Introduction to Radioanalytical Physics

233 Pages·1978·4.662 MB·English

by  G. Deconninck, T. Braun and E. Bujdosó (Auth.)

NUCLEAR METHODS MONOGRAPHS 1
INTRODUCTION
TO RADIOANALYTICAL
PHYSICS
by
G. DECONNINCK
Professor of Physics
Facultés Universitaires de Namur
and Université de Louvain~la-Neuve, Belgium
ELSEVIER SCIENTIFIC PUBLISHING COMPANY
AMSTERDAM - OXFORD - NEW YORK 1978
Coédition published by
Elsevier Scientific Publishing Company, Amsterdam, the Netherlands
and
Akadémiai Kiado,
The Publishing House of the Hungarian Academy of Sciences,
Budapest, Hungary
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Elsevier Scientific Publishing Company, 335 Jan van Galenstraat,
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Library of Congress Cataloging in Publication Data
Deconninck, G
Introduction to radioanalytical physics.
(Nuclear methods monograph; 1)
Includes index.
1. Radioactivation analysis. I. Title.
Π. Series.
QD606.D4 543\088 77-16185
ISBN 0-444-99796-2
Series ISBN 0-444-99803-9
Copyright © Akadémiai Kiado, Budapest 1978
All rights reserved. No part of this publication may be reproduced, stored in a
retrieval system, or transmitted, in any form or by any means, electronic,
mechanical, photocopying, recording or otherwise, without the prior permission
of the copyright owner.
Printed in Hungary
PREFACE
For most readers, radioanalytical methods probably mean neutron
activation or radioactive tracing, since these techniques have attained
widespread popularity with the availability of nuclear reactors. How-
ever, nuclear reactions induced by charged particles, or by high energy
photons, have long been recognized as suitable methods for elemental
analysis. The full development of these techniques had to wait for
technological advances. It is only during the last decade that high-resolu-
tion charged-particle and photon solid-state detectors have become com-
mercially available. The range of applications of nuclear methods has
been considerably extended by these new spectrometers. Non-destructive
investigation of thin layers, depth profiling, surface scanning and trace
analysis are now possible with particles from low energy accelerators.
The bulk analysis of trace elements is also possible by activation of the
sample in the intense bremsstrahlung radiation from a high energy electron
beam. These methods constitute a very promising analytical tool which
supplements and extends the range of other physical methods of analysis.
Many text-books already exist on neutron activation but very little
has been written on other nuclear methods. The aim of the present book
is to introduce the reader to the physical principles of radioanalytical
methods, excluding neutron activation. Nuclear reaction mechanisms,
interaction of charged particle beams with matter and practical formulae
for elemental analysis are discussed. Solved problems are also included
in the text.
The chapter contents were determined according to the various kinds
of detected radiation, i.e. X-rays, charged particles from elastic scattering,
gamma-rays from prompt or delayed nuclear reactions and product
particles from nuclear reactions. All these techniques have in common
that the sample to be analysed is bombarded with charged particles or
irradiated in an intense pencil of gamma-rays. Reaction product charac-
teristics of the elements present in the sample are detected during the
bombardment in the case of prompt methods, or after the bombardment
in the case of delayed methods.
In Chapter 1 nuclear reaction principles are discussed, namely,
kinematics, reaction mechanisms and cross sections. Wherever possible,
practical formulae are given for the reaction cross sections. The inter-
action of particle beams with matter is described in Chapter 2, where
practical formulae for the slowing down process are given and special
5
attention is paid to the calculation of straggling effects, which play a
dominant role in depth profile analysis. The interaction of particle
beams with matter results in the emission of characteristic X-rays used
for elemental analysis, and this is a technique also discussed in Chapter 2.
The backscattering of heavy charged particles is now a well established
technique for surface analysis of heavy atoms; the principles of this
technique as well as typical applications are discussed in Chapter 3.
