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Optimisation and symmetry in experimental radiation physics

174 pages
Nuclear energy and safety
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Commission of the European Communities
nuclear science and technology
EUR 10968 EN
Blow-up from microf r.he original Commission of the European Communities
nuclear science and technology
Visiting scientist
Commission of the European Communities
Joint Research Centre
l-lspra (21020)
PAr\ ' \ "ioth.
Directorate-General Science, Research and Development
Joint Research Centre
1988 CLEUR 10968 EN Published by the
Telecommunications, Information Industries and Innovation
Bâtiment Jean Monnet
Neither the Commission of the European Communities nor any person acting on behalf
of then is responsible for the use which might be made of the following
ECSC—EEC—EAEC Brussels - Luxembourg. 1988 PREFACE
The present monograph is concerned with the optimisation of geometric factors in radiation
physics experiments. The discussions are essentially confined to those systems in which
optimisation is equivalent to symmetrical configurations of the measurement systems. In spite
of this limitation, a surprisingly diverse variety of investigations come under the scope of
the monograph. They include, among others, measurements of interaction cross section of
diverse types, determination of polarisations, development of detectors with almost ideal
characteristics, production of radiations with continuously variable energies and development
of high efficiency spectrometers etc.
The monograph is intended for use by experimental physicists investigating primary interac­
tions of radiations with matter and associated technologies. We have illustrated the various
optimisation procedures by considering the cases of the so-called "14 MeV" on d-t neutrons
and gamma rays with energies less than 3 MeV. In recent years a number of small laborato­
ries have acquired d-t neutron generators thanks, among others, to the projects supported by
the International Atomic Energy Agency and it is hoped that the present monograph would
be of use to the research workers carrying out experimental measurements using these
generators. Developments in fusion technology are critically dependent on the availability
accurate cross sections of nuclei for fast neutrons of energies at least as high as d-t neutrons.
In this monograph we have discussed various techniques which can be used to improve the
accuracy of such measurements and have also presented a method for generating almost
monoenergetic neutrons in the 8 MeV to 13 MeV energy range which can be used to
measure cross ections in this sparingly investigated region.
The monograph is dedicated to the memory of my first research student and later colleague
Dr. Amalendu Nath whose untimely death cut short a brilliant and promising career in
radiation physics.
The author takes this opportunity to thank his students, colleagues and counterparts in Bose
Institute, Calcutta, India, Brookhaven National Laboratory, Upton, U.S.A., Arts and Science
University, Rangoon, Burma, Universiti Sains Malaysia, Penang, Malaysia, the University of
Surrey, Guildford, U.K., the State University of Mongolia, Ulan Bator, Mongolia and the
European Community Joint Research Centre, Ispra, Italy. He is thankful to Dr. R. Ramanna,
former Chairman of the Atomic Energy Commission of the Government of India, Dr. P.K.
Iyengar, Director, Bhabac Research Centre, India and Dr. A.K. Ganguly, former
Director, Chemical Group, Bhaba Atomic Research Centre, India for their advice, support
and encouragement. He is also thankful to the International Atomic Energy Agency, Vienna
and the U.S. National Bureau of Standards, U.S.A. for sponsoring research projects, the
results from some of which have been reported here.
The author is particularly thankful to Mr. John Hubbell of the U.S. National Bureau of
Standards, Prof. Richard Pratt of the University of Pittsburg, U.S.A., Prof. Daphne Jackson
and Dr. Walter Gilboy of the University of Surrey, U.K., Dr. Ante Ljubicic of the Ruder
Boscovitch Institute, Zagreb, Yugoslavia, Dr. David Bradley of the Royal Marsden Hospital,
London and Dr. Malcolm Cooper of the Warwick University, Coventry, U.K., Dr. A. Hanson
and Dr. K. Jones of Brookhaven National Laboratory, U.S.A., Prof. Suprakash Roy of Bose
Institute Calcutta, Prof. Madhya C.S. Chong of Universiti Sains Malaysia, Penang and Dr. T.
Vilaithong of the University of Chiang Mai, Thailand for supplying the author with
preprints, reprints and reports.
Ill The author expresses his gratitude to Prof. Dr. G.R. Bishop, Director General, European
Community Joint Research Centre, Ispra for granting him the facilities of Ispra as a visiting
scientist, which enabled him to write this monograph.
The monograph would not have seen the light of the day but for the continuous help, advice
and friendship of Dr. Walter Kley, Advisor to the Director General, JRC, Ispra from its
inception to conclusion.
Finally the author is taking this opportunity to express his gratitute to his teacher late Dr.
D.M. Bose, former Director, Bose Institue, for having introduced him to the joys and
challenges of radiation physics research.
