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Gamma and X-Ray Detection
Phone contact information
Benelux/Denmark (32) 2 481 85 30 • Canada 905-660-5373 • Central Europe +43 (0)2230 37000 • France (33) 1 39 48 52 00 • Germany (49) 6142 73820 • Japan 81-3-5844-2681 •
Russia (7-495) 429-6577 • United Kingdom (44) 1235 838333 • United States (1) 203-238-2351
For other international representative ofﬁces, visit our web site: or contact the CANBERRA U.S.A. ofﬁce. 6/06 Printed in U.S.A.
Figure 1.1 Efﬁciency Calibration
DETECTOR OVERVIEW
The kinds of detectors commonly used can be categorized as:
a. Gas-ﬁlled Detectors
b. Scintillation Detectors
c. Semiconductor Detectors
The choice of a particular detector type for an application depends
upon the X-ray or gamma energy range of interest and the applica-
tion’s resolution and efﬁciency requirements. Additional consider-
ations include count rate performance, the suitability of the detector
for timing experiments, and of course, price.
DETECTOR EFFICIENCY
The efﬁciency of a detector is a measure of how many pulses occur
for a given number of gamma rays. Various kinds of efﬁciency deﬁni-
tions are in common use for gamma ray detectors:
a. Absolute Efﬁciency: The ratio of the number of counts pro-
duced by the detector to the number of gamma rays emitted
by the source (in all directions).
b. Intrinsic Efﬁciency: The ratio of the number of pulses pro-
duced by the detector to the number of gamma rays striking
the detector.
c. Relative Efﬁciency: Efﬁciency of one detector relative to an-
other; commonly that of a germanium detector relative to a
3 in. diameter by 3 in. long NaI crystal, each at 25 cm from a
point source, and speciﬁed at 1.33 MeV only.
d. Full-Energy Peak (or Photopeak) Efﬁciency: The efﬁciency

for producing full-energy peak pulses only, rather than a
pulse of any size for the gamma ray.
Clearly, to be useful, the detector must be capable of absorbing a
large fraction of the gamma ray energy. This is accomplished by us-
ing a detector of suitable size, or by choosing a detector material of
suitable high Z. An example of a full-energy peak efﬁciency curve
for a germanium detector is shown in Figure 1.1.
DETECTOR RESOLUTION
Resolution is a measure of the width (full width half max) of a
single energy peak at a speciﬁc energy, either expressed in ab-
solute keV (as with Germanium Detectors), or as a percentage of
the energy at that point (Sodium Iodide Detectors). Better (lower
FWHM value) resolution enables the system to more clearly sep-
arate the peaks within a spectrum. Figure 1.2 shows two spec-
tra collected from the same source, one using a sodium iodide
(NaI(TI)) detector and one using germanium (HPGe). Even though
this is a rather simple spectrum, the peaks presented by the so-
dium iodide detector are overlapping to some degree, while those
from the germanium detector are clearly separated. In a complex
spectrum, with peaks numbering in the hundreds, the use of a
germanium detector becomes mandatory for analysis.
GAS-FILLED DETECTORS
A gas-ﬁlled detector is basically a metal chamber ﬁlled with gas and
containing a positively biased anode wire. A photon passing through
the gas produces free electrons and positive ions. The electrons are
attracted to the anode, producing an electric pulse.
At low anode voltages, the electrons may recombine with the ions.
Recombination may also occur for a high density of ions. At a sufﬁ-
ciently high voltage nearly all electrons are collected, and the detec-
tor is known as an ionization chamber. At higher voltages the elec-

trons are accelerated toward the anode at energies high enough to
ionize other atoms, thus creating a larger number of electrons. This
detector is known as a proportional counter. At higher voltages the
electron multiplication is even greater, and the number of electrons
collected is independent of the initial ionization. This detector is the
Geiger-Mueller counter, in which the large output pulse is the same
for all photons. At still higher voltages continuous discharge occurs.
The different voltage regions are indicated schematically in Figure
1.3. The actual voltages can vary widely from one detector to the
next, depending upon the detector geometry and the gas type and
pressure.
IONIZATION CHAMBER
The very low signal output for the ionization chamber makes this
detector difﬁcult to use for detecting individual gamma rays. It ﬁnds
use in high radiation ﬂuxes in which the total current produced can
be very large. Many radiation monitoring instruments use ionization
chambers. Absolute ionization measurements can be made, using
an electrometer for recording the output.
1
PROPORTIONAL COUNTER
Proportional counters are frequently used for X-ray measurements
where moderate energy resolution is required. A spectrum of
57
Co
is shown in Figure 1.5 in which 14.4 keV gamma rays are well-sepa-
rated from the 6.4 keV X rays from iron.
Proportional counters can be purchased in different sizes and
shapes, ranging from cylindrical with end or side windows to “pan-
cake” ﬂat cylinders. They may be sealed detectors or operate with
gas ﬂow, and may have thin beryllium windows or be windowless.

A detector is typically speciﬁed in terms of its physical size, ef-
fective window size and gas path length, operating voltage range
and resolution for the 5.9 keV X ray from a
55
Fe source (Mn X ray).
Typical resolutions are about 16 to 20% full-width at half maximum
(FWHM).
Operating voltages depend upon the ﬁll gas as well as the geom-
etry. For X rays, noble gases are often used, with xenon, krypton,
neon and argon common choices. Xenon and krypton are selected
for higher energy X rays or to get higher efﬁciencies, while neon
is selected when it is desired to detect low energy X rays in the
presence of unwanted higher energy X rays. Sometimes gas mix-
tures are used, such as P-10 gas, which is a mixture of 90% argon
and 10% methane. Gas pressures are typically one atmosphere.
The 2006 preampliﬁer available for proportional counters is shown
in Figure 1.4.
GEIGER-MUELLER COUNTER
The Geiger-Mueller counter produces a large voltage pulse that is
easily counted without further ampliﬁcation. No energy measure-
ments are possible since the output pulse height is independent
of initial ionization. Geiger-Mueller counters are available in a wide
variety of sizes, generally with a thin mica window. The operating
voltage is in the plateau region (see Figure 1.3), which can be rela-
Figure 1.2
Figure 1.3 Gas Detector Output vs. Anode Voltage
tively ﬂat over a range of bias voltage. The plateau is determined by
measuring the counting rate as a function of the anode voltage.
The discharge produced by an ionization must be quenched in or-
der for the detector to be returned to a neutral ionization state for

the next pulse. This is accomplished by using a ﬁll gas that contains
a small amount of halogen in addition to a noble gas. The voltage
drop across a large resistor between the anode and bias supply will
also serve to quench the discharge since the operating voltage will
be reduced below the plateau.
The Geiger-Mueller counter is inactive or “dead” after each pulse
until the quenching is complete. This dead time can be hundreds
of microseconds long, which limits the counter to low count rate
applications.
Figure 1.4 Proportional Counter and Preampliﬁer
SCINTILLATION DETECTORS
A gamma ray interacting with a scintillator produces a pulse of light,
which is converted to an electric pulse by a photomultiplier tube. The
photomultiplier consists of a photocathode, a focusing electrode and
10 or more dynodes that multiply the number of electrons striking
them several times each. The anode and dynodes are biased by a
chain of resistors typically located in a plug-on tube base assembly.
Complete assemblies including scintillator and photomultiplier tube
are commercially available from CANBERRA.
The properties of scintillation material required for good detectors
are transparency, availability in large size, and large light output
proportional to gamma ray energy. Relatively few materials have
good properties for detectors. Thallium activated NaI and CsI crys-
tals are commonly used, as well as a wide variety of plastics. LaBr
3
(Ce) crystals are a newer type of scintillation detector material of-
fering better resolution, but otherwise, similar characteristics to
Figure 1.5
57
Co Spectrum from Counter

SEMICONDUCTOR DETECTORS
A semiconductor is a material that can act as an insulator or as a
conductor. In electronics the term “solid state” is often used inter-
changeably with semiconductor, but in the detector ﬁeld the term
can obviously be applied to solid scintillators. Therefore, semicon-
ductor is the preferred term for those detectors which are fabricated
from either elemental or compound single crystal materials having
a band gap in the range of approximately 1 to 5 eV. The group IV
elements silicon and germanium are by far the most widely-used
semiconductors, although some compound semiconductor materi-
als are ﬁnding use in special applications as development work on
them continues.
Table 1.1 shows some of the key characteristics of various semicon-
ductors as detector materials:
Table 1.1 Element vs. Band Gap
Material Z Band Gap (eV) Energy/e-h
pair
(eV)
Si
Ge
CdTe
HgI
2
GaAs
14
32
48-52
80-53
31-33
1.12

