Dresner, R. A. Charpie and J. V. Dunworth (Auth.)

OTHER TITLES IN THE SERIES ON NUCLEAR ENERGY
Division II: NUCLEAR PHYSICS
Vol. 1. HUGHES—Neutron Cross Sections
Vol. 2. BRADLEY (Trans.)—Physics of Nuclear Fission
Vol. 3. Soviet Reviews of Nuclear Science
Division IV: ISOTOPES AND RADIATION
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Division V: HEALTH PHYSICS
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Division VI: MEDICINE
Vol. 1. MEAD and HOWTON—Radioisotope Studies of Fatty Acid Metabolism
Division X: REACTOR DESIGN PHYSICS
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Vol. 2. PRICE, HORTON and SPINNEY—Radiation Shielding Handbook
Vol. 3. GALANTN—Thermal Reactor Theory
Division XIV: PLASMA PHYSICS AND THERMONUCLEAR
RESEARCH
Vol. 1. SIMON—An Introduction to Thermonuclear Research
RESONANCE
ABSORPTION
IN
NUCLEAR REACTORS
by
LAWRENCE DRESNER
Physicist, Oak Ridge National Laboratory
PERGAMON PRESS
NEW YORK · OXFORD · LONDON · PARIS
1960
PERGAMON PRESS INC.
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Copyright
©
1960
PERGAMON PRESS INC.
Library of Congress Card Number 60-14192
Printed in Northern Ireland at The Universities Press, Belfast
TO BLANCHE
PREFACE
A MONOGRAPH, says Funk, is a "... systematic exposition of one
thing; a treatise written in great detail." Thus the purpose of this
monograph is to provide a systematic and detailed exposition of the
theory of resonance absorption in nuclear reactors. The fulfilment
of this purpose, however, is beset with difficulties one of which is the
fact that "a treatise written in great detail" must necessarily be
difficult to read. To avoid this generic disadvantage of monographs
the author has provided two interwoven texts, one a simplified
version of the other. In particular, the entire text has been divided
into sections, and the simplified version may be obtained by omitting
the reading of those sections marked with a star.
A second difficulty is the fact that many of the terms employed
in the text, especially those involving wave mechanical concepts,
cannot be adequately defined within the limited domain of the
subject matter. Thus, for example, the term "j-wave interaction"
is employed in Chapter 2 without definition in view of the obvious
difficulty of succinctly describing the quantum mechanical decomposi­
tion of a plane wave into its various angular momentum components.
Again, in Chapter 3 in the discussion of the velocity distribution of
nuclei in solids, such undefined terms as "zero point motion" and
"correspondence principle" occur. For those readers with some
knowledge of quantum physics these instances will cause no difficulty;
for other readers they can be passed over with no essential impedi­
ment to further reading of the book.
The plan of the book is as follows: In the first chapter a historical
review is given. In the second chapter resonance absorption in
homogeneous media is studied in general terms, that is, without
detailed specification of the cross sections. The latter part of the
second chapter, devoted to an alternative method of obtaining some
of the formulae found in the earlier part, consists of certain sections
marked with stars which can be omitted without subsequent diffi­
culty. In the third chapter the natural and Doppler broadened fine
shapes are introduced and explicit formulae for resonance absorption
in homogeneous media are given. The detailed derivation of the
ix
÷ PREFACE
dependence of the resonance absorption on the Doppler effect, as
well as the calculation of some second order corrections to the
formulae given earlier in the chapter, are given in some starred
sections. The fourth chapter is a short review of some results of
transport theory necessary for the study of the resonance absorption
problem in heterogeneous media. The latter problem is dealt with
in Chapters 5 and 6. Many sections in the second halves of these
chapters are starred, but these are invariably devoted to the estima­
tion of the errors introduced by the various simplifying assumptions
made in the text. The seventh chapter is a brief resume of certain
special topics, including the Dancoff effect and the estimation of
absorption in unresolved resonances. The eighth chapter is an
exhaustive comparison with experiment.
To Dr. A. M. Weinberg go the author's thanks for originally
interesting him in the subject of resonance absorption, and to Dr.
R. A. Charpie his thanks for suggesting that this book be written.
To Professor E. P. Wigner goes the author's deepest gratitude for
the suggestions and encouragement given during the completion of
his doctoral dissertation, on which the organization of this book
and some of its contents are based. Many heartfelt thanks are due
to Dr. L. W. Nordheim and to Dr. Ě. H. McKay for their cheerful
willingness to perform the burdensome task of reading the manu­
script, and for their many valuable suggestions. Thanks are also due
to Mrs. Yvonne Lovely for her swift and accurate typing of the
manuscript, and to Mr. R. M. Freestone for the excellence of his
illustrations.