Different types of nuclear reactions, namely, resonant reactions induced
by low energy protons, gamma-ray scattering and residual activity of
long-lived isotopes produced by bombardment with high-energy particles
or photons lead to the emission of gamma-rays in the final stage. Sur-
face and bulk analysis, depth profiling and trace analysis are possible
with these reactions and are discussed in Chapter 4. A further technique,
the concentration profile determination of light elements, is possible
by unfolding characteristic particle spectra from nuclear reactions
induced by low-energy projectiles and is discussed in Chapter 5. A survey
of the possible use of nuclear reactions as an analytical tool and examples
of investigations carried out in different disciplines are given in Chapter 6.
The scope of radioanalytical methods is very large. The author's in-
tention was to present a coherent text on the physical principles under-
lying these methods and to derive practical formulae for each situation.
In particular, the technical aspect of the analytical method is only briefly
mentioned. Thus, for instance, instrumentation, data handling and com-
parison with other analytical methods are not described. These topics
will be treated in future textbooks.
Introduction to Badioanalytical Physics has been designed as a text-
book for the use of scientists of diverse scientific backgrounds such as
engineers, physicists, biologists, chemists and metallurgists. Prior
knowledge of nuclear sciences is not essential, apart from elementary
courses on radioactivity.
If some originality is found in this text-book, it is entirely due to the
invaluable experience gained by the author in teaching nuclear reactions
at Louvain University and applied nuclear reactions at Namur and
Grenoble Universities over the past fourteen years. It is hoped that this
text-book will, in a minor way, contribute to a better understanding of
activation principles and assist in the education of scientists who intend
to use radioactivation as a means of studying biological, chemical, en-
gineering and industrial problems.
The manuscript was completed on sabbatical leave at the I.S.N. of
Grenoble. The author wishes to thank the staff of this institution for
kind hospitality. Special thanks are due to Dr. J. Cole, Mrs Deeonninck-
Moss and Mrs Honhon Viaina for reviewing the manuscript and for con-
structive suggestions, and to the staff of the Laboratoire d'Analyse par
Réactions Nucléaires des Facultés Universitaires de Namur for their
assistance in the reading and discussion of the work. The final form of
presentation was determined following constructive discussions and per-
tinent advice from Dr. T. Braun and Dr. E. Bujdoso.
Gaston Deconninck
6
SYMBOLS AND ABBREVIATIONS
a incident particle or projectile in nuclear reactions
A target nucleus in a nuclear reaction, usually at rest in the
lab. frame
A atomic mass number of nucleus B
B
Ä average atomic mass number of a compound
b outgoing particle, light product nucleus in a nuclear reaction
B heavy product nucleus in a nuclear reaction
c speed of light
c(x) concentration (proportion in weight) of a given atom in a solid
sample at a depth x below the surface
cm. centre of mass coordinate system
G compound nucleus
C* excited state of nucleus G
d symbol for deuteron (2H nucleus)
e elementary charge 4.803 xlO" 10 (erg · cm)1'2, 1.602 XlO"1· G
eV electron volt, 1.602 χ10~12 erg
E particle energy in MeV (10e eV) or keV(103 eV)
E incident energy, bombarding energy (lab. system)
0
Ε reaction energy, kinetic energy of a particle inducing a nuclear
λ
reaction (lab. system)
E resonance energy (lab. system)
R
E' particle energy in the centre of mass system
f isotopic abundance of nucleus A
A
FWHM full width at half maximum
E threshold energy for nuclear reaction
th
E neutron energy
n
E proton energy
p
E y-ray energy
y
E energy of particle b
b
h Planck constant 6.62559 X 10"27 erg · sec
ft h\2n = 1.054494 X 10 ~27 erg · sec
/ average ionization potential
I(t) beam intensity
1(E) area under a resonance curve
I total area under a resonance curve
m
k energy ratio in elastic scattering (kinematical factor)
11
m in Chapters 2 and 3, projectile mass number
M in Chapter 3 target nucleus mass number, in Chapter 4 mass of