0.74
1.47
2.13
1.43
3.61
2.98
4.43
6.5
5.2
Semiconductor detectors have a p-i-n diode structure in which the
intrinsic (i) region is created by depletion of charge carriers when
a reverse bias is applied across the diode. When photons interact
within the depletion region, charge carriers (holes and electrons)
are freed and are swept to their respective collecting electrode by
the electric ﬁeld. The resultant charge is integrated by a charge sen-
sitive preampliﬁer and converted to a voltage pulse with an ampli-
tude proportional to the original photon energy.
Since the depletion depth is inversely proportional to net electrical
impurity concentration, and since counting efﬁciency is also depen-
dent on the purity of the material, large volumes of very pure mate-
rial are needed to ensure high counting efﬁciency for high energy
photons.
NaI detector crystals. NaI is still the dominant material for gamma
detection because it provides good gamma ray resolution and is
economical. However, plastics have much faster pulse light decay
and ﬁnd use in timing applications, even though they often offer little
or no energy resolution.
NaI(Tl) SCINTILLATION DETECTORS
The high Z of iodine in NaI gives good efﬁciency for gamma ray
detection. A small amount of Tl is added in order to activate the

crystal, so that the designation is usually NaI(Tl) for the crystal.
The best resolution achievable ranges from 7.5%-8.5% for the 662
keV gamma ray from
137
Cs for 3 in. diameter by 3 in. long crystal,
and is slightly worse for smaller and larger sizes. Figure 1.7 shows,
respectively, the absorption efﬁciencies of various thicknesses
of NaI crystals and the transmission coefﬁcient through the most
commonly used entrance windows. Many conﬁgurations of NaI de-
tectors are commercially available, ranging from crystals for X-ray
measurements in which the detector is relatively thin (to optimize
resolution at the expense of efﬁciency at higher energies), to large
crystals with multiple phototubes. Crystals built with a well to allow
nearly spherical 4π geometry counting of weak samples are also a
widely-used conﬁguration. A typical preampliﬁer and ampliﬁer com-
bination is shown in Figure 1.6.
Figure 1.6 NaI(Tl) Detector Electronics
The light decay time constant in NaI is about 0.25 microseconds,
and typical charge sensitive preampliﬁers translate this into an
output pulse rise time of about 0.5 microseconds. For this reason,
NaI detectors are not as well-suited as plastic detectors for fast
coincidence measurements, where very short resolving times are
required. LaBr
3
(Ce) detectors have a light decay time constant of
0.03 microseconds making them another possible solution for coin-
cidence measurements.
Prior to the mid-1970’s the required purity levels of Si and Ge could
be achieved only by counter-doping p-type crystals with the n-type
impurity, lithium, in a process known as lithium-ion drifting. Although

this process is still widely used in the production of Si(Li) X-ray
detectors, it is no longer required for germanium detectors since
sufﬁciently pure crystals have been available since 1976.
The band gap ﬁgures in Table 1.1 signify the temperature sensitiv-
ity of the materials and the practical ways in which these materials
can be used as detectors. Just as Ge transistors have much lower
maximum operating temperatures than Si devices, so do Ge detec-
tors. As a practical matter both Ge and Si photon detectors must
be cooled in order to reduce the thermal charge carrier generation
(noise) to an acceptable level. This requirement is quite aside from
the lithium precipitation problem which made the old Ge(Li), and to
some degree Si(Li) detectors, perishable at room temperature.
The most common medium for detector cooling is liquid nitrogen,
however, recent advances in electrical cooling systems have made
electrically refrigerated cryostats a viable alternative for many
detector applications.
In liquid nitrogen (LN
2
) cooled detectors, the detector element (and
in some cases preampliﬁer components), are housed in a clean
vacuum chamber which is attached to or inserted in a LN
2
Dewar.
The detector is in thermal contact with the liquid nitrogen which
cools it to around 77 °K or –200 °C. At these temperatures, reverse
leakage currents are in the range of 10
-9
to 10
-12
amperes.

Figure 1.7
In electrically refrigerated detectors, both closed-cycle mixed re-
frigerant and helium refrigeration systems have been developed to
eliminate the need for liquid nitrogen. Besides the obvious advan-
tage of being able to operate where liquid nitrogen is unavailable or
supply is uncertain, refrigerated detectors are ideal for applications
requiring long-term unattended operation, or applications such as
undersea operation, where it is impractical to vent LN
2
gas from a
conventional cryostat to its surroundings.
A cross-sectional view of a typical liquid nitrogen cryostat is shown
in Figure 1.8.
DETECTOR STRUCTURE
The ﬁrst semiconductor photon detectors had a simple planar struc-
ture similar to their predecessor, the Silicon Surface Barrier (SSB)
detector. Soon the grooved planar Si(Li) detector evolved from
attempts to reduce leakage currents and thus improve resolution.
The coaxial Ge(Li) detector was developed in order to increase
overall detector volume, and thus detection efﬁciency, while keep-
ing depletion (drift) depths reasonable and minimizing capacitance.
Other variations on these structures have come, and some have
gone away, but there are several currently in use. These are il-
lustrated in Figure 1.9 with their salient features and approximate
energy ranges.
For more information on speciﬁc detector types refer to the Detector
Product Section of this catalog.
©2006 Canberra Industries, Inc. All rights reserved.
DETECTOR PERFORMANCE
Semiconductor detectors provide greatly improved energy resolu-

tion over other types of radiation detectors for many reasons. Fun-
damentally, the resolution advantage can be attributed to the small
amount of energy required to produce a charge carrier and the con-
sequent large “output signal” relative to other detector types for the
same incident photon energy. At 3 eV/e-h pair (see Table 1.1) the
number of charge carriers produced in Ge is about one and two or-
ders of magnitude higher than in gas and scintillation detectors re-
spectively. The charge multiplication that takes place in proportional
counters and in the electron multipliers associated with scintillation
detectors, resulting in large output signals, does nothing to improve
the fundamental statistics of charge production.
The resultant energy reduction in keV (FWHM) vs. energy for vari-
ous detector types is illustrated in Table 1.2.
Table 1.2 Energy Resolution (keV FWHM)
vs. Detector Type
Energy (keV) 5.9 1.22 1.332
Proportional Counter
X-ray NaI(Tl)
3 x 3 NaI(Tl)
Si(Li)
Low Energy Ge
Coaxial Ge
1.2
3.0
—
0.16
0.14
—
—
12.0

12.0
—
0.5
0.8
—
—
60
—
—
1.8
At low energies, detector efﬁciency is a function of cross-sectional
area and window thickness while at high energies total active detec-
tor volume more or less determines counting efﬁciency. Detectors
having thin contacts, e.g. Si(Li), Low-Energy Ge and Reverse Elec-
trode Ge detectors, are usually equipped with a Be or composite
carbon cryostat window to take full advantage of their intrinsic
energy response.
Coaxial Ge detectors are speciﬁed in terms of their relative full-
energy peak efﬁciency compared to that of a 3 in. x 3 in. NaI(Tl)
Scintillation detector at a detector to source distance of 25 cm. De-
tectors of greater than 100% relative efﬁciency have been fabricated
from germanium crystals ranging up to about 75 mm in diameter.
About two kg of germanium is required for such a detector.
Curves of detector efﬁciency vs. energy for various types of Ge
detectors can be found in the Detector Product Section of this
catalog.
Figure 1.8 Model 7500SL Vertical Dipstick Cryostat
Figure 1.9 Detector Structures and Energy Ranges
1. A.C. Melissinos, Experiments in Modern Physics, Academic Press,
New York (1966), p. 178.

Charged Particle Detection
Phone contact information
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Russia (7-495) 429-6577 • United Kingdom (44) 1235 838333 • United States (1) 203-238-2351
For other international representative ofﬁces, visit our web site: or contact the CANBERRA U.S.A. ofﬁce. 6/06 Printed in U.S.A.
SILICON CHARGED PARTICLE DETECTORS
Silicon Charged Particle detectors have a P-I-N structure in which
a depletion region is formed by applying reverse bias, with the re-
sultant electric ﬁeld collecting the electron-hole pairs produced by
an incident charged particle. The resistivity of the silicon must be
high enough to allow a large enough depletion region at moderate
bias voltages. A traditional example of this type of detector is the
Silicon Surface Barrier (SSB) detector. In this detector, the n-type
silicon has a gold surface-barrier contact as the positive contact,
and deposited aluminum is used at the back of the detector as the
ohmic contact.
A modern version of the charged particle detector is the CANBERRA
PIPS
®
detector (Passivated Implanted Planar Silicon). This detec-
tor employs implanted rather than surface barrier contacts and is
therefore more rugged and reliable than the Silicon Surface Barrier
(SSB) detector it replaces.
At the junction there is a repulsion of majority carriers (electrons in
the n-type and holes in p-type) so that a depleted region exists. An
applied reverse bias widens this depleted region which is the sensi-
tive detector volume, and can be extended to the limit of breakdown
voltage. Detectors are generally available with depletion depths of
100 to 700 µm.
Detectors are speciﬁed in terms of surface area and alpha or beta

particle resolution as well as depletion depth. The resolution de-
pends largely upon detector size, being best for small area detec-
tors. Alpha resolution of 12 to 35 keV and beta resolutions of 6 to
30 keV are typical. Areas of 25 to 5000 mm
2
are available as stan-
dard, with larger detectors available in various geometries for cus-
tom applications. Additionally, PIPS detectors are available fully
depleted, so that a dE/dx energy loss measurement can be made
by stacking detectors on axis. Detectors for this application are sup-
plied in a transmission mount, (i.e. with the bias connector on the
side of the detector).
A chart of the energies of various particles measured at several
depletion depths is shown in Table 1.3. Note that even the thinnest
detector is adequate for alpha particles from radioactive sources,
but that only very low energy electrons are fully absorbed. However,
for a detector viewing a source of electron lines, such as conversion
electron lines, sharp peaks will be observed since some electron
path lengths will lie fully in depleted region. Figure 1.10 shows rang-
es of particles commonly occurring in nuclear reactions.
Table 1.3 Particle Ranges and PIPS Depletion Depth
Maximum Particle Energy
Depletion
Depth
(Range) in µm

Electron

Proton

Alpha
100
300
500
700
1000
0.15
0.31
0.45
0.52
0.73
7
15
21
27
33
15
55
85
105
130
Since charge collected from the particle ionization is so small that it
is impractical to use the resultant pulses without intermediate am-
pliﬁcation, a charge-sensitive preampliﬁer is used to initially prepare
the signal.
Figure 1.11 illustrates the electronics used in single-input alpha
spectroscopy application. Note that the sample and detector are lo-
cated inside a vacuum chamber so that the energy loss in air is not
involved.
LIQUID SCINTILLATORS

