Geiger Mueller Counting Table of Contents -
Transcript of Geiger Mueller Counting Table of Contents -
Geiger Mueller Counting
Formal ReportDavid Sirajuddin
Partners: Nick Krupansky, Yongping Qiu
Table of Contents
I. Abstract…………………………………………………………………………….......2
II. Introduction…………………………………………………………………………2-3
III. Theory…………………………………………………………………….................3-27
3.1 Avalanche Formation………………………………………………...............4-53.2 Townsend Avalanche………………………………………………...............5-73.3 The Geiger Discharge………………………………………………..............7-83.4 Multiplication Factor………………………………………………................8-93.5 Criticality in a Geiger Tube………………………………………….............9-103.6 G-M Tube Geometry, Electric Field Dependence, and the Multiplication
Region……………………………………………………………….........10-113.7 G-M Tube Construction…………………………………………...............11-133.8 Fill and Quench Gases…………………………………………….............14-153.9 Solid Angles in a G-M Tube……………………………………….............15-163.10 Regions of Detection………………………………………………...........16-183.11 Output Pulses in a Geiger Counter………………………………...............18-193.12 Geiger Counting Curves…………………………………………...............19-213.13 Dead, Recovery, and Resolving Time……………………………................21-223.14 Measuring Dead Time: Two-Source Measurement………………................23-243.15 Beta Attentuation………………………………………………….............24-253.16 Gamma Rays Detection…………………………………………................25-27
IV. Experiment………………………………………………………………................27-37
4.1 Pulse Height vs. Ionization Type and Energy……………………………..28-304.2 Counting Curve and Pulse Height vs. Voltage…………………………….30-324.3 Beta Attentuation……………………………………………………....…32-354.4 Dead Time and Recovery Time…………………………………………...35-37
V. Conclusions……………………………………………………………………….37-38
VI. Appendix
6.1 Bibliography………………………………………………………..................386.2 Data Tables………………………………………………………………38-39
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I. Abstract
Geiger-Mueller (G-M) detectors were investigated in this lab. To determine the
sort of pulses a G-M counter records, different sources were placed in the tube with a
constant high voltage where their respective pulse amplitudes were recorded. The sources
used were Cl-36, Cs-137, Sr-90, and Co-60. The effect was then explored further by
blocking all decay except high energy radiation (gamma decay), and comparing the different
pulses recorded among the sources in this fashion. Despite differing sorts and energies of
radiation interacting with the G-M tube through these different sources, the pulses detected
by the G-M counter were found to be nearly constant implying that differing ionization
types and energies yield nearly identical amplitudes in a G-M apparatus. This hints at the
idea that a theoretical G-M counter always yields identical amplitudes no matter what the
source when operating at a constant high voltage.
The nature of the G-M counting mechanism was investigated by using one source,
and recording how the count rate varied with high voltage. A similar process was done to
investigate the relation between the high voltage and pulse amplitude. Graphs of the
counting rate vs. high voltage indicated a plateau region where a one-to-one correspondence
region exists. In this region, each pulse is counted by the G-M unit. Above this voltage
region, a sharp sloping of count rates was observed which indicated the onset of continuous
discharge. Below the plateau region, the count rate decreased with decreasing voltage until a
certain voltage where no detection was possible. This analysis gave insight into the region in
which a G-M tube can operate to give tangible, and beneficial results as a counter. The
plateau found in the graph is precisely this region. The amplitude was investigated with
applied high voltage, and was found to intuitively increase as the high voltage did.
Beta attenuation due to an aluminum absorber was also analyzed. A Sr-90 source
was inserted into a G-M tube apparatus. The fraction of detected particles was then
measured with differing thickness of the absorber. Expectedly, the fraction of particles able
to be detected decreased with increased absorber thickness. Only those beta particles with
sufficient energy could tunnel through the material and be detected. This relationship was
observed to be nonlinear, and approximately exponential in character, and was attributed to
the continuous spectrum of energies of the beta particles emitted. The exponential character
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of the resulting graph was further verified through graphing the natural logarithm of the
fraction vs. the absorber thickness. The graph was found to be linear, and from there a
constant of proportionality, the absorption coefficient was found.
Finally, dead time of the G-M tube was measured using two methods and a metallic
thorium source. First, the thorium source was manually placed as close as possible to the
Geiger tube radiation entrance window, and an oscilloscope was used to display and
calculate the dead, and resolving time. Secondly, the two-source method was used. This method
involved measuring the count rate of two thorium sources separately, and then together and
with the assumption of a nonparalyzable model, the dead time was calculated using
formulary developed in the theory section of this lab report. In all cases, the theory was
found to match up closely with the results found in lab.
II. Introduction
The objective of this work was to better examine the operational mechanics of the
Geiger-Mueller Counter. The G-M tube was used in Lab 3, but its methodology of
operation was neglected as the aim of the previous lab was to investigate counting statistics.
This lab provided an exercise in learning the operations of the G-M counter. The
significance of gaining an understanding of G-M counter operations stems from both
historical and practical roots.
Scientists Geiger and Mueller instituted the G-M counter in 1928. To this day, it
remains one of the oldest radiation detectors; however, it still remains in widespread use due
to practical reasons such as its ‘simplicity, low cost, and ease of operation” (Knoll, 201). It is
therefore of importance to understand the operations of this device to recognize historical
progression, and also to acclimate oneself with its advantages and disadvantages.
Familiarizing oneself with its inherent limitations is beneficial in the regard of enabling
oneself to make a proper choice of detector, and then if a G-M counter is used it helps to be
able to work around these limitations to better interpret the data received. The limitations in
a G-M counter are a large dead time, nonlinear amplification of charge leading to energy
information loss, solid angle matters, and recovery time.
The G-M counter is a gas filled detector based on ionization. Its methods of
detection hold characteristic qualities distinguishing it from other types of detectors, and it
was the aim of this lab to discern those qualities. Such inherent qualities that were of key
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interest in this lab were the sort of pulses it records, the nature of its counting mechanism,
its response to beta radiation under various attenuation conditions, and its dead/recovery
time. Each of these qualities were discerned with using multiple sources at a set voltage,
recording amplitude and count rate with voltage change, measuring the count rates of a beta
emitter under different absorber thicknesses, and utilizing both the oscilloscope and the two
source method to measure the apparatus’ long dead time.