Chapter I Introduction
Chapter II Spherical Symmetry: Sphere Transmission and Equivalent
Techniques in Their Ideal Forms 7
Chapter III The Reciprocity Theorem 19
Chapter IV Sphere Transmission in Practice: Multiple Interactions
in the Target 29
Chapter V Practical Sphere Transmission: Source, Detector and
Miscellaneous Factors
Chapter VI Axially Symmetric Systems
Chapter VII Circular Arc Method and Its Modifications
Chapter VIII Continuously Variable Energy Secondary Radiations Sources 137
Chapter IX Notes on Cylindrical Symmetry 147
Chapter X Further Applications of Symmetry 151
References 157 Chapter I
1.1 The Optimisation Problem in Radiation Physics
In the design of experiments in physical sciences an important role is played by those factors
which are concerned with the enhancement of the ratio R of the signal S to the noise Ν
pertaining to the measurements
R­S/N . (1.1)
Theoptimumvalueof R is a direct measure of the accuracy which canbeattainedby
followingtheparticular method of measurement used in the experiment.Itisnowonder,
therefore,thatinevery properly designed experiment considerable careisexercisedto
optimisethevalueof this ratio. In this monograph we shall discuss someofthegeneral
designconsiderationswhich are useful in solving this optimisation probleminexperimental
The types of experiments with which we shall be mainly concerned here are those aimed at
investigating the interactions of radiations with matter. The essential elements of the
experimental arrangement for such a measurement are a source of radiation, a sample or
target (scatterer or absorber) and a detector. The factors relevant to the optimisation process
can, therefore, be conveniently divided into three groups viz. the source factors the ith
member of which will be denoted by s¡t the target factors the jth member of which will be
denoted by t. and the detector factor the kth member of which will be denoted by dk. If we
now assume that the factors are so chosen that they can be varied independently and are at
the same time complete in the sense that the ratio R can be completely described in terms of
them, the optimisation process would involve the solution of the three sets of partial
differential equations
aR/asj­O aR/a^­0 3R/adk ­ 0 , (1.2)
where the indices, i.j.k vary over theirrespectiverangesof values. A generalformulation
and solution of the optimisation problemis,therefore,a prohibitingly complextask.
Moreover, the solutions will, in general, refertoidealsystems and it would benecessaryto
extend the analysis further before they becomeusefulinthe practical design of experiments.
We shall, therefore, give up the direct mathematicalapproach to solve the optimisation
problem and search for alternative methods which are, though not strictly general, neverthe­
less applicable to a large variety of physical systems. The method which we shall study
extensively in this monograph is based on spatial symmetry.
1.2 Systems with Spatial Symmetries [il
In many investigations in radiation physics, the physical entities under study possess inherent
spatial symmetries which follow, for example, from their dependence on the angular
coordinates appropriate to the measurements. In such cases the optimisation process can be
conveniently developed by utilising these symmetries. In general, the optimisation process
would confer ideal attributes to the source, target and detector factors. For instance, an
optimised system might consist of a point source, an infinitesimially thin target and a
perfectly black detector. In almost all cases the ideal factors would differ from their counterparts in the laboratory in a significant manner. It would, therefore, be necessary to
examine the effects of deviations from ¡deal values on the accuracies of the measurements
performed under realistic conditions. We note the interesting fact that due to the very
existence of spatial symmetries small deviations <1 along the symmetry related directions q1
are such that the resultant correction factors contain only second and higher order terms
in Sy The mathematical connection between optimisation and symmetry or equivalently that
between the symmetry related vanishing of the first order correction terms and the
optimisation equations (1.2) will not be discussed here. We shall limit ourselves to the use of
geometrical and physical reasonings which would lead, in a natural way, to the adoption of a
specific type of spatial symmetry for the optimised (within practical limits) measurement of
a given physical quantity. In fact, the ideal symmetry suitable for a number of measurements
can be determined in a quite straight forward manner as indicated below.
The line SD joining the effective centres of the source S and the detector D can be taken as
the symmetry axis of a measurement system in which the source has no preferred direction
of emission (Fig. 1). The natural choice for one of the angular coordinates is the angle of
scattering Θ, which is the angle between the lines joining a typical point Τ on the target with
S and D. The second angular coordinate is the angle 0, the azimuthal angle, which measures
the rotation of the plane STD around the axis SD, as measured from a fixed standard
S =the effective centre of the source,
D =the effective centre of the detector,
SO=the symmetry axis of the system,
Τ = typical point on the targete,
Ρ = fixed reference plane through SD,
θ =the angle of scattering and
φ =the azimuthal angle.
Fig. 1 Angular coordinates in a typical radiation physics
When the phenomenon or the entity under study is independent of the angular coordinates θ
and 0, the inherent geometry of the system is obviously spherically symmetric. This is the
basis of the well­known sphere transmission technique (Fig. 2), which has been used rather
extensively to measure such entities. In its ideal form the spherically symmetric measuring
system consists of a point isotropic source, surrounded by an infinitesimally thin concentric
spherical target and an omnidirectional (at least within the tangent cone from D to the target
surface S) detector. The spectral response of the detector is determined by the quantity