Two very important beta-emitting isotopes, tritium and
14
C, have
very low energy beta rays. These are at 19 and 156 keV respec-
tively, too low to detect reliably with solid scintillators. The liquid
scintillation technique involves mixing a liquid scintillator with the
sample, and then observing the light pulses with one or more pho-
tomultiplier tubes. The efﬁciency of such a counter is virtually 100%
– essentially 4π geometry with no attenuation between source and
detector. Pulse processing of the resultant Photomultiplier outputs
allows the rejection of cosmic events, and the separation, if desired,
of alpha and beta events. The increased sensitivity of the Liquid
Scintillation counter, coupled with advances in sample preparation
techniques, has led to its increasing use for low-level alpha and beta
measurements.
Figure 1.10 Range-Energy Curves in Silicon
Figure 1.11
©2006 Canberra Industries, Inc. All rights reserved.
Basic Counting Systems
Phone contact information
Benelux/Denmark (32) 2 481 85 30 • Canada 905-660-5373 • Central Europe +43 (0)2230 37000 • France (33) 1 39 48 52 00 • Germany (49) 6142 73820 • Japan 81-3-5844-2681 •
Russia (7-495) 429-6577 • United Kingdom (44) 1235 838333 • United States (1) 203-238-2351
For other international representative ofﬁces, visit our web site: or contact the CANBERRA U.S.A. ofﬁce. 6/06 Printed in U.S.A.
PULSE ELECTRONICS
The nuclear electronics industry has standardized the signal deﬁ-
nitions, power supply voltages and physical dimensions of basic
nuclear instrumentation modules using the Nuclear Instrumentation
Methods (NIM) standard initiated in the 1960s. This standardiza-
tion provides users with the ability to interchange modules, and the
ﬂexibility to reconﬁgure or expand nuclear counting systems, as

their counting applications change or grow. CANBERRA is a lead-
ing supplier of Nuclear Instrumentation Modules (also called NIM),
which are presented in greater detail in Section 1 of this catalog. In
the past several years, the industry trend has been to offer modular
detector electronics with the multichannel analyzer (MCA) and all
supporting instrumentation for spectroscopy with a single detec-
tor combined in a compact, stand-alone enclosure. These modular
MCAs are smaller, lighter and use less power than the NIM-based
counting systems that preceded them. However, their performance
is equal to, or greater than, comparable NIM-based systems.
CANBERRA is also a leading supplier of these modular detector
electronics which are described in the Multichannel Analyzers Sec-
tion of this catalog. Depending on the application and budget, NIM
or modular electronics may be the best counting equipment solution
for the user, and CANBERRA supports both of these form factors
with a wide variety of products.
Basic electronic principals, components and conﬁgurations which
are fundamental in solving common nuclear applications are
discussed below.
PREAMPLIFIERS AND AMPLIFIERS
Most detectors can be represented as a capacitor into which a
charge is deposited, (as shown in Figure 1.12). By applying detec-
tor bias, an electric ﬁeld is created which causes the charge carriers
to migrate and be collected. During the charge collection a small
current ﬂows, and the voltage drop across the bias resistor is the
pulse voltage.
The preampliﬁer is isolated from the high voltage by a capacitor. The
rise time of the preampliﬁer’s output pulse is related to the collection
time of the charge, while the decay time of the preampliﬁer’s output
pulse is the RC time constant characteristic of the preampliﬁer itself.

Rise times range from a few nanoseconds to a few microseconds,
while decay times are usually set at about 50 microseconds.
Charge-sensitive preampliﬁers are commonly used for most solid
state detectors. In charge-sensitive preampliﬁers, an output voltage
pulse is produced that is proportional to the input charge. The output
voltage is essentially independent of detector capacitance, which is
especially important in silicon charged particle detection (i.e. PIPS
®

detectors), since the detector capacitance depends strongly upon
the bias voltage. However, noise is also affected by the capaci-
tance.
To maximize performance, the preampliﬁer should be located at the
detector to reduce capacitance of the leads, which can degrade the
rise time as well as lower the effective signal size. Additionally, the
preampliﬁer also serves to provide a match between the high im-
pedance of the detector and the low impedance of coaxial cables
to the ampliﬁer, which may be located at great distances from the
preampliﬁer.
The ampliﬁer serves to shape the pulse as well as further amplify it.
The long delay time of the preampliﬁer pulse may not be returned
to zero voltage before another pulse occurs, so it is important to
shorten it and only preserve the detector information in the pulse
rise time. The RC clipping technique can be used in which the pulse
is differentiated to remove the slowly varying decay time, and then
integrated somewhat to reduce the noise. The unipolar pulse that
results is much shorter. The actual circuitry used is an active ﬁlter
for selected frequencies. A near-Gaussian pulse shape is produced,
yielding optimum signal-to-noise characteristics and count rate
performance.

Figure 1.12 Basic Detector and Ampliﬁcation
Figure 1.13 Standard Pulse Waveforms
A second differentiation produces a bipolar pulse. This bipolar pulse
has the advantage of nearly equal amounts of positive and negative
area, so that the net voltage is zero. When a bipolar pulse passes
from one stage of a circuit to another through a capacitor, no charge
is left on the capacitor between pulses. With a unipolar pulse, the
charge must leak off through associated resistance, or be reset to
zero with a baseline restorer.
High performance gamma spectrometers are often designed today
using Digital Signal Processing (DSP) techniques rather than ana-
log shaping ampliﬁers. The shaping functions are then performed in
the digital domain rather than with analog circuitry. This is discussed
later in this section.
Typical preampliﬁer and ampliﬁer pulses are shown in Figure 1.13.
The dashed line in the unipolar pulse indicates undershoot which can
occur when, at medium to high count rates, a substantial amount of
the ampliﬁer’s output pulses begin to ride on the undershoot of the
previous pulse. If left uncorrected, the measured pulse amplitudes
for these pulses would be too low, and when added to pulses whose
amplitudes are correct, would lead to spectrum broadening of peaks
in acquired spectra. To compensate for this effect, pole/zero cancel-
lation quickly returns the pulse to the zero baseline voltage.
The bipolar pulse has the further advantage over unipolar in that
the zero crossing point is nearly independent of time (relative to the
start of the pulse) for a wide range of amplitudes. This is very useful
in timing applications such as the ones discussed below. However,
the unipolar pulse has lower noise, and constant fraction discrimina-
tors have been developed for timing with unipolar pulses.
For further discussions on preampliﬁer and ampliﬁer characteristics,

please refer to each applicable module’s subsection.
Figure 1.14 Multichannel Analyzer Components with Analog Signal Processing
PULSE HEIGHT ANALYSIS AND COUNTING TECHNIQUES
Pulse Height Analysis may consist of a simple discriminator that
can be set above noise level and which produces a standard log-
ic pulse (see Figure 1.13) for use in a pulse counter or as gating
signal. However, most data consists of a range of pulse heights of
which only a small portion is of interest. One can employ either of
the following:
1. Single Channel Analyzer and Counter
2. Multichannel Analyzer
The single channel analyzer (SCA) has a lower and an upper level
discriminator, and produces an output logic pulse whenever an in-
put pulse falls between the discriminator levels. With this device, all
voltage pulses in a speciﬁc range can be selected and counted. If
additional voltage ranges are of interest, additional SCAs and coun-
ters (i.e. scalers) can be added as required, but the expense and
complexity of multiple SCAs and counters usually make this con-
ﬁguration impractical.
If a full voltage (i.e. energy) spectrum is desired, the SCA’s discrimi-
nators can be set to a narrow range (i.e. window) and then stepped
through a range of voltages. If the counts are recorded and plotted
for each step, an energy spectrum will result. In a typical example
of the use of the Model 2030 SCA, the lower level discriminator
(LLD) and window can be manually or externally (for instance, by
a computer) incremented, and the counts recorded for each step.
However, the preferred method of collecting a full energy spectrum
is with a multichannel analyzer.
The multichannel analyzer (MCA), which can be considered as a
series of SCAs with incrementing narrow windows, basically con-

sists of an analog-to-digital converter (ADC), control logic, memory
and display. The multichannel analyzer collects pulses in all voltage
ranges at once and displays this information in real time, providing
a major improvement over SCA spectrum analysis.
Figure 1.14 illustrates a typical MCA block diagram. An input energy
pulse is checked to see if it is within the selected SCA range, and
then passed to the ADC. The ADC converts the pulse to a number
proportional to the energy of the event. This number is taken to be
the address of a memory location, and one count is added to the
contents of that memory location. After collecting data for some pe-
riod of time, the memory contains a list of numbers corresponding
to the number of pulses at each discrete voltage. The memory is
accessed by a host computer which is responsible for spectrum dis-
play and analysis as well as control of the MCA. Depending on the
speciﬁc model MCA, the host computer may be either a dedicated,
embedded processor or a standard off-the-shelf computer.
PULSE HEIGHT ANALYSIS WITH DIGITAL SIGNAL
PROCESSORS
Today’s high performance Multichannel Analyzer systems are de-
signed using Digital Signal Processing (DSP) techniques rather
than the traditional analog methods. DSP ﬁlters and processes the
signals using high speed digital calculations rather than manipula-
tion of the time varying voltage signals in the analog domain. The
preampliﬁer signal ﬁrst passes through an analog differentiator,
then is delivered to a high speed digitizing ADC (Figure 1.15). The
output of the ADC is a series of digital values that represent the dif-
ferentiated pulse. Those signals are then ﬁltered using high-speed
digital calculations within the Digital Signal Processor.
For optimal speed and accuracy in signal processing, a trapezoidal
ﬁlter algorithm is deployed in the DSP implementation. Trapezoidal