III. Theory
3.1 Avalanche Formation
Geiger-Mueller Counters and Proportional Counters operate on the principal of gas
multiplication. Due to many shared characteristics, a G-M Counter can be defined with the
help of contrast to a proportional counter. Gas multiplication is a phenomenon that
essentially amplifies charges of ion pairs naturally formed within a gas. In a G-M Tube, a
directed electric field helps to maximize this multiplication. One of the differences between
a proportional and G-M counter is that the latter involves substantially larger electric field
strengths. Given a generic gas-filled apparatus consisting of both positive and negative
collecting electrodes (Fig 3.1), where collecting electrodes are labeled as cathode and anode
respectively), ion pairs are created in this fill gas by incident radiation, and - in the absence of
an electric field - are gathered at their respective collecting electrodes.
Figure 3.1 Generic model of a gas-filled detector
During the paths of the ions to their collecting electrodes, collisions incur involving energy
transfer. These energy transfers are small and thereby insignificant for any detective use.
Little can be done to increase energy transfers in these sorts of collisions due to their
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typically large masses; however, the electrons liberated during the ionization process can be
dealt with in a manner to induce a sufficient energy transfer of practical use. The free
electrons are readily accelerated by an induced electric field. If these electrons are given
sufficient threshold energy such that the energy acquired by way of the electric field allows its
total energy to be greater than or equal to the ionization energy of a neutral gas molecule of
the fill gas, a secondary ionization can occur. This newly liberated electron can go on to
actuate yet another ionization and so on if energy is sufficient causing a chain reaction for
subsequent electron-neutral gas molecule interactions called a Townsend Avalanche. It takes
but one free electron to cause an avalanche. Since a liberated electron is caused by incident
radiation, an apparatus that makes use of this principal can be used to measure radiation as a
measure ion pairs originally created. Put another way, in a Townsend Avalanche, free
electrons can beget more free electrons through collisions with neutral gas molecules when
ionization results.
3.2 Townsend Avalanche
The Townsend equation describes the fractional increase in the number of electrons
per unit path length in a typical townsend avalanche:
dnn
= a dx (3.1)
where α is the first Townsend coefficient corresponding to the fill gas. The quantity α is
zero for electric field strengths below the threshold energy, and tends to increases for electric
field values greater than or equal to the threshold energy (Fig. 3.2).
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Figure 3.2 Values of the Townsend Coefficient α change as the electric field in the tube changes. Below the threshold electric field strength, α is zero.
It follows that the solution to the differential equation above yields:
n (x ) = n (0 )ea
(3.2)
This can be interpreted as electron density with respect to the spatial coordinate x along an
avalanche’s path. In accordance with intuition, it is evident that the electron density
increases with x. More liberated electrons per unit path length are found further along in an
avalanche’s path than near its beginning. Recalling that an avalanche is a sort of chain
reaction, this electron density increase is exactly what would be expected. In a proportional
counter, an avalanche continues until all free electrons have been collected at the anode
(depicted in Fig 3.3) and often leads to either true or limited proportionality between the
amplified charge output pulse and the original radiation (discussed in section 3.10).
Figure 3.3 Two views of the anode wire are shown attracting a single avalanche as simulated by aMonte Carlo calculation. In accordance with Eq. 3.2, the electron density increases with x.
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The same is true for G-M counters, but individual avalanches have a strong probability of
inducing at least one other avalanche due to its increased electric field. The output pulse of a
G-M counter is then not a single avalanche, but the charge associated with a number of
avalanches. While a proportional counter outputs a pulse that can be used to determine the
number of original ion pairs created within a counter, a Geiger counter output pulse loses all
original energy information due to its variable number of avalanches and nonlinear
amplification of charge. In fact, additives are often present in proportional counters to
absorb photons preferentially and prevent further avalanche. The process that leads to an
output pulse in a G-M counter deals with the initiation and termination of an avalanche
progression and is termed under the blanket nomer, the Geiger discharge.
3.3 The Geiger Discharge
The other possibility for high energy interactions between free electrons and neutral
gas molecules is producing excited atoms. These excited atoms will typically decay to their
ground state within a few nanoseconds by emission of a photon. The emitted photon’s
wavelength may be in the visible or ultraviolet region, and perpetuates a multiple avalanche
process in two ways: (1) the photon is absorbed by another neutral gas molecule and gives
rise to a photoelectron, and (2) it could be absorbed in the cathode wall accompanied by the
release of a free electron. In both cases, the free electron goes onto causing another
avalanche within a few mean free paths of the original because the photon begets free
electrons preferentially near its parent avalanche. The previous statement makes sense in
that an electron in the multiplication region (discussed in 3.10) will not have to travel far to
collide with another neutral gas molecule, and thereby ionize it. This process propagates in
both directions along the anode wire with typical velocity of 2-4 cm/μs until the entire
anode wire is engaged (see Fig 3.4). In the section of G-M tube construction (section 3.7),
this involvement of the entire anode wire will give leeway in geometric considerations as well
as uniformity in the assembly of a G-M tube in comparison with proportional and ion
chamber detectors where a more precision is needed.
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Figure 3.4 Additional avalanches are created through UV photons giving rise to photoelectrons that trigger subsequent avalanches. The avalanches envelope the entire anode wire
A Geiger tube involves many avalanches that originate at random radial positions in
the multiplying region of the tube. It is the positive ions that form during the consequential
avalanches that are the source of the chain reaction’s termination. The electric field
accelerates the electrons readily, but in the few microseconds it takes the electrons to reach
the anode wire the positive ions are caused to move little if at all. As avalanches persist,
these positive ions increase in density until the concentration is great enough to decrease the
electric field strength. The cloud of positive ions formed around the anode wire can be
alternatively viewed as an increase in anode diameter, thus causing the electric field in Eq. 3.6
to decrease. When the electric field is decreased sufficiently such that the electrons do not
acquire the threshold energy necessary to create avalanches, gas multiplication can no longer
take place and the Geiger discharge is terminated thereby outputting a pulse. The Geiger
discharge process is perpetuated with probabilities rooted in the concept of achieving
criticality, which is dependent on the Gas Multiplication Factor.