LAWRENCE DRESNER
Oak Ridge, Tennessee
December 1959
CHAPTER 1
HISTORICAL REVIEW
1. In chain reactions in which thermal neutrons are employed as
the chain carriers it is always necessary to slow down the energetic
neutrons from fission. This process is accomplished by allowing
elastic collisions of the fast neutrons from fission with the nuclei of
some suitable material, called a moderator. During this process of
moderation the neutrons are subject to removal from the chain by
reacting with any material present in the assembly which does not
yield neutrons. Because historically radiative capture in the sharp
nuclear resonance lines of U 238 was the first such parasitic reaction
considered, the process of absorption during moderation has been
named resonance absorption.
2. The resonance absorption problem proved to be the chief
enigma in the first attempts to decide the possibility of a natural
uranium fueled self-sustaining chain reaction. TURNER (1940)
writing in January 1940, concluded on the basis of a measurement of
the fission neutron multiplicity carried out by ANDERSON, FERMI
and SZILARD (1939), that, except for the unknown extent of resonance
absorption, the chances for establishing a chain reaction were good.
Bohr also noted the further possibility that even if the chain reaction
could be established while the uranium in the chain reactor was cold,
the evolution of fission heat in the uranium would increase its
resonance absorption through Doppler broadening of the resonance
lines, and possibly shut off the chain reaction (CREUTZ et al 1955a).
Even before any reliable data were available on the resonance
absorption process, it was recognized that disposing the uranium in
the form of lumps, rather than mixing it homogeneously with the
moderator, would substantially decrease the amount of resonance
absorption. Fermi and Szilard are credited with this crucial observa­
tion in the United States, but the suggestion of lumping the uranium
was also made independently by Harteck in Germany, and by
Halban, Kowarski and Joliot in France (CREUTZ et al 1955a). The
U.S.S.R. also claims independent discovery (FURSOV 1955).
1
2 HISTORICAL REVIEW
The lumping of the uranium is not without disadvantages. In
addition to decreasing the parasitic resonance capture of neutrons in
the uranium, it also decreases the fission-producing capture of
thermal neutrons in the uranium. Thus, the early problem of reactor
design was the choice of an optimum lattice of uranium lumps and
moderating material in which the multiplication constant was a
maximum. One sine qua non for the solution of this problem was
quantitative information on the magnitude of the resonance ab­
sorption in bulk uranium, and its dependence on size, shape, tem­
perature and dilution (as by the oxygen in U0 , for example).
2
3. The first experiments aimed at supplying this information were
begun by E. C. Creutz, R. R. Wilson and collaborators, at the
Princeton University cyclotron in 1941. The results of these experi­
ments were finally reported in two companion papers in the Journal
of Applied Physics in 1955 (CREUTZ et al. 1955b, c). Accompanying
these papers was a paper by WIGNER et al (1955) reporting pioneering
theoretical work also carried out in 1941 for the dual purpose of
providing a preliminary estimate of the magnitude of the resonance
absorption by lumped uranium, and providing a basis for the design
and interpretation of the experiments. Other theoretical work
carried out in the United States during 1939-41 but never published
is due to Fisk, Shockley, Eckart and Wheeler (CREUTZ et al. 1955a).
Interest in the resonance absorption problem was not diminished
by the very successful beginning made by the Princeton group. In
1944 activation measurements were made on homogeneous mixtures
of uranium and various moderators by MITCHELL et al. (1944) at the
Indiana University cyclotron. Nearly simultaneously with this
experimental work DANCOFF and GINSBURG (1944) completed a
detailed theoretical study. Up to the time of the First International
Conference on the Peaceful Uses of Atomic Energy held at Geneva
in 1955 five other experiments were undertaken in the U.S., viz:
work similar to Mitchell's on homogeneous uranium bearing systems
by HUGHES and GOLDSTEIN (1946), and similar work for thorium by
HUGHES and EGGLER (1945); pile oscillator work on lumped uranium
by MUEHLHAUSE and UNTERMYER (1949); danger coefficient work on
lumped thorium by UNTERMYER and EGGLER (1951); and finally
activation studies on lumped uranium by RISSER et al. (1951).