ﬁltering has been shown to allow for the highest throughput perfor-
mance with the least degradation of spectral resolution. Addition-
ally, the DSP based design is intrinsically more stable, resulting in
better performance over a range of environmental conditions.
COUNTERS AND RATEMETERS
Counters and ratemeters are used to record the number of logic
pulses, either on an individual basis as in a counter, or as an aver-
age count rate as in a ratemeter. Counters and ratemeters are built
with very high count rate capabilities so that dead times are mini-
mized. Counters are usually used in combination with a timer (either
Figure 1.15
Multichannel Analyzer Components with Digital Signal Processing
Figure 1.16 NaI Detector and Counter/Timer
with Alarm Ratemeter
built-in, or external), so that the number of pulses per unit of time are
recorded. Ratemeters feature a built-in timer, so that the count rate
per unit of time is automatically displayed. Whereas counters have
an LED or LCD for the number of logic pulses, ratemeters have a
mechanical meter for real-time display of the count rate. Typically,
most counters are designed with 8-decade count capacity and offer
an optional external control/output interface, while ratemeters are
designed with linear or log count rate scales, recorder outputs and
optional alarm level presets/outputs. Additional information may be
found in the Counters and Ratemeters Introduction.
SIMPLE COUNTING SYSTEMS
As related above, pulse height analysis can consist of a simple sin-
gle channel analyzer and counter, or a multichannel analyzer. Gen-
erally, low resolution/high efﬁciency detectors (such as proportional
counters and NaI(Tl) detectors) are used in X ray or low-energy
gamma ray applications where only a few peaks occur. An example

of a simple NaI(Tl) detector-based counting system of this type is
illustrated in Figure 1.16.
In this conﬁguration, a Model 2015A Ampliﬁer/SCA is used to gen-
erate a logic pulse for every ampliﬁed (detector) pulse that falls
within the SCA’s “energy window”. The logic pulse is then used as
an input to the Model 512 Counter/Timer which provides the user
with a choice of either preset time or preset count operation. The
Model 512 is equipped with an RS-232 interface, which enables
it to be controlled and read out to a computer for data storage or
further analysis.
Alternatively, Model 1481LA Linear/Log Ratemeter is used as the
counter, with an alarm relay that will trigger if the count rate exceeds
a user preset value.
Although counters are still used in some applications, most of
today’s counting systems include a multichannel analyzer (MCA).
Besides being more cost effective than multiple SCA-based sys-
tems, a MCA-based system can provide complete pulse height
analysis such that all nuclides, (i.e., even those not expected), can
be easily viewed and/or analyzed.
NaI(Tl) DETECTORS AND MULTICHANNEL ANALYZERS
The need for a single-input Pulse Height Analysis system for use with
a Sodium Iodide detector is served most simply by a photomultiplier
tube (PMT) base MCA such as the uniSpec (Figure 1.17). The uni-
Spec MCA includes a high voltage power supply, preampliﬁer, am-
pliﬁer, spectrum stabilizer and ADC in addition to its MCA functions,
and thus, there is no need for any NIM modules or a NIM Bin. All of
Figure 1.18 HPGe Detector and Analog MCA Conﬁguration
this capability is provided in an enclosure no larger than a standard
tube base preampliﬁer, and the computer interface is via a USB port
on the host computer or a USB hub. Further technical discussions

concerning multichannel analyzers and multichannel analysis sys-
tems (including spectroscopy software) may be found in the Multi-
channel Analyzers and Counting Room Software sections.
GERMANIUM DETECTORS AND MULTICHANNEL
ANALYZERS
A typical analog HPGe detector-based gamma spectroscopy sys-
tem consists of a HPGe detector, high voltage power supply, pream-
pliﬁer (which is usually sold as part of the detector), ampliﬁer, ADC
and multichannel analyzer. As will be discussed in more detail later,
DSP conﬁgurations replace the ampliﬁer and ADC with digital signal
processing electronics.
The analog system components are available in several different
types, allowing the system to be tailored to the precise needs of the
application and the available budget. For example, low-end ampli-
ﬁers such as the Model 2022 offer basic capabilities, but users with
higher count rate or resolution requirements may consider the Mod-
el 2026 or 2025 with Pileup Rejection/Live Time Correction (PUR/
LTC) feature and both Gaussian and triangular shaping. Similarly,
the ADC chosen for a system including a 556A NIM MCA could be
either an economical Wilkinson ADC like the Model 8701 or a faster
Fixed Dead Time (FDT) ADC like Model and 8715. For more
Figure 1.17 NaI Detector and MCA Conﬁguration
information about selecting speciﬁc modules, refer to the introduc-
tion sections for those speciﬁc components.
For applications requiring security of the signal processing,
CANBERRA offers a variety of computer controlled electronics
which require access via a host computer, rather than unprotected
front panel for adjustment. For example, the AIM/ICB NIM family is
a network based, computer controlled signal processing line that
can be controlled remotely by a Genie 2000 or Genie-ESP spec-

troscopy workstation.
Spectroscopy systems based on Digital Signal Processing (DSP)
have been widely accepted as the state of the art. In a DSP based
system, the ampliﬁer and ADC are replaced by a set of digital cir-
cuits which implement the ﬁltering functions in high speed digital
calculations. CANBERRA offers several DSP based products, all
of which offer superior environmental stability, higher count rate
throughput performance and better resolution over a range of count
rate conditions. Models 2060, 9660, DSA-1000, DSA-2000 and the
InSpector 2000 all employ this advanced DSP technology.
Figures 1.18, 1.19 and 1.20 show several of the available
Germanium Detectors/MCA conﬁgurations. Optional LN
2
Monitors,
Level Alarms, and Control Systems are available for most types of
detectors.
LEGe AND Si(Li) DETECTORS WITH MULTICHANNEL
ANALYZERS
Low Energy Germanium (LEGe) and Si(Li) detectors require special
circuitry to provide the long time constants required in the ampliﬁer
to achieve maximum resolution, and to properly handle the reset
signals of their preampliﬁers. Although several CANBERRA ampli-
ﬁers are suitable, the best resolution for analog MCA systems will
be obtained with the Model 2025 AFT Research Ampliﬁer. Besides
allowing the user to select a long shaping time constant, the Model
2025 features an enhanced baseline restorer which is ideal for re-
set preampliﬁers. Any of the CANBERRA Digital Signal Processing
MCAs or components can be used with these detectors and provide
even better throughput and resolution performance.
MULTIPLE INPUT SYSTEMS

CANBERRA offers two solutions for multiple input counting systems
which process the ampliﬁed signals from a number of detectors. A
multiple input scenario would typically be considered six or more
detector inputs – or the point at which multiple independent MCA
systems become cost prohibitive for a given counting application.
The Multiport II (Figure 1.18) is the ﬁrst solution and, also, the more
robust of the two. It offers the capability for up to six totally indepen-
dent MCAs and ADCs housed in one double-wide NIM. Because
the MCAs and ADCs are separate from each other, any combina-
tion of detectors and channel number settings may be used for each
input.
Figure 1.20 HPGe Detector with DSA-2000 Digital Signal Processor (DSP)
Figure 1.19 HPGe Detector with DSA-1000 or InSpector 2000 Digital Signal Processor (DSP)
The second solution employs a Model 8224 Multiplexer (or Mixer/
Router) to route the signals from multiple detectors to a single ADC
for digitizing and on to a 556A MCA for processing as shown in
Figure 1.21. Since this conﬁguration shares the MCA and ADC
among the detectors, it has a lower cost per input than the Multi-
port II – particularly for large numbers of detectors. However, the
Multiplexer conﬁguration has a major drawback due to the single
ADC; the count rate of the individual detectors must be relatively
low to avoid excessive signal pileup. Additionally, a Multiplexer must
allocate the memory of the MCA to its various inputs (same amount
for each input), which decreases the number of channels available
for each individual detector. Within these constraints, Multiplexers
can be quite efﬁcient for applications such as low-level environmen-
tal alpha spectroscopy in which multiple low-intensity inputs are col-
lected in MCA memory segments of 512 channels or less. Low-level
gamma counting with NaI detectors, which typically don’t need more
than 1024 channels, is another application that can make use of a

Multiplexer. An example conﬁguration is depicted in Figure 1.21.
It should be noted that the Multiport II and the 8224 Multiplexer do
not include spectroscopy ampliﬁers or detector bias supplies. These
components must be supplied by other parts of the signal chain.
Also, these two solutions do not include the beneﬁts of Digital Sig-
nal Processing.
Advances in electronics technology have dramatically lowered the
cost of MCAs, so that today, it is frequently more effective to use
multiple complete MCA systems (or the Multiport II) in place of a
Multiplexer.
LOW LEVEL GAMMA RAY COUNTING
Large volume HPGe detectors have become dominant over other
detector types for low level gamma ray spectroscopy because of
their inherently good resolution and linearity. It is only in the analy-
sis of single radionuclides that NaI(Tl) detectors can compare in
sensitivity with HPGe detectors. Since the majority of all gamma
spectroscopy applications require the analysis of more complex,
multi-radionuclide samples, the following discussion will be limited
to the application of HPGe detectors to low level counting.
The sensitivity of a HPGe spectrometer system depends on sev-
eral factors, including detector efﬁciency, detector resolution,
background radiation, sample constituency, sample geometry and
counting time. The following paragraphs discuss the role these fac-
tors play in low level gamma ray counting.
1. EFFICIENCY: Generally, the sensitivity of a HPGe system
will be in direct proportion to the detector efﬁciency. HPGe
detectors are almost universally speciﬁed for efﬁciency rela-
tive to a 3 in. NaI(Tl) at 25 cm detector-to-source distance at
1.33 MeV, and from this benchmark one may roughly com-
pute the efﬁciency at lower energies. However, for the cus-

tomer who is counting weak samples with lower gamma
energies, for instance 100-800 keV, the following subtle con-
siderations to the detector design are important to system
performance:
a. The detector should have an adequate diameter. This as-
sures that the efﬁciency at medium and low energies will
be high relative to the efﬁciency at 1.33 MeV, where it is
bought and paid for.
b. The detector-to-end-cap distance should be minimal – ﬁve
millimeters or less. The inverse square law is real and will
affect sensitivity.
c. The detector should be of closed end coaxial geometry, to
assure that the entire front face is active.
2. RESOLUTION: Generally, the superior resolution of a HPGe
detector is sufﬁcient enough to avoid the problem of peak
convolution, (i.e., all peaks are separate and distinct). The
sensitivity of a system improves as the resolution improves
because higher resolution means that spectral line widths
are smaller, and fewer background counts are therefore in-
volved in calculating peak integrals.
Since the sensitivity is inversely related to the square root of
the background, that is,

improvements in resolution will not improve sensitivity as
dramatically as increased efﬁciency.
Figure 1.21 Multiple Input NaI Detector System
Sensitivity =
1
Bkg