3.4 Multiplication Factor
The total charge Q accumulated from avalanches created by n0 original ion pairs is
given by the following relation:
Q = n0eM, (3.3)
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Where e is the charge of an electron (1.6 x 10-19 C), and M is the multiplication factor.
Assuming no electrons are lost through the formation of negative ion formation, and
neglecting the positive ion space charge that accumulates, the multiplication factor can be
generally approximated by the equation:
ln M = óõa
rca (r ) (3.4)
where a is the anode radius, rc is the critical distance from the center beyond which gas
multiplication cannot occur, and α is a function of both the type of gas and electric field. In
cylindrical geometry, such as the G-M tube, the solution to this integral yields:
ln M =V
ln 0ba1
$ln 2DV
æççè
lnV
pa ln 0ba1
K ln Kö÷÷ø
(3.5)
Where V is the applied voltage, a and b are the radii of the anode and cathode respectively, p
is the gas pressure, ΔV is the potential difference the electron moves through between
ionizing events, and K is the minimum value of E/P such that gas multiplication is possible.
It follows that the multiplication factor varies as a function of the exponential of the right
side of the equation. Usually the pressure is fixed, and a and b are fixed since that would
require changing the tube construction. If the slow growing logarithm term is neglected,
then the quantity M changes nonlinearly as an exponential of the applied voltage. Gas
multiplication should then increase with increased applied voltage, namely M α exp(V). The
multiplication factor plays a key role in the perpetuation of the multiple avalanching process
characteristic of a Geiger counter with regards to the concept of criticality, as it provides a
quantitative measure of the multiplication of gas.
3.5 Criticality in a Geiger Tube
In a proportional tube, the multiplication factor M is comparatively low to that of a
G-M tube (102~104 in comparison with 106~108). Denoting the probability of photoelectric
absorption as p, and the number of excited molecules formed in an avalanche n0`, then in a
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proportional tube, the probability of new avalanches being created is n0`p << 1. This
condition is called sub-critical. Since a proportional tube can only remain proportionality with
few avalanches, oft a fill gas contains additives to absorb photons inhibiting further
avalanche.
It is desirable in a G-M tube to have multiple avalanches, and such additives are not
present in a Geiger tube’s fill gas to achieve this. In fact, in a G-M tube a quench gas is used
to promote further avalanche, and is discussed in section 3.8. The multiplication factor M is
much larger in this case implying that the number of excited molecules n0` is much larger.
Then the probability of additional avalanche is n0`p ≥ 1. Typically, any given avalanche is
likely to produce at least one other avalanche. A probability of this value is said to be critical,
and is exactly what is desired in a G-M tube. This criticality lends itself to perpetuating a
Geiger discharge and the output of an eventual pulse.
3.6 G-M Tube Geometry, Electric Field Dependence, and the Multiplication
Region
In accordance with Figure 3.1, a G-M tube is constructed with cylindrical geometry.
An anode wire of small radius sits along the axis of the large hollow cathode tube. In an
appropriate induced voltage, the polarity of the operating apparatus will attract the free
electrons. Gas multiplication in a G-M tube demands large electric field strength in
comparison with ion chambers, and proportional tubes. So large – in fact – that all
knowledge of original ion pair information is lost due to the nonlinear amplification of
charge during a Geiger discharge. In this cylindrical geometry, the electric field E at radius r
from the center axial wire is given by the equation:
E (r ) =V
r ln 0ba1
(3.6)
Where V is the applied voltage, and a and b are respectively the radii of the anode and
cathode measured from the tube’s center. This equation implies that, for a given voltage, the
electric field is a maximum at the anode’s center (r = 0), and decreases on an inverse
proportional basis as it is measured at various radii further away from the center (Fig. 3.5).
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Figure 3.5 Electric field strength E as a function of the radius r measured from the center of the tube. E exhibits 1/r character, and decreases as r increases
A dependence on a and b is also evident, but often these parameters are not adjustable in a
lab setting; however, the voltage parameter is adjustable and is discussed in the Output Pulses
in a Geiger Counter section 3.11. Since the electric field is greater near the anode, and the free
electrons need to attain an energy greater than or equal to the ionization energy of a neutral
gas molecule, this implies that this energy requirement can only be met within a certain
region of the tube where the electric field strength is sufficient, dubbed the multiplication region.
The multiplication region is labeled in the previous figure.
3.7 G-M Tube Construction
Unlike a proportional counter, G-M counter mechanics give rise to certain forms of
leniency in its assembly. The G-M counter is thusly less demanding in design than a
proportional counter and ion chamber. In fact, Knoll points out that a G-M counter is so
elementary in design that both ‘a simple wire loop anode inserted into an arbitrary volume
enclosed by a conducting cathode will normally work as a Geiger counter’ (Knoll, 211), and
that ‘some designs can be used interchangeably as proportional or Geiger tubes’ (210). Such
leniency in design originates from the Geiger discharge. The avalanches have sufficient
criticality to initiate multiple avalanches that envelope the entire anode wire, and any
nonuniformities are averaged out over the span of the wire. A common G-M tube is the
end-window type. A cross-sectional view of this apparatus is shown in Figure 3.6
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Figure 3.6 Cross-section of an end window type G-M tube.
The thin anode wire is supported on only one side, and radiation is allowed to enter
through a thin window at the end usually made of mica. The cathode forms the cylinder’s
skeleton, and is conventionally made of metal or glass with a metallized inner coating. The
cylindrical geometry creates an electric field in accordance of Eq. 3.6. This tube is also filled
with gas(es) as discussed in the fill and quench gases section, and the tube is connected into
appropriate circuitry to provide detection.
A schematic of a typical Geiger detection unit is shown in Figure 3.7. The resistance R is
the circuit’s load resistance acquired by the introduction of a high voltage supply. The time
constant of the charge collection circuit is determined by the parallel combination of this
resistance R with the tube capacitance Cs. The coupling capacitor Cc is necessitated by
desiring an output pulse from the tube while blocking the high voltage.