4. The necessity of obtaining experimental data on heterogeneous
resonance absorption was also apparent in other countries in the
early 1940's. CREUTZ et al. (1955a) mention a considerable number
HISTORICAL REVIEW 3
of British and French workers whose reports were still classified at
the time of the writing of the paper of CREUTZ et al. These works
bear dates from 1942-1944. The earliest Russian experimental work
on heterogeneous resonance absorption known to the author is that
of Popov and Shapiro done by activation techniques in an exponen­
tial assembly presumably used in the design of the first Soviet
uranium graphite reactor (GROSHEV et al. 1955). The date of this
work is not known. After the first Soviet reactor went critical
further measurements of the activation type, also of uncertain date,
were carried out by EGIAZAROV et al. (1955). Other Soviet work on
resonance absorption published prior to the first Geneva Conference
included experiments by BURGOV (1955) in D 0 exponential as­
2
semblies, and by Rudik (BURGOV 1955) in the uranium-D 0 reactor
2
of the Soviet Academy of Sciences, which went critical in 1949. The
resonance absorption in both these works was studied indirectly
through a knowledge of all other factors in the four factor formula;
according to BURGOV (1955) this method is unsatisfactory.
Theoretical research on resonance absorption began in the Soviet
Union in 1943 with the work of GUREVICH and POMERANCHOUK
(1955), finally published in the proceedings of the first Geneva
Conference. Other names mentioned at the Conference in connection
with Soviet theoretical research were A. D. Galanin and F. L.
Shapiro.
5. Five other papers on resonance absorption were also presented
at the first Geneva Conference. A survey of all previous U.S. work
was reported by MACKLIN and POMERANCE (1955a) including both
the experiments on bulk absorption already mentioned, as well as a
compilation of results on the resonance absorption by very thin foils.
A Russian paper by SPIVAK et al. (1955) reported a similar compila­
tion. A report was given by CROCKER (1955) of the U.K. on work
done on U 238 by self-indication techniques in a collimated neutron
beam, and another was given by ERIKSEN (1955) of JENER describing
work done on lumped uranium by the pile oscillator technique. A
theoretical paper was presented by VAN DER HELD (1955) of the
Netherlands, which unfortunately suffered from the inadequacy of
the nuclear data used. A sixth paper, not specifically on resonance
absorption but containing some important ideas on this subject,
was written by CHERNICK (1955).
6. After the first Geneva Conference a continuation of experi­
mental and theoretical effort on resonance absorption occurred.
4 HISTORICAL REVIEW
Reported during the years 1956 and 1957 were experiments of the
activation type performed by HELLSTRAND (1957), BAILLY DU BOIS
et al (1956), SHER (1957), KLEIN et al (1956), and NIEMUTH (1956);
and experiments of the reactivity change type performed by DAVIS
(1957a, b, c) and DAYTON and PETTUS (1958). Furthermore during
these years quantitative estimates of resonance absorption from the
analysis of exponential and critical lattice experiments were published.
Such works were signed by DAVEY (1955), MUMMERY (1955, 1956),
ANTHONY et al (1957), PERSSON et al (1956), and KOUTS and SHER
(1956).
During 1956 and 1957 theoretical effort on resonance absorption
also developed rapidly along three distinct lines. First, interest was
shown in the problem of resonance absorption in homogeneous
media, largely because it was felt to be tractable. An interesting
paper along this line, but with much bearing on problems of hetero­
geneous absorption, was written by SPINNEY (1956, 1957). A novel
second-order correction to the usual homogeneous resonance escape
formula was suggested by WEINBERG and WIGNER (1956); and a
variational solution of the homogeneous resonance absorption
problem was invented by CORNGOLD (1957a). Secondly, there was
an attempt to understand resonance absorption in realistic hetero­
geneous situations by numerical methods, especially the Monte
Carlo method. Papers pursuing this approach were written by
RICHTMYER (1956), SAMPSON (1956), ST. JOHN (1956), and CHERNICK
(1956). The third approach was motivated by the hope of solving
the combined slowing-down transport problem of heterogeneous
absorption approximately in analytic terms. In this approach the
original analysis of WIGNER et al (1955) was followed, with such
refinements added as: the elimination of certain geometric approxi­
mations, the exact handling of the Doppler effect, and the improve­
ment of the treatment of the wide low-energy resonances. Papers
employing this approach were written by CORNGOLD (1957b),
NEUMANN (1956), STEIN (1956), and DRESNER (1955, 1956a, b). A
review paper was written by SAMPSON and CHERNICK (1957).
7. The year 1958 saw the continuation of the third theoretical
approach mentioned in the last paragraph with publication of papers
by CHERNICK and VERNON (1958), DRESNER (1958C), GORDEEV et al
(1958), MEMMERT (1958), ADLER et al (1958), and SPINRAD et al
(1958). The last two works cited were papers given at the second
Geneva Conference. Also presented at the second Conference was