recoiling nucleus (in grams)
m electron rest mass
0
m , m m. . . mass of projectiles (often replaced by the atomic mass
a b> c
number)
m proton mass 1.67252 xlO"24 g
p
Uy number of gamma-rays detected in activation analysis
SK Avogadro constant 6.02252XlO23 mole-1
N number of X-rays or y-rays detected during a bombardment
(^ for sample, N for a standard)
s st
N total number of projectiles
0
N number of nuclei A in one gram of a given sample
A
N number of isotopes present in the sample at the end of the
r
bombardment
Q energy balance in a nuclear reaction, mass defect
t thin foil thickness, surface barrier detector thickness
t time in seconds
t symbol for triton (3H nucleus)
T absolute temperature
T transmission coefficient froiïi optical model calculations
l
V particle velocity in cm · sec^1
R interaction radius, nuclear radius
R(E) Range of charged particles of energy E in a given sample
(in gram)
8(E) stopping power in MeV (g · cm-2)-1 of a given sample for a
charged particle of energy E
Y(E) calculated yield of particles (straggling effects not included)
Y (E) observed yield or calculated yield including energy spreading
0
z atomic number of projectile (charge number)
Z atomic number of target nucleus
Z average atomic number of a compound
Z atomic number of nucleus A
A
a alpha particle, fast 4He+ or 4He+ + ions
V
ß = — ratio of projectile velocity to speed of light
y photon emitted in nuclear interactions (gamma-ray)
Γ FWHM of a resonance or a gaussian curve
Γ partial width for channel a
α
r total spreading width
tot
δ energy step in an excitation curve (MeV or keV)
δ standard deviation in gaussian distribution
0
Δ energy loss (also thermal Doppler width in Chapter 4)
A average energy loss
0
A FWHM of the beam energy distribution, also called beam
b
resolution
A FWHM of the response function of a charged particle detector,
d
also called detector resolution
12
AE energy variation
Δε energy interval
ε detection sensitivity (product of detector solid angle and
detector efficiency)
ε particle energy (in energy loss calculations)
C emission angle of heavy product in the lab. system
0 emission angle of light product in the center-of-mass system;
emission angle of radiation; target tilt on the beam direction
κ Vavilov parameter
k wavelength
λ decay constant
μ absorption coefficient for X-rays and gamma-rays
μθ micro Coulomb
ρ diameter of a circular particle detector; number of nuclei
per gram
σ cross section
a cross section for emission of particle 6 in a A (a, b)B reaction
ab
σ(ψ) differential cross section
Σ macroscopic cross section for neutrons
Σ summation symbol
x symbol for 3He ions
r half life of a radioactive nucleus
x nuclear temperature of residual nucleus B* in evaporation
B
mechanism
ψ emission angle of light product in the lab. system
13
Chapter 1
NUCLEAR REACTIONS
1.1 Introduction
The study of low energy nuclear reactions constitutes a significant
part of nuclear and subnuclear physics and involves many different
aspects of the subject. In the interaction of fast ions with a solid sample,
nuclear reactions can occur between the projectiles and nuclei supposed
to be at rest, embedded in solid matter. Two kinds of events can occur,
the simple deflection of the projectile by the nucleus (elastic scattering)
or a rearrangement of nuclear matter leaving one or both partners in a
modified physical state.
The essential parameter governing the process is the velocity of the
incident particle (often called the projectile). This is related to a more
accessible quantity, the energy by
7^1.384 /--i-lOOcm . sec" 1 (1)
\ A
(in the non relativistic approximation) where V is the velocity, E the
energy in MeV and A the atomic mass number of the projectile.
Because of their ease of production and acceleration the most frequently
used projectiles are protons (p, A — !), deuterons (d, A = 2), 3He ions
(r, A = 3), 4He ions (a, A = 4) and heavy ions.
The considered range of velocity is roughly:
3X108<V<3X109 cm . sec"1
corresponding to low energy nuclear reactions where mechanisms are
rather well understood. Also a great deal of experimental data exist
largely due to the fact that in this energy range ions can be easily produced
and detected using standard and relatively inexpensive equipments.