Figure 3.7 A schematic of counting pulses with a G-M tube
In order to maximize performance, the time constant RCs is chosen to be small (on the
order of microseconds) to preserve only the fast rising part of the pulses, and RCc is chosen
to be large so as to avoid attenuation of the pulse amplitude. A general scheme of the effect
of the time constant RC on outputted pulses is shown in Figure 3.8.
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Figure 3.8 Shape of the output pulse with differing time constants. The output amplitude V is graphed as a function of the time t. A small time constant implies only the fast rising components of the
pulse are preserved.
A small time constant is observed to maintain only the fast rising pulses character. This
small value reflects in the shape of the pulse in the manifestation of a long exponential like
tail. Because it is of interest to shape pulses in order to properly process and count them, it
is interesting to note that the output pulse of the G-M tube without a pre-amplifier with a
small time constant chosen exhibits similar character to a general pulse outputted from a
pre-amplifier. In short, a G-M tube’s outputted pulse appears as if it had been sent through
a pre-amplifier when it had not. This indicates that it is possible to send this pulse directly to
an amplifier for shaping, and onto being counted without the need of a pre-amplifier.
For more intrinsic reasons, a preamplifier is often not used due to a G-M tube’s mode of
operation. A G-M tube operates on a Geiger discharge, which significantly amplifies the
charge collected. This amplified charge is significantly larger than any noise present and
allows for a better signal-to-noise ratio, eliminating the need for preamplifiers in most cases.
3.8 Fill and Quench Gases
Universal in all gas-filled detectors is the need for incident radiation to create ion
pairs consisting of an electron and a positive ion. Thus, any gas that has potential to
produce negative ions, such as O2 gas, must be avoided. Noble gases are most often used in
G-M tubes such as Helium, Argon, or Neon. Valuable to note is that the conditions of the
fill gases contribute to the energy acquired by ions. The energy gained by ions depends on
the ratio E/p accordingly with the following relation:
v =mEp
, (3.7)
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Where v is the ion drift velocity, μ is the mobility, E is the electric field strength, and p is the
pressure of the gas. Since velocity is integral in the kinetic energy attained by an ion, it
follows that the ion energy increases with the ratio E/p. Smaller values of pressure
necessitate lesser electric field strengths to reach a desired energy of ions. It also follows that
the number of excited molecules n0` increases with the ratio E/p thereby increasing the
probability for additional avalanche. Manipulation of these system parameters can then be
used to reach the threshold energy necessary for free electrons to cause avalanche.
An inherent problem with Geiger tubes arises from its large abundance of positive
ions created through its multiple avalanching process. As discussed in The Geiger Discharge
section, the positive ions formed barely move in comparison to free electrons and thusly the
avalanches. However, the positive ions do move slowly and are attracted to the cathode wall.
The ions are absorbed, and release an energy equal to the difference of the ionization energy
of a neutral gas molecule and the energy needed to liberate an electron from the cathode
surface. If the energy released is greater than the cathode surface work function, a free
electron may be emitted from the cathode surface. The probability of this is little to none in
an ion chamber detector, and small for a proportional counter, but in a G-M tube with its
large amounts of excited molecules, and abundance of positive ions the probability becomes
great enough that at least one electron is likely to be emitted. This electron will go onto
actuating another full Geiger discharge, and the process will repeat. Thus, after being set off
into this cycle, the Geiger detector would output continuous multiple pulses construing data.
A proportional counter holds a relationship between the output pulse and the number of
original ion pairs created in a fill gas, and the output pulse would be occasional but always
small in amplitude corresponding to one avalanche initiated by this liberated electron
allowing for a way to preferentially pick out pulses that do not reflect incident radiation. In a
G-M counter, the free electron would initiate a full Geiger discharge, implying that it would
continue until the density of positive ions terminated the process. The resulting output
pulse would then be the same amplitude as the pulses created by the original ion pairs
generated by the incident radiation. It would not be possible to distinguish this extra pulse
from the desired pulses. In order to rectify these excess pulses, it has become common
practice to fill the tube with a second component called a quench gas.
A quench gas typically is more complex in molecular structure, lower in ionization
energy, and occupies approximately 10-15% of the tube gas concentration. The gas
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‘quenches’ certain positive ions formed under incident radiation by a transfer of charge. The
positive ions will drift and collide with gas molecules of the fill gas and sometimes of the
quench gas. Upon a collision with a quench gas molecule, it being of a lesser ionization
energy, will likely result in the fill gas’ positive ion transferring its positive charge to the
neutral molecule of the quench gas. The fill gas molecule is neutralized by this transfer of
positive charge and an eventual electron transfer from the quench gas. The positive ion of
the quench gas then begins to drift toward the cathode wall. Given a sufficient
concentration of quench gas, all positive ions in the tube arriving at the cathode wall will be
of the quench gas. Upon reaching the wall, the molecules are neutralized leaving the excess
energy more likely to be used in dissociation of the complex molecule rather than to liberate
a free electron. This dissociation; however, implies a finite lifetime for the quench gas, and
the need for either refilling the tube, or the need for a replenishable quench gas.
Halogen gas (X2) is often used to remedy the situation. A halogen gas molecule’s
excess energy still preferentially goes into disassociating the molecule, but a halogen X can
later undergo radical chemistry reactions involving single electrons enabling the molecules to
reform. An example is shown below for the case of Bromine gas (Br2) in Figure 3.9:
Figure 3.9 Free radical mechanism of two dissociated Bromine atoms recombining to replenish the quench gas.
The single valence electron on each isolated bromine atom will rapidly donate its electron to
another bromine atom allowing for a reformation of the more stable gas molecule. The
renewable nature of a halogen gas gives the quench gas a theoretically infinite lifetime, but
this is not so for the Geiger tube. Factors that contribute to the finite lifetime of a Geiger
tube include contamination of the gas by byproducts of the Geiger discharge, and the
alteration of the anode surface caused by polymerization reaction products.
3.9 Solid Angles G-M Tube
Incident radiation from a source s is constricted in the direction it may pass through
the window of the G-M tube. This restriction falls out of the geometry of the window as
shown in Figure 3.10:
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Figure 3.10 A source emitting radiation may only enter the detector through a range of angles.