√
3. BACKGROUND RADIATION AND SAMPLE CONSTITU-
ENCY: Interfering background in gamma spectra originates
either from within the sample being counted (Compton-pro-
duced) or from the environment. If the sample being ana-
lyzed has a high content of high-energy gamma emitting
radioisotopes, the Compton-produced background will eas-
ily outweigh the environmental background. For extremely
weak samples, the environmental background becomes
more signiﬁcant. Obviously, massive shielding will do little to
improve system sensitivity for low energy gamma rays in the
presence of relatively intense higher energy radiation. How-
ever, Compton-suppression can be very effective in reducing
this background.
4. SAMPLE GEOMETRY: An often overlooked aspect of HPGe
detector sensitivity is the sample geometry. For a given sam-
ple size (and the sample size should be as a large as prac-
ticable for maximum sensitivity), the sample should be dis-
tributed so as to minimize the distance between the sample
volume and the detector itself.
This rules out analyzing “test tube” samples with non-well
type detectors, or “large area ﬂat samples” with standard de-
tectors. It does rule in favor of using re-entrant or Marinelli-
beaker-type sample containers, which distribute part of the
sample around the circumference of the detector.
GERMANIUM DETECTORS WITH INERT SHIELDS
There are many different types of shield designs that are available,
and because of the difﬁculty in determining the background contri-
bution of the materials used in a given shield, it is difﬁcult to assign
performance levels to various types of shields. However, some crite-

ria for shield designs have evolved over the years, such as:
1. The shield should not be designed to contain unnecessary
components like the Dewar. It will only contribute to increased
background if it is within the walls of the shield, as well as
unnecessarily increase the shield’s size, weight and cost.
2. The detector should be readily installed and removable from
the shield.
Pity the person who has to move lead bricks (at 12 kg each)
to disengage a HPGe detector. A HPGe detector and shield
system should have a liquid nitrogen transfer system to avoid
removing the detector for the weekly ﬁlling.
3. Sample entry should be convenient to the operator.
4. The shield should accommodate a variety of sample sizes
and conﬁgurations.
The HPGe detector should be located in the center of the
shield so as to minimize scatter from the walls. In this posi-
tion, the shield must accommodate the largest sample that
is anticipated. Also, sample placement should be accurately
repeatable and easily veriﬁed by the operator.
The shield design that has all these features and is moderately
priced is the CANBERRA Model 747 Lead Shield illustrated in
Figures 1.22 and 1.23.
Figure 1.22 Detector located in center of chamber
without requirement for extended end-cap
Figure 1.23 Model 747 Lead Shield
The performance of the shield using a CANBERRA HPGe detector
is given below:
Shield Specs: Inside Dimensions
Wall Thickness
Material

28 cm dia. x 40.5 cm high
10 cm
Low Background Lead
HPGe Specs: Relative Efﬁciency
Resolution
12%
1.95 keV FWHM at 1.33 MeV
0.90 keV FWHM at 1.22 keV
Background
Count:

2.25 counts/second in the 50 keV–2.7 MeV range
Sensitivity: Table 1.4 lists the sensitivities of several single
radioisotopes, assuming a counting time of
50 000 seconds, a 50% error and a detector-to-
point-source distance of 1 cm.
Table 1.4 Radioisotope vs. Sensitivity
RADIONUCLIDE ENERGY
in keV
SENSITIVITY
in pC
57
Co
139
Ce
137
Cs
60
Co
122

165
662
133
2
3
6
10
LOW BACKGROUND CRYOSTATS
The design or conﬁguration of the cryostat is another factor in sys-
tem performance. Some cryostat/shield designs do not prevent
streaming from the outside environment, nor do they provide self-
shielding from their own relatively hot components. Through an
improper choice of material types and/or thicknesses, the cryostat
may appreciably contribute to the background. CANBERRA has
developed sources for select, low-background, materials, and has
invested in the design and fabrication of low-background cryostats,
as described in the Introduction to the Cryostats and Cryostat
Options Section.
HPGe COMPTON SUPPRESSION SPECTROMETER
When the ultimate in low level counting is required, a Compton
Suppression Spectrometer, in conjunction with an appropriate low-
background shield/cryostat design, is the answer. In this conﬁgura-
tion, the HPGe detector is surrounded by an active NaI(Tl) or plastic
scintillation guard detector (also known as an annulus detector),
with the electronics conﬁgured in an anticoincidence counting mode.
The Compton continuum, which is primarily caused by gamma rays
which sustain one or more inelastic collisions and escape (i.e. scat-
ter out of) the germanium detector material without imparting their
full energy, can lead to concealment of low activity peaks. Since
this is undesirable in low level counting applications, a Compton

Suppression Spectrometer can be used to gate (i.e. turn off) data
acquisition whenever one of the incompletely absorbed photons es-
capes the germanium detector and is “seen” by the annulus detec-
tor. When acquisition is complete, the resultant spectrum contains
only peaks attributed to gamma rays which have imparted their full
energy within the detector material.
It should be pointed out that some radioisotopes (those having co-
incident gamma rays) such as
60
Co, will not be analyzed properly
by the anticoincidence spectrum from a Compton Suppression Sys-
tem. Therefore, two spectra are usually obtained from such a spec-
trometer – one in the anticoincidence mode, and the other in the
normal (ungated) mode.
Figure 1.24 illustrates a typical example of a Compton Suppression
System.
One type of annulus has six (6) 5.08 cm (2-inch) diameter photo-
multiplier tubes (PMTs) on one end, and a 7.62 cm (3-inch) diam-
eter NaI(Tl) plug with one PMT (which is operated in parallel with
the other PMT) on the other end. A simpler type of annulus detector
uses a 15.24 cm (6-inch) diameter NaI(Tl) well detector on a single
PMT. In either conﬁguration, the annulus must be large enough to
allow the insertion of the HPGe detector’s endcap along with the
sample.
Figure 1.24 Compton Suppression System
While some endorse the use of a fairly complex Timing Chain to
derive the anti-Compton gate signal, CANBERRA has found that
the simpliﬁed circuit shown in Figure 1.24 yields equivalent results.
2

The “Incoming Count Rate” signals from the Spectroscopy Ampli-
ﬁers are checked for coincidence, and, if it exists, the 2040 Co-
incidence Analyzer’s output is used as an anti-coincidence input
to the ADC’s Gate. When coincidence occurs, this gate “turns off”
the delayed unipolar signal from the Spectroscopy Ampliﬁer. Typical
Compton Suppression Spectrometer results are illustrated in Figure
1.25. It can be seen that the ‘ﬁgure of merit’ – the value of the
137
Cs
peak at 662 keV divided by the average contents of the Compton
continuum (the energy range 358-382 keV) – is on the order of
1000:1.
HIGH COUNT RATE GAMMA RAY SYSTEMS
High count rate applications require special techniques to assure
good resolution and/or good throughput. In general, “high count
rate” is used to refer to incoming count rate, that is, the number
of events seen by the detector. The term “throughput rate” may be
of more interest to the researcher, being a measure of the rate at
which the system can accurately process these incoming counts.
In high count rate HPGe detector applications, problems such as
the loss of resolution, excessively long counting times, erroneous
peak to background ratios, inaccurate counting statistics or system
shutdown due to overload and saturation begin to appear. In some
experiments, the solution to these problems merely lies in reducing
the incoming count rate to the detector, or by employing electron-
ics which inhibit the processing of pulses through the electronics
when events are occurring so fast that they are overlapping (pulse
pileup). In this latter solution, system throughput will of course be
reduced, but parameters such as resolution will be enhanced. Table
1.5 indicates the throughput limitations of the major components of

a spectroscopy chain. Note that the term “energy rate limited” refers
to the fact that the component’s performance is not only affected
by the incoming count rate, but by the relative energy (amplitude)
of the incoming counts as well. Each element in the chain can be
2. Compton Suppression Made Easy, Application Note
Figure 1.25 Ge Spectra with Compton Suppression
optimized for high count rate performance.
THE DETECTOR
For the detector itself, the charge collection time is the limiting fac-
tor, and this parameter is a function of the detector geometry – when
a photon interaction takes place, charge carriers in the form of holes
and electrons are produced, and the time taken for these carriers to
be swept to the p and n electrodes of the detector is the time for full
energy collection. In a germanium detector, this time is a function of
detector size, as the charge carriers travel about 0.1 mm/ns. As the
charge collection time increases, the Ampliﬁer must take a longer
time to process the signal and develop its linear pulse, or else not
all of the incident energy will be reﬂected in that pulse (“ballistic deﬁ-
cit”). Thus, larger detectors require longer ampliﬁer time constants,
or more sophisticated peak shapes.
Some ways to address high count rate in the detector include mov-
ing the detector farther away from the source, or collimating the de-
tector – which in both cases reduces the number of events seen by
the detector – or using a detector of lesser efﬁciency. The detector
in the latter case will ‘see’ fewer events, and furthermore will have a
lower charge collection time.
THE PREAMPLIFIER
Most Germanium detectors in use today are equipped with RC-
feedback, charge sensitive preampliﬁers. In the RC-feedback pre-
ampliﬁer, a feedback resistor discharges the integrator, typically in