For analytical purposes two classes of nuclear reactions are consid-
ered: nuclear activation and prompt nuclear reactions. Nuclear acti-
vation and more specifically neutron activation has been used almost
since the beginning of the nuclear age. Consequently a great deal of
literature, in the form of reviews and text books, already exists on the
subject, for which reason it will be only briefly mentioned in this book.
Prompt nuclear reactions applications are more recent and the subject
is still in development. The use of this technique requires a good knowl-
edge of cross sections behaviour, kinematics and interaction of particles
with matter.
15
If the product radiation is a charged particle, information contained
in its energy, identity, and angle of deviation may be related to properties
of the bombarded sample: chemical composition, depth profile con-
centration of impurities, isotopic composition, etc.
In this chapter we shall describe the principal methods used to inter-
pret particle spectra from nuclear reactions and in some cases to predict
such spectra. There are two main features:
(a) The simpler and perhaps most useful feature stems from the fact
that classical mechanics imposes so called "kinematic restrict ions' ' on
the energy of the reaction products.
(b) The reaction rate and the angular distribution of the reaction
products is governed by the physical interaction between the interacting
nuclei. Although a detailed understanding of these phenomena does not
exist in nuclear physics, certain general rules and average properties
can be given which permit the prediction of nuclear reaction cross
sections in many cases.
1.2 Kinematics and consequences
1.2.1 Kinematical relations
The most frequent nuclear reaction is the two body reaction which
may be represented by the symbolic equation:
a + A -> B + b (2)
In this relation, which is also written as A (a, b)B, a is the projectile,
A the target nucleus supposed to be at rest in the laboratory reference
system, b is the light product and B the heavy reaction product. Thus
the two sides of equation (2) represent the physical situation before
and after the interaction.
For atomic and nuclear collisions two systems of reference are often
used: the laboratory system and the centre-of-mass (cm.) system.
A collision in the laboratory frame of reference is described in Eig.
1.1(a). The projectile a has mass m and impinges on the target J.,
a
mass m , which is at rest. Product 6, mass m , is emitted at an angle ψ,
A b
product B mass m at an angle ζ. We suppose that m > m and call
t B B b
B the heavy product. The centre-of-mass system is the frame of reference
in which the interaction is most simply described. The coordinate origin
is the centre-of-mass G of the colliding particles. Particle b is emitted
at angle Θ and B at an angle (π — Θ) with respect to the incident
particle direction. Nuclear scattering data may of course be presented
in either system. Often the incident particle energy is given in the
laboratory system and the angular coordinates in the centre-of-mass
system. The formulae for transforming between these systems are given
in the tables of Marion and Young [1].
16
Nuclear reaction a+A- »B+b
(a) Geometry
jKflight product
/
/
projectile target v eh
y
heavy product
(b) Experimental device
scattering chamber
collimators
Faraday cup
particle beam
from accelerator to current
'to spectrometer " integrator
Fig. 1.1 (a) Laboratory and centre-of-mass reference coordinate systems;
(b) experimental arrangement for prompt nuclear reaction with detection of
charged particles
In a nuclear reaction the total energy is conserved:
E = E + E +Q
a b B (3)
where E is the laboratory energy of the projectile (sometimes called
a
the acceleration energy), E and E the reaction products laboratory
b B
energies. Here Q is the energy balance usually expressed with the other
quantities of equation (3) in MeV or keV and given by:
Q = K + ™>A — ™>bm B)c2 MeV (4)
For this calculation atomic mass units are used (a.m.u.).m is then the
a
mass of the neutral atom a (including its full complement of electrons).
Thus the actual nuclear mass is not used in energy balance calculations.
The conversion of mass to MeV is accomplished using:
1 a.m.u. = 931.478 MeV/c2
Complete tables of reaction Q-values are available [2, 3].
If Q is positive, the reaction is said to be exoergic and kinetic energy
is gained in the reaction.
2 Introduction 17