The angle at which the radiation enters the detector with respect to the source is called the
solid angle Ω. Elementary geometry and calculus analysis yields that the solid angle can be
computed by the following relation:
U =
óôôôõA
cos (a )
r2dA
(3.8)
where r is distance from the source to the detector, dA is the differential surface area
element of the detector, and α is the angle between the normal of the surface element and
the incident radiation direction. Evaluation of the integral provides a formulaic calculation
of the solid angle:
U = 2p æçè
1 K d
d2 C a2
ö÷ø
(3.9)
It is evident that as the quantity (d2 + a2) increases, the solid angle decreases.
3.10 Regions of Detection
Three types of gas-filled counters are similar in operation: ion chambers,
proportional counters, and G-M counters. Their differences can be shown through an
examination of the output pulse amplitude as a function of the applied voltage (Fig. 3.11)
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Figure 3.11 The output pulse amplitude as a function of the applied voltage for two differing energy values present in the fill gas. Labeled are the different regions of detector operation.
Ion chambers operate on the collection of charge of original ion pairs created by
incident radiation. From the amount of charge collected, information of the incident
radiation can be discerned. Below the ion saturation region, there is not sufficient electric
field strength to prevent electrons from recombining with their counterpart positive ions and
therefore the pulses observed is less than the charge represented by original ion pairs. As
the voltage is increased the state of ion saturation is achieved by providing sufficient energy
to inhibit recombination, and charge collection can take place. Ion chambers can be used to
measure both counting and energy information about the incident radiation in this region.
Increasing the voltage the threshold energy for gas multiplication accomplished. The
collected charge multiplies linearly over the ‘proportional region’ labeled above. Since the
linearity can be deduced, most proportional counters operate between these voltage limits so
as to preserve energy information of the output pulses. Leads to the proportional and limited
proportional regions where proportional counters may be used.
Above this region is that of limited proportionality. The name limited
proportionality results from nonlinearities being introduced to the output pulse amplitude.
Positive ion density created from both primary and secondary ionizations change the electric
field character. Since a proportional counts relies on the principle of gas multiplication,
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sufficient change in electric field strength can terminate this process at differing times, and
lead to nonlinear amplification of charge. A detector can still be used as a counter, but to
ascertain energy information, knowledge of the nonlinear amplification is necessary if
possible at all.
A distinguishing quality of the Geiger tube is its significantly higher electric field in
comparison with a proportional, and ion chamber detectors. The Geiger discharge
eliminates any information of energy, and is strictly a counter. Under these high electric field
strengths, avalanching occurs and terminates when a sufficient density of positive ions has
been reached. Thus, no matter what sort of radiation causes the discharge, an avalanching
process will terminate when the same amount of positive charge has been accumulated
leading to constant amplitude given a constant voltage as a result of the same amount of
accumulated charge.
3.11 Output pulses in a Geiger counter
a. Constant Electric Field
If an applied voltage is held constant, the same positive ion density will be needed to
terminate the discharge. No matter the type of ionization, or how many ion pairs created in
the fill gas, the discharge ceases at the same point. This implies that the output pulse will
accumulate the same amount of charge no matter the source at a set voltage. All amplitudes
of output pulses will thusly be the same implying the G-M device can only give information
as a counter, and contains no information of the properties the specific radiation.
b. Variable Electric Field
Differing voltages demand different positive ion densities necessary to terminate a
Geiger discharge. A low voltage involves a lesser density of ion density needed due to a
lower electric field strength necessitating less ions to decrease the electric field below a
critical value, and vice versa. In general, the output pulse will increase in amplitude as the
voltage is increased. Knoll discusses the amplitudes increasing with the overvoltage, the
difference between the applied and minimum voltage required to induce a Geiger discharge
(203). Qualitatively, this is shown below as average pulse height H vs. Voltage. Since the
electron density increases according to the Townsend Equation (Eq. 3.1) nonlinearly, it is
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expected that the total collected charge (i.e. output pulse amplitude) in varying voltages
would increase nonlinearly as well, and is confirmed in Figure 3.12.
Figure 3.12 The average pulse height increases with increased applied voltage
3.12 Geiger Counting Curves
Any counting apparatus depends on finding a one-to-one correspondence between
each pulse outputted and counts registered. In a G-M counter, this is accomplished by
observing the counting rate with respect to the applied high voltage HV in order to find a
region of uniformity, that is to say: a plateau. This plateau is illustrated in the following figure:
Figure 3.13 The counting rate of a Geiger tube as a function of the high voltage HV. A plateau is observed indicating a proper region of operation for counting.
20
An approximate plateau is observed, and this demarks a region where each pulse is counted.
The overall shape of the counting graph is intuitive. Below a certain value of the HV the
counting rate is observed to be zero. This is due to the HV not being high enough to create
a sufficient electric field strength that would allow for gas multiplication. As the HV is
increased, the counting rates are observed to rapidly increase until the plateau region.
Further raising of the HV beyond this point does little to increase the counting rate in this
correspondence region because of the onset of gas multiplication and the HV’s inability to
alter the inner workings of the G-M tube (i.e. the discharge process). This region is the
proper operating region of a Geiger tube because each pulse is counted. However, if the
HV is increased significantly, then the start of continuous discharge begins to occur. This
region is caused by irregularities arising in the anode wire due to the polymerization reactions
that lend themselves to the limited lifetime of a Geiger tube (discussed in Fill and Quench
Gases). These irregularities in output pulses in tandem with failure of the quench gas to
prevent positive ions of the fill gas from drifting to the cathode wall to emit an electron
initiating another full Geiger discharge allow for multiple pulses to be outputted attributing
to this continuous discharge region.
The plateau region in practice is not completely flat. The plateau has a finite slope,
and is evidenced to be caused by a low-amplitude tail that is evident in the differential height
spectrum (Fig. 3.14):
Figure 3.14 The low-amplitude tail evident on this differential height spectrum is the root of the finite slope of the plateau region.