one or two milliseconds. If the incoming energy rate (count rate X
energy/count) produces a current that exceeds the capability of the
resistor to bleed it off, the output will increase until, in the extreme,
the preampliﬁer saturates and ceases to operate. This limit occurs
at approximately 200k MeV/s. The saturated condition remains un-
til the count rate is reduced. The saturation limit is dependent on
both energy and count rate and is usually speciﬁed in terms of the
“energy/rate limit”. The energy/rate limit can be increased by lower-
ing the value of the feedback resistor, but this in turn allows more
noise to pass through the preampliﬁer, resulting in a degradation in
Table 1.5
Major System Components and their Throughput Limitations
When a Coaxial Germanium detector is used in applications requir-
ing high throughput, the Model 2101 Transistor Reset Preampliﬁer
(TRP) is favored over traditional RC feedback Preampliﬁers. The
higher cost of the TRP is justiﬁed by its much higher energy rate ca-
pacity, an enhancement obtained by replacing the Feedback Resis-
tor of a typical RC feedback preampliﬁer with a special reset circuit.
This circuit monitors the dc level of the preampliﬁer and discharges
the feedback capacitor whenever the output reaches a predeter-
mined reset threshold. At moderate to high count rates (i.e. above
20 000 cps), the absence of the feedback resistor and its attendant
noise and secondary time constant contributions lead to: 1) lower
preampliﬁer noise contributions, 2) inherently better resolution and
reduced spectrum broadening vs. count rate, 3) elimination of the
need for pole/zero cancellation, and 4) elimination of ‘lock-up’ due
to saturation. Figure 1.26 illustrates the throughout performance of
the two preampliﬁer styles.
Although the Model 2101 TRP virtually never shuts down due to
saturation, its reset process and the ampliﬁer overload which it

causes does induce intervals of dead time into the counting system.
The Model 2101 has been designed with a small Charge Gain (50
mV/MeV) and a wide Dynamic Range (4 V) to signiﬁcantly reduce
the dead time due to resets in comparison to competitive units.
DIGITAL SIGNAL PROCESSOR
As we described in an earlier section, Digital Signal Processors
(DSP) have come to replace the analog shaping ampliﬁer and ADC
in most high performance gamma spectroscopy systems. It is in
applications involving high count rate performance where the
advantages of DSP become most pronounced.
In gamma spectroscopy systems, the DSP replaces the functional-
ity of both the shaping ampliﬁer and the ADC. The DSP ﬁrst ﬁlters
the signal for optimum signal to noise ratio and to provide gain. It
then detects the peak amplitude of the ﬁltered pulse to calculate the
memory address of the MCA channel into which the event is to be
stored.
In the DSP, the analog signal from the preampliﬁer is ﬁrst differenti-
ated in the analog domain to provide a rapid return to baseline. This
is depicted in Figure 1.27. The resulting time varying voltage signal
is sampled by a high speed sampling analog to digital converter. This
results in a digitized proﬁle of the differentiated preampliﬁer signal
represented in internal memory of the DSP. From this point on, the
signal is processed in the digital domain by the DSP – essentially
a high speed digital computer executing calculations as opposed
to analog circuits manipulating time varying voltage signals.
Figure 1.26 Throughput vs. Count Rate:
Throughput Optimization
Figure 1.27 Typical Ampliﬁer Pulses
Figure 1.28 Trapezoidal Pulse
Waveform as processed in DSP

Processing the signals digitally allows more sophisticated ﬁltering
functions to be applied to the signal. It also allows greater ﬂexibility
to the user in terms of adjusting ﬁltering parameters – more possi-
ble settings are available because they are handled as digital com-
mands, not the selection of discrete analog components. Finally,
the use of high speed digital electronics allows the signals to be
processed more rapidly, thus contributing further to the count rate
performance of the system.
CANBERRA’s DSP products deploy a trapezoidal ﬁltering algorithm
as shown in Figure 1.28. Two parameters are available for user
adjustment – the rise/fall time of the trapezoid (hereafter referred to
as rise time) and the ﬂat top time.
Adjusting the rise time changes the ﬁlter characteristics to optimize
for noise characteristics. The larger the rise time, the better the sig-
nal to noise ratio. Shorter rise times will adversely affect signal to
noise ratio and degrade the resolution of the system. Flat top ad-
justments are made to accommodate the variations in pulse rise
time which in turn is proportional to the charge collection time in
the detector. Larger detectors tend to have a larger number of long
rise time (large charger collection time) events, thus requiring a lon-
ger ﬂat top time. Failure to set the DSP rise time long enough to
accommodate the longest charge collection time events results in
degraded resolution, an effect known as ballistic deﬁcit. Note that for
some types of smaller detectors, the ﬂat top time can be set near or
very close to zero, resulting in a triangular shape.
Figure 1.29 A comparison of the system throughput as a function
of input count rate for a DSP and an analog system optimized for
high throughput for a small detector (11%)
Figure 1.30 A comparison of the system resolution as a function
of input count rate for a DSP and an analog system optimized

for maximum throughput for a small detector (11%)
Figure 1.31 A comparison of the system throughput as a function
of input count rate for an analog system optimized for maximum
throughput with a DSP system set for a similar throughput
These two parameters together control the total event processing
time. The total processing time for an event processed with the DSP
trapezoidal algorithm is deﬁned by the equation:
T
p
= (2T
r
) + T
ﬂat top
We see that the settings for both parameters effect the total pro-
cessing time, which in turn effects the count rate throughput of the
system. As we noted earlier, setting either parameter too fast can
result in lost resolution. Increasing the settings improve resolution,
but lengthen processing time and sacriﬁce throughput. A tradeoff
exists (as it did in analog systems) between count rate throughput
and resolution. Higher throughput can be attained with a loss of
resolution and better resolution can be attained at a loss of through-
put – up to the limits imposed by the performance of the detector
and preampliﬁer components.
These tradeoffs also existed in traditional analog systems, but the
tradeoffs can now be made at a higher level – the DSP provides
both improved throughput and improved resolution as compared to
analog. This is due to a number of factors. First, the trapezoidal
algorithm is simply more efﬁcient and can process the signals more
accurately and rapidly than analog electronics.
Secondly, the user has much more ﬂexibility to vary the components

of the processing time. In analog systems, the processing was con-
trolled by a single parameter – the shaping time. Now with DSP, two
parameters are available – one to accommodate noise level and
one to accommodate detector pulse rise time. By adjusting these
two separately, optimum settings can more readily be attained re-
sulting, generally, in shorter total processing time to reach the same
resolution result. Additionally, the analog ampliﬁers typically were
limited to six or fewer shaping time selections. If, say, 2 µs shaping
was too short, the next available selection was usually 4 µs – twice
the processing time. With the CANBERRA DSP products, the user
can typically select from 35 to 40 rise times and 21 ﬂat top times.
Again, this greater granularity of adjustment makes it possible to
more closely optimize the performance.
Note that the CANBERRA DSP products also implement Pile Up
Rejection/Live Time Correction (PUR/LTC). Earlier products imple-
mented this feature with analog circuitry, but in the DSP this is in-
corporated into the digital domain functions. Pulse pileup occurs
when a new pulse from the preampliﬁer reaches the input stages
of the DSP before the previous pulse is fully processed. In such
cases, the PUR/LTC function a) inhibits the processing of any inval-
id, composite pulses and b) turns off the live time clock during the
time pulse processing is gated off. In this manner, piled up events
– which would serve only to distort the spectrum – are rejected
before storage by the MCA and the actual live counting time of the
MCA remains correct.
The improved performance of the DSP as compared to analog
systems is shown in Figures 1.29 to 1.34. Figures 1.29 and 1.30 show
real performance data collected with a DSP and an analog gated
integrator and fast ADC (the fastest available using analog technol-
ogy). For this experiment, a Model 2060 DSP was set for rise time

of 0.72 µs and ﬂat top time of 0.68 µs. The analog gated integrator
ampliﬁer (Model 2024) was set for shaping of 0.25 µs and paired with a
800 ns Fixed Dead Time ADC. These settings were chosen for op-
timal throughput with a relatively small (≈11% efﬁcient) germanium
detector.
As we can see from Figure 1.29, the DSP based system provides
higher throughput by approximately 50%. Figure 1.30 shows the
resolution comparison for the same experiment and demonstrates
that the DSP also provides signiﬁcantly better resolution once the
input count rate exceeds approximately 150 kcps. Note that the
shape of the resolution curve in Figure 1.30 is also much ﬂatter,
indicating that widely varying count rates can be accommodated at
a relatively constant resolution.
Note that with these settings chosen for highest throughput, the res-
olution performance at lower count rates is actually slightly worse
with the DSP. However, in an application involving those count rates,
it is unlikely those settings would be used. Figures 1.31 and 1.32
show the same analog data compared to the DSP system with the
rise time extended to 1.24 µs. This reduces the throughput of the
DSP system although it is still superior to that of the analog. Further,
we see now that with these settings, the resolution of the DSP is su-
perior to the analog across the full range of incoming count rates.
Figures 1.33 and 1.34 compare a Model 2060 DSP to a Gauss-
ian analog system consisting of a Model 2025 ampliﬁer and Model
8715 ADC. In this case, the settings of both systems were chosen
to provide optimal resolution under the high incoming count rates.
Analog systems were set for 2 µs and 4 µs Gaussian shaping times
while the DSP settings were 5.6 µs rise time and 0.8 µs ﬂat top. Fig-
ure 1.33 shows that, with these settings, the throughput of the DSP
system is approximately equal to that of the 2 µs Gaussian system.

