Tsoulfanidis N. Measurement and detection of radiation
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458
MEASUREMENT
AND
DETECTION OF RADIATION
As
shown in Fig. 13.23, the particles enter the spectrometer through a slit,
whose size defines the solid angle accepting particles from the source. This solid
angle should be as large as possible, because the more particles that enter the
spectrometer, the less the necessary counting time is. Since magnetic spectrome-
ters are commonly used with accelerators, reduction of the counting time means
less operational time for the accelerator. When the solid angle increases,
however, the probability also increases that particles with nonparallel paths will
enter the spectrometer. Such particles will not focus at the same point even if
they have the same momentum. This "defocusing" is a difficult problem,
corrected by using magnetic fields that focus at a spot or a line of the detector
all the particles entering through a certain solid angle and having the same
momentum.
The first magnetic spectrometers used photographic plates for the detection
of the deflected particles. Today, position-sensitive semiconductor detectors or
multiwire proportional chambers are used (see
Sec. 13.10). These detectors are
better than photographic plates because they have the capability of on-line data
collection, provide time information for coincidence experiments, and measure
the energy of the particle.
t
13.9
ELECTROSTATIC SPECTROMETERS
Electrostatic spectrometers (or analyzers) do not have such extensive use as
magnetic spectrometers. They are only used for certain types of experiments
where an electrostatic field is more convenient than a magnetic one.
An
electrostatic spectrometer uses a radial electric field formed between
two cylindrical electrodes, as shown in Fig. 13.24.
If
there is a potential
difference
V
between the electrodes EF and E'F', the electric field in the space
Figure
13.24
An
electrostatic spec-
trometer
using
a radial field.
CHARGED-PARTICLE SPECTROSCOPY
459
between the two electrodes is equal to
where
r
is the distance from the center of the electrodes.
A
particle entering the
spectrometer at
EE'
with velocity
v
perpendicular to
EE'
will follow under the
influence of the radial force
a circular path of radius
rf.
It can be show# that particles entering at
EE'
with
the same speed but traveling along a direction slightly different from the normal
to
EE'
will focus at the point
Fo,
provided the angle
4
=
.rr/
=
127O17'
(Fig.
13.24).
All the particles that arrive at
Fo
have a kinetic energy that can be
calculated in terms of the radius
rf
and the strength of the electric field.67 More
details about the focusing properties and energy resolution of electrostatic
spectrometers can be found in Refs.
68-70.
Electrostatic analyzers with parallel
plates have also been constructed.
13.10
POSITION-SENSITIVE DETECTORS
Detectors that in addition to the measurement of the energy also indicate the
position of the particle have been developed for application with magnetic or
electrostatic spectrometers and for imaging devices used in biological and
medical research.
As
discussed in Secs.
13.8
and
13.9,
magnetic or electrostatic
spectrometers are mostly used with high-energy particles. Biological and medical
imaging devices, on the other hand, involve mostly X-rays and, in general,
low-energy radiation. It is because of the latter use that position-sensitive
detectors are briefly discussed here.
13.10.1
Position-Sensitive Semiconductor Detectors
Most of the position-sensitive semiconductor detectors determine the position of
the incident particle by employing the method of
resistive-charge divi~ion.~'
To
illustrate the method, consider the detector in Fig.
13.25.
The detector is a
reverse-biased p-n junction with electrodes on both front and back. The front
electrode with considerable resistivity has two electrical contacts a distance
L
apart. The back electrode has low resistivity and provides a good electrical
contact to the base material. When a particle enters the detector, electrons and
holes are created that move under the influence of the electric field.
If
the
resistivity of the front electrode is homogeneous, and charge-sensitive low-im-
pedance amplifiers are used, the charge collected at one of the two contacts of
the front electrode is proportional to the distance between the point of impact
460
MEASUREMENT
AND DETECTION
OF
RADIATION
Particle
qa
I
imp1 if ier
TTL~~T~~~~~~~
1
1
Front (positive) electrode'
U
,
C
I I
/
/
Si
-
Amplifier
-
Back electrode
40
filter
Figure 13.25
A
position-sensitive semiconductor detector using resistive-charge division (from Ref.
71).
and the other contact. The total charge
q,
collected through the single contact
of the back side is, of course, proportional to the energy deposited in the
sensitive region of the junction. This technique of determining the position by
comparing the signals from
q,
and
q,
is called the
amplitude method.
The signal
q,
changes with time, as shown in Fig. 13.26. The timescale is in
units of the time constant
rD
=
RDCD, where RD and C, are the resistance and
capacitance of the detector, respectively. Figure 13.26 shows that the risetime of
the signal depends on the position. This property is the basis of a second
technique for determination of position, called the
time method.
The position is
Divider
0
-?
0.80
"
u
-
f
0.60
c
0
*
3
a
*
0.40
d
0.20
'0 0.10 0.20 0.30 0.40 0.50 0.60
Time,
(~/TD)
-E
Figure 13.26
Time dependence of the position
signal for different positions of incidence (from
Ref. 71).
CHARGED-PARTICLE SPECTROSCOPY
461
now determined from the difference in arrival times of the signals from the
charges
q,
and
q,
(Fig.
13.25).
The detector described above is of the "continuous" type. Position-sensitive
detectors of the "discrete" type have also been developed.72 They consist of
individual semiconductor elements all placed on the same base material, with
each element connected to its own preamplifier-amplifier system. Two-dimen-
sional detectors of
the
continuous type73 as well
as
of the discrete type74 have
also been tried.
13.10.2
Multiwire Proportional Chambers
Mulitwire proportional chambers (MWPC)? have been developed for use as
position-sensitive focal detectors for magnetic
spectrometer^.^^-^^
They can
provide excellent position resolution, operate with counting rates as high as
lo6
counts/s, and provide a large solid angle at the focal plane of the spectrometer.