21
This low-amplitude tail may be the result of several factors. Non-uniform electric field in
the tube, particular in the multiplication region offset outputted pulses. The ends of the tube
may have a lower electric field as a result of the construction. This electric field may be low
enough to prevent avalanche from beginning, and as a result the discharges at these parts of
the tube may be lower than other regions. This difference in electric field throughout the
tube also lends itself to causing a difference in the active volume of the tube. The inactive
end regions of the tube may become active with increased voltage thereby increasing the
active volume of the tube and contributing to a difference in output pulses compared to
lower voltages in the plateau region. A pulse arising during the system’s recovery time
attribute to a difference in output pulse as well. The quench gas could fail to take on all the
positive charge from the fill gas’ positive ions and these ions could reach the cathode surface
enabling an extra outputted pulse. Finally, the tube may exhibit a hypteresis effect that stems
from the insulators of the tube being slow to equilibrate electric charges. These charges will
influence the electric field of the tube, and thusly the outputted pulses.
3.13 Dead, Recovery, and Resolving time
A Geiger discharge is terminated by a sufficient density of formed positive ions.
These positive ions enervate the electric field strength preventing further gas multiplication.
As these ions slowly drift to the cathode wall, the electric field strength begins to increase.
When sufficient positive ions have been dispersed from the multiplication region, the electric
field will be enough to supply sufficient threshold to ion pairs to cause another Geiger
discharge. The time between the original output pulse and the second is the detector’s dead
time. During this time, any incident radiation will not be detected because gas multiplication
cannot occur.
The positive ions move slowly, a consequence then arises in a G-M tube in that it has
a long inherent dead time due to its inner workings. All positive ions need not dissociate
from the multiplication region to enable consequential Geiger discharges. If the enough ions
move out of the vicinity of the multiplication region, and the electric field is large enough to
cause gas multiplication, it will. This resulting Geiger discharge will be of a lesser amplitude
than the original pulse due to the presence of positive ions before the discharge was initiated.
If positive ions are present, it will necessitate less new positive ion formation to terminate
the discharge, and the outputted amplitude will be smaller than the original as a result. This
22
process implies that the first few pulses after an original pulse will be diminished in
amplitude until all the positive ions have drifted to the cathode providing the original electric
field before positive ion formation. Once this original state is reached, another output pulse
of the same amplitude can be attained. This is diagrammatically shown in Figure 3.15. An
often synonymous term with dead time is the resolving time. In a G-M counting unit, a finite
pulse amplitude is achieved before a second pulse is registered. The time taken to create a
second pulse that exceeds this amplitude is called the resolving time. Finally, recovery time is
the time it takes a G-M tube to output a second pulse of equal amplitude of the original.
Figure 3.15 Oscilloscope sketch of an original pulse, and subsequent pulses in a G-M tube.
The dead time is another difference between a G-M tube and other gas-filled
detectors. In a G-M tube, its dead time is due to its inner mechanics while in other gas-filled
detectors it is due to the processing circuitry used to count and measure the radiation. In an
ion chamber, two incoming charges individually flow through its tandem circuitry. If the
time between events is short enough, these charges will result as a single superimposed pulse.
The details of the lost information is determined by the shaping and processing circuitry,
external to the detector. The G-M tube’s operating methods cause its large dead time that
no amount of processing can remedy. The dead time is important to consider so that a
relationship between the experimental counts and the actual counts are known. Without
knowledge of the dead time, basing a sources radiation activity on experiment alone could
amount to a large miscalculation.
23
3.14 Measuring Dead Time: Two-Source Method
The two-source method helps to calculate the dead time of a detector. The
measured counting rate varies nonlinearly with the true rate, and this method takes
advantage of that tenet to estimate the dead time. If either a paralyzable, or non-paralyzable
model is appropriate for the detector type, the dead time can be calculated by measuring the
count rate for two different true rates that differ by a known ratio.
The two-source method involves measuring the rates of two sources alone and together.
The combined rate is expected to be less than the sum of the two sources because the
counting loses will be nonlinear. Deriving a formulary for dead time using this method: let
n1, n2, and n12 be the true count rates for source 1, 2, and the two combined respectively, m1,
m2, and m12 be the respective measured rates, and nb, mb be the true and measured rates of
the background noise then:
n12 K nb = (n1 K nb ) C (n2 K nb ) (3.10)
n12 C nb = n1 C n2(3.11)
Recall that the true count rate found in a nonparalyzable model is given by the following
relation:
n =m
1K mt(3.12)
If a nonparalyzable model is assumed, then combining Eq. 3.11 with Eq. 3.10, and solving
for the dead time τ, it is found that:
t =X (1 K 1 K Z )
Z(3.13)
Where: X = m1m2K mbm12
Y = m1m2 (m12 C mb ) K mbm12 (m1 C m2 )
Z = Y0m1 C m2K m12K mb1
X2
24
Thus, by measuring two sources separately and in tandem with each other the dead time of
the system can then be found. Using the dead time, it is then possible to find the true
counting rate of the detector.
3.15 Beta Attenuation
An attenuation is witnessed when beta particles are directed towards a material acting
as an absorber. In the case of monoenergetic electrons, the fraction of particles that tunnel
through the material and reach the detector decreases in a smooth curve as the thickness t of
the absorber increases. This is not the case with beta particles of differing energies. The
shape of the graph found is experimentally nearly exponential in shape implying a linear
character when graphed on a semilog plot. The difference in character is attributed to low
energy beta particles being readily absorbed in even small thicknesses, giving rise to a large
slope initially. An approximated relation of the fraction of beta particles tunneling through
the material and the absorber thickness is given by:
II0
= eK(3.13)
Where I0 and I are the counting rates detected with and without the absorber respectively, t
is the thickness, and n is the absorption coefficient. The resulting experiments of incident
beta particle energy vs. different thicknesses of aluminum exhibits linearity on a semilog plot
as shown below in Figure 3.16:
25
Figure 3.16 plotting beta particle energy as a function of the absorption coefficient n yields linear character in a semilog plot implying an exponential shape in the absence of a semilog axis. (Baltamens)
A simple analysis of Eq. 3.13 reveals an expected behavior, the fraction of particles that are
not absorbed by the material decreases as the absorber thickness t increases.