Yet Figure 1.34 shows the resolution of the DSP system is superior
to the 4 µs Gaussian system. Again, the DSP allows the spectros-
copist to achieve a signiﬁcantly better tradeoff between throughput
and resolution.
LOSS FREE COUNTING APPLICATIONS
The correction of the Live Time Clock as described above, effec-
tively extending the counting time to account for those periods when
the system could not accept an input, is adequate for most samples,
in particular those for which the count rate is relatively constant.
However, for short half-lived samples, or samples whose constitu-
ents change (as in a ﬂow monitoring application), this method will
not be accurate. In addition, even if the “counts per unit time” are
accurate using the traditional method for dead time correction, the
“real” counting time will have been extended by an amount equal to
the dead time, which may in fact increase the actual collection time
to an undesirable length.
The principal goal of Loss Free Counting (LFC) is to insure that at
the end of any data acquisition interval, the electronics have accu-
mulated all of the events that occurred regardless of any dead time
that may have been present in the system. LFC is based on the
concept that by adding “n” counts per event to an MCA’s channel
register, rather than digitizing and storing a single count at a time,
a “zero dead time” energy spectrum can be accumulated that as-
sures all counts are included in the spectrum. Assuming that “n” is
correctly derived, (“n” should equal “1” plus a “weighting factor” rep-
resenting the number of events that were lost since the last event
was stored), and the data is truly random in nature, the concept is
statistically valid. The factor “n” is derived on a continuous basis by
examining the state of the Ampliﬁer and ADC every 200 ns. The pro-
portion of time during which the Ampliﬁer and ADC are processing a

pulse provides a measure for the magnitude of the weighting factor
“n”, which is updated every 20 µs. Loss free counting requires that
the MCA support “add-n” or multiple “add-one” data transfer; consult
the factory for details.
Figure 1.32 A comparison of the resolution between an analog
system optimized for maximum throughput and a DSP system
set for a similar throughput
Figure 1.33 A comparison of the system throughput as
a function of input count rate for a DSP and two
analog systems optimized for resolution
Figure 1.34 A comparison of the system resolution as
a function of input count rate for a DSP and two
analog systems optimized for resolution
©2006 Canberra Industries, Inc. All rights reserved.
Unfortunately, counting statistics in a Loss Free Counting system
cannot be calculated from the corrected spectrum. One basic as-
sumption used by all peak ﬁtting algorithms is that of Poisson count-
ing statistics. That is, the uncertainty of the counts is proportional
to the square root of the number of counts. While this assumption
is true for traditional “add-1” front-ends, it is not true of the “add-n”
Loss Free Counting front-end. This assumption is especially poor
as the weighting factor becomes large. To properly quantify the un-
certainty in each channel’s contents, the peak ﬁtting program must
have access to both the corrected “add-n” and the uncorrected
“add-1” spectra. Therefore, CANBERRA also offers a “Dual-LFC”
hardware option for the Model 599 Loss Free Counting Module
which allows the collection of both of these spectra so that statisti-
cally correct peak ﬁlling can occur. Note that the correction software
for the “Dual-LFC” system is only available for VMS-based Genie
Systems.

PIPS DETECTORS AND MULTICHANNEL ANALYZERS
Alpha spectroscopy measurements of low-level samples require
long counting times. A large area PIPS detector, when conﬁgured
Figure 1.35 Example Large Scale Alpha Spectroscopy System based on the Alpha Analyst
with a CANBERRA alpha spectrometer and multichannel analyzer,
provides a high resolution, low background, counting system that
will satisfy a multitude of alpha spectroscopy applications.
An example of a single chamber alpha spectroscopy system (that
can easily be upgraded) is illustrated in Figure 1.11. Note that the
Model 7401 Alpha Spectrometer is a complete, self-contained, dou-
ble-width NIM module that contains a vacuum chamber, vacuum
gage, detector bias supply, preampliﬁer/ampliﬁer, SCA, counter/tim-
er and pulser for setup and test. Multiple Model 7401 Alpha Spec-
trometers can be conﬁgured with a vacuum system that allows indi-
vidual vacuum chambers to be opened and loaded without affecting
the vacuum or data acquisition of the other spectrometers.
However, where numerous samples are counted simultaneously, it
is more cost effective and user efﬁcient to select a system based on
the Alpha Analyst (Figure 1.35). This turn-key system supports mul-
tiple detectors in a comprehensive software environment featuring
full computer control of all vacuum elements and acquisition elec-
tronics. To learn more about CANBERRA’s Alpha Analyst, please
refer to Section 1 of this catalog.
Timing and Coincidence Counting
Systems
Phone contact information
Benelux/Denmark (32) 2 481 85 30 • Canada 905-660-5373 • Central Europe +43 (0)2230 37000 • France (33) 1 39 48 52 00 • Germany (49) 6142 73820 • Japan 81-3-5844-2681 •
Russia (7-495) 429-6577 • United Kingdom (44) 1235 838333 • United States (1) 203-238-2351
For other international representative ofﬁces, visit our web site: or contact the CANBERRA U.S.A. ofﬁce. 6/06 Printed in U.S.A.
COINCIDENCE TECHNIQUES

There are many applications that require the measurement of events
that occur in two separate detectors within a given time interval, or
the measurement of the time delay between the two events. These
two approaches are used in gamma-gamma or particle-gamma co-
incidence measurements, positron lifetime studies, decay scheme
studies and similar applications, and are titled coincidence or timing
measurements.
A coincidence system determines when two events occur within
a certain ﬁxed time period. However, in practice it’s not possible
to analyze coincidence events with 100% conﬁdence due to the
uncertainties associated with the statistical nature of the process.
Statistical timing errors may occur from the detection process and
uncertainties in the electronics resulting from timing jitter, amplitude
walk and noise, which lead to statistically variable time delays be-
tween processed events. A simple coincidence circuit solves this
problem by essentially summing the two input pulses, passing the
resultant sum pulse through a discriminator level, and generating
an output pulse when the two input pulses overlap. Figure 1.36
illustrates this process. Note that the period of time in which the two
input pulses can be accepted is deﬁned as the resolving time, which
is determined by the width of the pulses, τ, such that the resolving
time is equal to 2τ.
The 2040 Coincidence Analyzer uses a more sophisticated scheme
allowing analysis of several input signals. It produces a logic pulse
output when the input pulses, on the active inputs, occur within the
resolving time window selected by the front panel control.
Since detector events occur at random times, accidental coinci-
dences can occur between two pulses which produce background
in the coincidence counting. The rate of accidental or random coin-
cidences is given by:

N
acc
=N
1
N
2
(2τ)
Where:
N
1
= Count rate in detector number 1
N
2
= Count rate in detector number 2
2τ = The resolving time of the coincidence circuit
The number of counts in the detectors depends upon the experiment
and the detectors, so the best way to reduce accidental coincidences
is to make the resolving time as small as possible. However, the
resolving time cannot be reduced below the amount of time jitter in
the detector pulses without losing true coincidences, so the type of
detector determines the minimum resolving time usable.
A coincidence setup with NaI detectors is shown in Figure 1.37.
The unipolar pulse from the 2022 Ampliﬁer is processed by a Model
2037A Constant Fraction Timing SCA to produce a standard NIM
logic pulse for the 2040 Coincidence unit. The 814FP Pulser is used
to set up delays and test operation.
Figure 1.36 Coincidence Pulses
Figure 1.37 Coincidence Electronics
In order to properly operate the system, a delay curve is obtained
in which coincidences are measured as a function of relative delay

between the two detectors. In the ideal case of no time jitter in either
detector, the solid curve in Figure 1.38 is obtained. However, real
detectors will produce the dashed curve, and the minimum resolv-
ing time setting is where there is a ﬂat region (indicating all true
coincidences are collected). Thus, the proper relative delay is the
value for the center of the ﬂat region.
Typical resolving times are 10 nanoseconds or better, for an energy
range of 0.1 to 1 MeV. Shorter resolving times are possible for plas-
tic scintillators and silicon charged particle detectors, even down to
less than 1 nanosecond. In general, the shorter the rise time of the
preampliﬁer pulse, the smaller the resolving time. This is discussed
further with fast discriminators.
Another coincidence technique involves the direct measurement of
the time delay between two pulses. A time-to-amplitude converter
(TAC) converts a time difference between two input pulses to a 0 to
10 volt pulse. This analog pulse can then be used as an input to an
SCA, or ADC and MCA. The Model 2145 TAC provides an integral
SCA capability as well as an output pulse, gate delays and other
features.
Figure 1.39 Coincidence Electronics with TAC Unit
The use of a 2145 TAC with NaI detectors in exact analogy with the
2040 Coincidence unit is shown in Figure 1.39. There are several
advantages to the use of a TAC. First, no delay curve needs to be
taken since all relative decays occurring are recorded, and second,
no resolving time setting is involved.
The natural time spectrum of the two detectors can be stored
directly in an MCA, and if a window is set very narrow, as in Figure
1.40, then there are a minimum number of accidental coincidences
recorded. The 2058 Nanosecond Delay is required to delay one de-
tector pulse from the other so that a measurable time difference

occurs.
TIMING DISCRIMINATORS
A crucial part of any coincidence system is the timing discrimina-
tor used to determine when a pulse occurs. There are two general
categories:
• Slow (or energy) Timing
• Fast Timing
The timing single channel analyzers used in Figures 1.37 and 1.39
are examples of slow timing. The single channel analyzer operates
with shaped pulses to select the range of energies involved in the
coincidence, and produces an output logic pulse that is, ideally, in-
dependent of input pulse amplitude. Fast timing uses pulses directly
from the detector, without regard to speciﬁc energy.
Three basic techniques are used in both fast and slow modes for
acquiring timing information:
• Leading Edge
• Crossover
• Constant Fraction
CANBERRA provides electronic modules for performing any of
these techniques, and the proper choice depends upon the detec-
tor and application, as discussed below.
Figure 1.38 Resolving Time Curve
The most fundamental timing circuit generates a logic signal when
the leading edge of an input pulse crosses through a discriminator
level as shown in Figure 1.41.
The main problem is that the time of the output pulse varies mark-
edly with amplitude, as can be seen by comparing the two signals
shown. This effect can be reduced by setting the discriminator at a
very low level, such as just above noise. The Model 2037A Timing
SCA sets the discriminator up to a maximum of 200 millivolts.