The basic design of an MWPC is shown in Fig.
13.27.
A
series of thin,
equally spaced anode wires is positioned between two parallel plates serving as
cathodes.
A
noble gas mixed with an organic component fills the space between
the cathodes.
A
positive voltage is applied to the anode wires. When a particle
goes through the counter, electrons and ions are created by the processes
explained in Chap.
5.
The electric field close to the wires is so intense that the
primary electrons acquire enough energy to produce secondary ionization. Thus,
an avalanche of electrons is produced that is collected within a time of
1
ns, but
that leaves behind a cloud of positive ions.
It is significant that the pulse produced by the counter is not due to the
motion of the electrons, but to that of the ions.76 As the positive ions move away
from the anode wires, they generate a fast-rising
(-
10
ns) negative pulse that
gradually slows down and lasts a few microseconds. The pulse induced in the
neighboring wires is positive. Thus, the active wire (the wire close to the
trajectory of the particle) is distinguished from the others. The signals from the
wires are processed and read by either digital or analog systems.77
The position resolution depends on the spacing between the wires, but it is
better than the actual size of the spacing. The smallest wire spacing is about
1
'single-wire position-sensitive proportional counters operating by charge division (as described
in Sec.
13.10.1)
have also been used?'
Anode wires
Cathode
planes
Figure
13.27
The basic design of an MWPC.
462
MEASUREMENT AND
DETECTION
OF
RADIATION
mm, while position resolutions better than
100
pm have been rep~rted.~~,'~
Such space resolution has been achieved because the position is determined
from the well-defined centroid of the charge distribution generated by the
passage of the particle.
A
variation of the detector described above is the so-called "drift chamber."
The drift chamber determines the position from the time it takes the electrons
produced by the incoming particle to drift to the nearest anode wire.89
A
two-dimensional
MWPC
has also been constructed for detection of neutrons
scattered from biological samples?' It is a 3~e gas-filled counter that detects
neutrons through the
(n,
p)
reaction.
PROBLEMS
13.1
Prove that the maximum energy transfer to an electron as a result of a collision with a particle
of mass
M
and speed
u
=
pc
is equal to
13.2
Show that AE,,, of Prob. 13.1 takes the form
if
T
=
+MU'
(nonrelativistic particle) and
m
4
M.
133
Calculate the energy loss of a 6-MeV alpha particle going through an aluminum foil with
thickness equal to one-fourth of the range of the alpha (remember dE/dx is not constant as the
particle slows down).
13.4
A
monoenergetic beam of 10-MeV alpha particles goes through a nickel foil with a thickness
equal to 1/30 of the range of the alphas. What is the width of the emerging beam (in keV)? If the
emerging particles are counted by a silicon detector with a resolution of
15
keV, what is the total
width of the measured alpha beam (measurement performed in vacuum)?
13.5
What is the thickness of a nickel foil that will cause energy loss equal to 1/50 of the energy of
a 10-MeV proton traversing it?
13.6
Show that the backscattering fraction of electrons is given by
where
g,
T,
and
E'
are defined in Fig. 13.9;
u
is the standard deviation of the Gaussian.
13.7
If the stopping power for a heavy ion can be represented by the equation
where
k
and
b
are constants, what is the expression for the range as a function of energy for such
ions? What is the energy of the ion as a function of distance traveled?
13.8
If the expression for dE/d! given for Prob.
13.7
is valid, what fraction of the initial kinetic
energy of the ion is lost in the first half of its range?
CHARGED-PARTICLE SPECTROSCOPY
463
13.9 A thin fission foil was prepared using natural uranium. Calculate the ratio of alpha activities
due to the isotopes 234~, 235~, and
238~.
The abundance
a
and half-lives of the three isotopes are
234
U:
a
=
0.0057% TI/,
=
2.47
X
lo5 y
235~:
a
=
0.711% TI,,
=
7.10
X
10' y
Assume that every decay gives off an alpha; i.e., neglect decay by spontaneous fission.
13.10 Verify the curves of Fig. 13.22.
13.11 Prove that the energy resolution of a magnetic spectrometer is given (relativistically) by the
equation
(Definition of the symbols used is given in
Sec. 13.8.)
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CHAPTER
FOURTEEN
NEUTRON DETECTION AND SPECTROSCOPY
14.1
INTRODUCTION
Since neutrons do not directly ionize atoms, they are detected "indirectly7' upon
producing a charged particle or a photon, which is then recorded with the help
of an appropriate detector. The charged particle or the photon is the result of a
neutron interaction with a nucleus. If the mechanism of the interaction is
known, information about the neutron can be extracted by studying the products
of the reaction. Many types of interactions are used, divided into absorptive and
scattering reactions.
Absorptive reactions are (n,
a),
(n, p), (n, y), or
(n,
fission). In the case of
an (n, y) reaction, the neutron may be detected through the interactions of the
gamma emitted at the time of the capture, or it may be detected through the
radiation emitted by the radioisotope produced after the neutron is captured.
The radioisotope may emit
P
or
P+
or y or a combination of them. By
counting the activity of the isotope, information is obtained about the neutron
flux
that produced it. This is called the activation method. If the reaction is
fission, two fission fragments are emitted; being heavy charged particles, these
are detected easily.
The main scattering reaction used is neutron-proton collision, called the
proton-recoil method. The knocked-out proton is the particle recorded.
With the exception of the proton-recoil method, which functions for fast
neutrons only
(En
>
1.0
keV), all the other interactions can be used with
neutrons of any energy. However, at every neutron energy, one method may be
better than another. The best method will be selected based on the neutron