3.16 Gamma Rays in G-M Tubes
In a G-M tube, a gamma ray can only be detected through the formation of an
electron which would thereafter initiate a Geiger discharge. As discussed in section 3.3 The
Geiger discharge, a gamma ray has a chance of emitting an electron upon absorption by the
cathode wall. If an incident gamma ray can interact with the cathode surface, emit a free
electron, and that electron makes it to the fill gas the gamma ray can be detected through the
consequential Geiger discharge. The efficiency of gamma ray detection then depends on
both the probability of a gamma ray interacting with the wall to produce an electron, and the
probability of the free electron reaching the fill gas. The latter condition depends on the
thickness of the wall and also the Z number of the material of which it is made. Secondary
electrons of significant contribution are only those that originate from the innermost layer of
the wall due to range constrictions, as shown in Figure 3.17:
26
Figure 3.17 A gamma ray entering a G-M tube may spawn a free electron via interaction with the innermost layer of the cathode tube. If an electron is created within sufficient range, it can reach the fill
gas to give an outputted pulse.
This innermost region has a thickness on the order of one or two millimeters. In an
absorber, electrons may only progress a certain range, and if they are formed beyond a
certain point they have no possibility of making it to the fill gas. Gamma ray detection
efficiency increases with the Z number of the inner wall material. Bismuth (Z = 83) is a
common material choice for gamma ray detection. However, even for high Z number
material, gamma ray efficiency is low. Figure 3.18 maps the counting efficiency (%) vs
Gamma ray energy (MeV) for several high Z number materials used for cathode walls:
Figure 3.18 even with high Z materials and high energy gamma rays, the percent of detected gamma rays does not reach higher than a few percent.
27
As can be seen from the graph, gamma ray counting efficiencies rarely rise above a few
percent. Gamma ray efficiency can; however, be maximized if a different approach is taken.
Using a high Z gas such as Xenon or Krypton, sufficiently low energy gamma rays’
interaction with fill gas molecules are present. The process is maximized by using as high a
pressure as possible, and for gamma ray energies below approximately 10 keV, a nearly
100% efficiency can be reached.
IV. Experiment
The experiment involved four parts, and are labeled as 4.x in accordance with the lab
handout (attached in appendix) such that x is the corresponding number on the handout.
Equipment and materials used are listed below:
Equipment/Materials
Ortec 572 AmplifierOrtec Timing SCA SS1Ortec 994 Dual Counter/TimerTennelec TC 952 High Voltage SupplyHewlett Packard 54610B Oscilloscope, 500 MhzG-M Tube Lead Shield, Model No. AL144, Serial No. 453Preamp (HV SIG)Cs-137, 5.5 μCu, half life: 38 years, May 1989, Nucleus Inc.Co-60, 10.21μCu, 15 Oct 1998, S/N: 619-80-5Cl-36Sr-90, 22 September 1995, ES 883
Additionally, the experimental setup is depicted in a block diagram below:
Figure 4.1 Block diagram of the experimental setup
28
4.1 Pulse Height vs. Ionization Type and Energy
To determine the dependence of ionization type on pulse height outputted by the G-
M unit, various sources were placed in the tube at a fixed voltage. The voltage was set at 836
V, a median point in the plateau region of counting curve as discussed in section 3.12. This
voltage was determined using Cl-36 as a reference. Different sources’ output amplitude was
aimed to be observed at this fixed voltage on two sides of the source, shown below in Figure
4.2.
Figure 4.2 two sides of a radioisotope source, (a) an opening allows for all radiation to come from the source. (b) on the opposite side, a protective coating only allows high energy gammas to penetrate.
One side (the ‘regular side’) allowed for all radiation types to be exposed to the G-M tube
through an opening in its protective coating, Fig. 4.1a above. The other side, Figure 4.1b,
was covered in a coating that prevented soft radiation (such as beta particles) from being
emitted by absorption in the material, and only allowed for gamma emission (hence, the
‘gamma side’). Thus, by using different sources and measuring the output amplitude on
both the regular and gamma side, a measurement was found of the different sources’
different radiation types. Since different sources were used, in case two sources shared a
certain type of radiation, the result would still be beneficial because different sources emit
different energied radiations. The resulting output amplitudes for these different sources at
a fixed voltage of 836 V is tabulated below.
29
Output Amplitude (mV) at High Voltage = 836 V
Source Regular Side Gamma Side
Cl-36 41.56 ± 5 0
Co-60 41.56 ± 5 1.250 ± 2
Cs-137 42.19 ± 6 60.94 ± 12
Sr-90 42.19 ± 5 41.58 ± 5
Table 4.1 Output amplitudes of various sources’ regular and gamma side at a fixed high voltage of 836 V
The observed pulses for the regular side are nearly constant. This is consistent with G-M
tube theory in that no matter the type of ionization, any incident radiation will cause a
Geiger discharge that will terminate at approximately the same point of accumulated charge,
thereby outputting the same pulse. This can be seen further by examining the sort of
radiation emitted from each of these sources, as tabulated below:
Source Decay type
Cl-36 β-, β+, EC
Co-60 β-, γ
Cs-137 β-, γ
Sr-90 β-
Table 4.2 Sources listed with their corresponding decay types (Chart of Nuclides)
where EC denotes electron capture. Since each of these sources emit different types of
radiation at different energies, and the output pulse is still relatively constant, it can be
concluded that at a fixed voltage the Geiger tube output pulse is independent of the type or
energy of radiation incident in the tube. The rationale is simple, no matter what kind of
radiation causes the Geiger discharge, at a given voltage the same amount of positive ion
charge is necessitated to terminate it, resulting in the same accumulation of charge in every
case, even in gamma decay. The results from table 4.1 show this pattern, for the regular side
of the source the pulses are approximately of the same amplitude.
The gamma side illustrates a more robust nature. Cl-36 exhibited no gamma
detection as expected as The Chart of Nuclides indicates that no gamma rays are emitted. Co-
60 indicated a pulse of around 1.250mV. This amplitude is too low to be the result of a
30
Geiger discharge, and can be attributed to background noise and a detection of a gamma ray.
The low efficiency of gamma detection can be accredited to a gamma ray not being detected
(as discussed in section 3.16). Cs-137 yielded a gamma pulse around 60.94mV, this is an ≈
46% increase in pulse amplitude, and must be caused by the gamma ray, as Cs-137 does emit
gamma rays. The large amplitude could be due to a failure of the quench gas, involving an
interaction with the cathode, eventually causing a contribution to the output pulse through
interaction with the fill gas. Sr-90 exhibited a pulse consistent with those of the regular side
of the sources. Since this source emits no gamma rays, this must be the work of a high
energy β- particle penetrating through the shielding of the source and reaching the fill gas to
where it was eventually detected, since the half life is of the order of tens of years it is
unlikely that this source emitted a gamma ray. With only slight reservation, it can be
concluded that even gamma rays, if detected, will yield the same pulse amplitude as other
types of radiation.