Crossover timing relies on the fact that the zero-crossing point in a
bipolar pulse is very nearly independent of pulse amplitude. (See
Figure 1.42). The Model 2037A Timing Single Channel Analyzer
offers a crossover mode of operation for bipolar input pulses. The
crossover technique has some limitations in that there is still time
dependence or “walk” for different amplitudes, and that signals with
varying rise times from the same detector (such as occurs with
germanium detectors), will produce walk.
Figure 1.40 TAC Spectrum
Figure 1.41 Leading Edge Timing
The constant fraction technique will eliminate most of the short-
comings of the two former methods of timing. The constant fraction
timing technique is similar to a discriminator, but with a threshold
that is a constant fraction of the signal amplitude. A discussion of
the constant fraction technique, as implemented in the Model 2126
Constant Fraction Discriminator, is given in the Timing Section.
This module can be connected to NaI or fast plastic detectors with
negative amplitude output signals ranging from –5 mV to –5 V, and
rise times down to 1 nanosecond. The 2126 performs no signal pro-
cessing on the input and is very often attached directly to the anode
of a photomultiplier tube. As mentioned above, constant fraction
discrimination is a method that offers a timing output signal when
a constant ratio of the pulse height is reached. This ratio, once set,
is consistent from pulse to pulse, thus removing the amplitude and
rise time errors that arise. The main problem with this method is
that it is still sensitive to pulse shape distortion, exhibiting poor time
resolution for energies less than 200 keV and for poorly shaped or
noisy pulses.
Whenever noise or low amplitude is a signiﬁcant characteristic of a
detector, a ﬁlter network is required between the signal source and

ampliﬁer to alleviate the noise distortion. The Model 2111 Timing Fil-
ter Ampliﬁer has a built-in ﬁlter that attenuates the noise component
before ampliﬁcation of a low signal. When used with a constant frac-
tion discriminator such as the 2126, a stable time reference can be
derived. The 2111/2126 combination has widespread application in
gamma-gamma coincidence and lifetime studies, offering excellent
time resolution, which in connection with the high resolution of large
germanium detectors, increases the rate of useful data collection.
The 2111 Timing Filter Ampliﬁer is applicable for both surface bar-
rier and germanium timing applications. Both of these detectors
produce signals of low amplitude, distorted with noise, and in the
case of germanium detectors, poorly shaped rise times. A gamma-
gamma coincidence system with NaI and germanium detectors is
shown in Figure 1.43. This is an example of a “fast-slow” coincidence
system in which Model 2111 and 2126 constant fraction discrimina-
tors are used to indicate the presence of a pulse, and an energy
range on the NaI detector is selected. The energy spectrum of the
germanium detector is stored in the MCA if the ADC gate is opened
by a coincidence pulse representing a combination of proper NaI-
germanium timing and the selected NaI energy. A Model 2145 TAC
is used to set the true coincidence range because of the set-up
convenience offered, as described above. The TAC SCA output and
the Timing SCA output of a Model 2015A Ampliﬁer/Timing SCA are
placed in coincidence with Model 2040 Coincidence unit. If desired,
an energy requirement could be placed on the germanium detec-
tor by adding a Model 2037A Timing SCA on the 2025 ampliﬁer’s
bipolar output, and feeding the 2037A’s output to the Reset/Inhibit
input on the 2145 TAC.
Anticoincidence systems are occasionally required, as mentioned
above for Compton suppression in germanium detectors (see

Figure 1.24) or cosmic ray suppression in alpha/beta counting.
Figure 1.42 Bipolar Pulses and Crossover Timing
©2006 Canberra Industries, Inc. All rights reserved.
Figure 1.43 NaI-Ge Fast-Slow Coincidence Electronics
Spectrum Analysis
Phone contact information
Benelux/Denmark (32) 2 481 85 30 • Canada 905-660-5373 • Central Europe +43 (0)2230 37000 • France (33) 1 39 48 52 00 • Germany (49) 6142 73820 • Japan 81-3-5844-2681 •
Russia (7-495) 429-6577 • United Kingdom (44) 1235 838333 • United States (1) 203-238-2351
For other international representative ofﬁces, visit our web site: or contact the CANBERRA U.S.A. ofﬁce. 6/06 Printed in U.S.A.
CANBERRA offers a variety of nuclear systems which perform
data analysis as well as data acquisition. These systems range
from small stand alone systems to more sophisticated conﬁgura-
tions involving a variety of computer platforms. Typical applications
include Environmental Monitoring, Body Burden Analysis, Nuclear
Waste Assay, Safeguards and other applications. Details of these
systems are provided later in this catalog, or in various brochures
that are available from CANBERRA. The following section presents
some of the typical procedures and calculations involved in nuclear
applications.
COUNTING STATISTICS
Radioactive decay occurs randomly in time, so the measurement of
the number of events detected in a given time period is never ex-
act, but represents an average value with some uncertainty. Better
average values can be obtained by acquiring data over longer time
periods. But, since this is not always possible, it is necessary to be
able to estimate the accuracy of any given average.
Nuclear events follow a Poisson distribution which is the limiting
case of a binomial distribution for an inﬁnite number of time inter-
vals, and closely resembles a Gaussian distribution when the num-
ber of observed events is large. The Poisson distribution for observ-

ing N events when the average is N, is given by:

P
N

=
and has standard deviation σ (sigma) equal to √N. A graph of P
N

for N equal to 3 and to 10 is shown in Figure 1.44. The curves are
asymmetric and have the property that N is not exactly the most
probable value but is close to it. However, as N increases the curve
becomes more symmetric, and approaches the Gaussian distribu-
tion:
P
N

= • e
–x
2
/ 2N
= • e
–x / 2σ
2
Where: x = N – N
The integral of the area under the Gaussian curve is often used to
report errors in terms of a conﬁdence level in percent. For example,
in the value reported as 64 ± 8, 8 is equal to σ and represents 68%
of the area under the appropriate Gaussian curve for N=64. It may
be stated as the value one is 68% conﬁdent of obtaining if the mea-

surement is repeated. Traditionally, many of CANBERRA’s MCAs
have used 1.65 σ, which corresponds to a 90% conﬁdence level.
Probable error is often used, which corresponds to a 50% conﬁ-
dence level. These can be user-set to other values, such as:
Value of σ % Conﬁdence
0.68
1.0
1.15
1.65
1.96
50
68.3
75
90
95
Figure 1.44 Poisson Distributions for N=3 and 10
N
N
e
–N
N!
1
√2πN
1
√2πα
Since the uncertainty depends upon the square root of the counts,
improvements in accuracy by counting longer, or by using a more
efﬁcient detector, only increase as the square root. For example, if
564 counts are obtained in an hour for σ ≈ √564 ≈ 24 for a 24/564
= 4.3% accuracy, counting for two hours to get 1133 counts with σ

≈ 34 only gives an improvement to 3.0%. In other words, counting
twice as long gives an improvement of √2 = 1.4, or 40%.
Examples of data in which counting statistics apply include: the
counts in a counter, the counts in a single channel of an MCA spec-
trum, or the sum of counts in a group of channels in an MCA spec-
trum. The situation becomes even more complicated when subtract-
ing a background as shown in the following separate, but frequent,
cases.
• Subtracting background counts, as in one counter’s value
from another, or for each channel (when subtracting one
spectrum from another).
• Subtracting a straight line background from a peak on top of
the background in a spectrum, such as a HPGe peak on top
of Compton pulses from higher energy gamma rays.
The error in adding or subtracting two Poisson distributed numbers
with errors, as in:
N
total
= (N
1
± √N
1
) ± (N
2
± √N
2
)
is given by:
σ
N

total
=
√
(
√
N
1
)
2
+ (
√
N
2
)
2
Consider a low level counting situation in which 56 counts are ob-
tained in 10 minutes, and a background of 38 counts in 10 minutes
was measured without the sample. The result is 56–38 = 18 counts,
with an error of √56 + 38 = √94 = or approximately 9.7, a σ value
of 54%.
A better procedure is to measure the background over a longer
period of time to obtain a small percentage error and factor to the
appropriate time for each sample analyzed. Using the same exam-
ple as above, but with a 100 minute background of 380 counts, the
result would be 56–(380/10) = 18 counts, with an error of
√56 + ([
10
/
100
]

2
x 380) = √56 + 38 = √59.8

or approximately 7.7, a σ value of 43%.
NET AREA CALCULATION
For the case in which a peak lies on a background that cannot be
subtracted by a background spectrum, such as shown in Figure
1.45 for an MCA spectrum from a HPGe detector:
The area above the background represents the total counts between
the vertical lines minus the trapezoidal area below the horizontal
line. If the total counts are P and the end-points of the horizontal line
are B
1
and B
2
, then the net area is given by:

A = P – (B
1
+ B
2
)
Where: n = The number of channels between B
1
and B
2
.
It is tempting to calculate the uncertainty by just using the formula
for subtracting two numbers, with standard deviations of:
σ

N
=
√
P + (B
1
+ B
2
)
However, this is incorrect because the trapezoidal area is not Pois-
son distributed and its error is not just the square root of the counts,
but depends upon how the errors in B
1
and B
2
affect the horizontal
line across the entire region. The proper procedure, which is imple-
mented in CANBERRA MCAs and in analysis of peak areas in vari-
ous HPGe software packages, is derived as follows:
The standard deviation in a function A is given by:
A = f (N
1
N
2
N
n
)

where N
n
is the counts in channel N.

Figure 1.45 Net Area Determination
n
2
n
2
∂f
∂N
1
∂f
∂N
n
n
2
n
2
n
2
n
2
B
1
n
1
B
2
n
2
n
2
B

1
n
1
The estimate of the standard deviation in A is given by:
σ (A) =
2
σ
2
(N
1
) +
2
σ
2
(N
2
)
1/2

= (P
1
+ P
n
) +
2
(√B
1
)
2
+

2
(√B
2
)
2

1/2
= P +
2
(B
1
+ B
2
)
1/2
Where P
1
P
n
are the channels in the peak (inside B
1
and B
2
) not
including the channels with contents of B
1
and B
2
.
END-POINT AVERAGING

If the background is large compared to the peak area, a better
determination of background can be made by averaging over sev-
eral channels. If B
1
is an average over n
1
channels, and B
2
over n
2

channels, the area is then:
A = P – +

and the standard deviation is:
σ(A) = P +
2
+
1/2
B
2
n
2
2 2

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