4.2 Counting Curve and Pulse Height vs. Voltage
A metallic thorium source was placed near the bottom of the tray of the G-M tube to
minimize dead time interference. The LLD was set above a level to discriminate background
noise previously. Starting at the high voltage of minimum amplitude peaks, the counting rate
and average pulse height was recorded with respect to increased high voltage. The counting
rate was graphed vs. high voltage as shown below according to the data collected (appendix
data table A.1):
31
Count rate vs. High Voltage
0
50
100
150
200
250
300
350
400
450
0 200 400 600 800 1000 1200
High Voltage (V)
Co
un
t ra
te (
1/s
)
Figure 4.3 The counting rate of the G-M tube with a metallic thorium source is graphed vs. the high voltage. A plateau region is evident.
The quality of this graph reflects that of Figure 3.13. Below a threshold voltage, no counts
are observed, the curve then sharply increases towards the plateau region. Upon further
increasing of the voltage the count rate sharply slopes upward, indicating the onset of
continuous discharge that was discussed in section 3.12. Apparent in this data is an
obviously finite slope. The slope is found through elementary calculations to be, eyeballing
the data points at which the start and end of the plateau region:
Slope = (362.8 – 347.7) / (960-890) counts/Vs
= 0.2157 counts/Vs
Possible reasons for this finite slope lie in a hidden low-amplitude tail present in the
differential height spectrum (shown in Figure 3.14). The tube may not have a uniform
electric field, thereby swaggering the count rate observed. This occurs because the electric
fields near the end of the tube may be lower than in other parts, since the electric field needs
to provide sufficient energy to the ions to initiate a Geiger discharge, the discharge at these
parts may be lower than those at the rest of the tube. Also, the difference in electric field
may manifest itself in a decrease of active volume as a result of enervating the multiplication
32
region throughout the tube. Pulses could have arisen during the systems recovery time, and
also there is the hysteresis effect discussed in section 3.12.
Addtionally, the average amplitude of the output pulses were recorded. This served
as a contrast to part 4.1 of the experiment where the voltage was steady. This time, the
amplitude’s relationship with the high voltage was analyzed. A graph of the average pulse
height vs. the high voltage is shown in figure 4.4:
Average Output Pulse Height vs. High Voltage
0
20
40
60
80
100
120
0 200 400 600 800 1000 1200
High Voltage (V)
Ave
rag
e p
uls
e h
eig
ht
(mV
)
Figure 4.4 As the high voltage increased, the average output pulse did as well
The graph is disjunct in appearance, but does show the qualitative character that should have
taken place. The average output pulse height was shown to increase with the high voltage.
As the high voltage is raised, the magnitude of the Geiger discharge increases and thusly will
accumulate more charge outputting a larger pulse. This can also be viewed as when the high
voltage is raised, more positive ions need be accumulated in order for this density to
sufficiently decrease the electric field below the point of gas multiplication where the
discharge terminates, and a larger pulse amplitude is observed as a result.
SHOULD THIS BE THE SAME SHAPE AS THE MAKESHIFT MAPLE GRAPH
ABOVE IN THEORY?
4.3 Beta Attentuation
Beta attenuation was measured using Sr-90 as the beta source. The source was
placed in second tray position from the top of the Geiger unit, and counting rate was
33
measured when different thicknesses of aluminum were placed on top of the source tray. A
complete table can be found in the appendix (Table A.2). The natural log of the net beta
count rate vs. the absorber thickness is graphed below, where the net beta count rate is the
ratio between the number of beta particles that penetrate the absorber and the number of
beta particles emitted without an absorber (I/I0):
Natural log of (I/I_0) vs. Absorber Thickness t
-6
-5
-4
-3
-2
-1
0
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
Absorber Thickness t
ln (
I/I_
0)
Figure 4.5 Graphing the natural log of the fraction of detected beta particles vs. the absorber thickness exhibits a linearity.
The graph exhibits linear character. The graph has the natural logarithm of the ratio I/I0 as
its y-axis, and an independent variable t, the absorber thickness. Quantitatively, the graph
above shows linear character with some finite slope n. A general model of this line can then
be noticed to be of the form y = mx + b, where b is the y-intercept, and m is the slope of
the line. Fitting appropriate variables to this situation, the following can be arrived at:
ln æè
II0
öø
= K nt C b, (4.1)
where n is a constant of proportionality acting as the slope of the line. The elimination of
the y-intercept b can be obtained by the realization that the y variable (in this case [I/I0])
being operated on by the natural log function. Solving for the ratio I/I0, the equation above
becomes:
34
(3.13)
Where eb is simply a multiplicative factor that can be absorbed in the constant n. This small
matter of work reveals this equation to be exactly that of Eq. 3.13, thereby identifying the
constant of proportionality n as the absorption coefficient. It is thereby an easy matter to
discern its value by taking the logarithm of both sides, as is the case in Eq. 3.13, yielding
exactly that which was graphed in Figure 4.3:
lnæè
II0
öø
= K nt (4.2)
This function is linear, and the absorption coefficient t is simply the slope of the graph.
Using values from table A.2, the absorption coefficient is found to be:
[ ln (I2/I0) – ln (I1/I0) ] / (t2 – t1)
ln (I2 / I1) / (t2 – t1)
ln (103.36 / 87.54) / (0.04 – 0.032)
n = 41.531
where I2 and t2, I1 and t1 are corresponding pairs of arbitrary data points taken from table A.2.
This could be alternatively calculated by algebraically solving for the absorption coefficient n,
such that:
n = K
æççè
lnæè
II0
öø
t
ö÷÷ø
, (4.3)
where I and t can be any arbitrary data point. The calculation is shown for comparison to
the above method.
35
n = - [ ln (128/365) ] / (0.025)
n = 41.912
In both cases the absorption coefficient was found to be approximately 42. Using Figure
3.16, it was possible to estimate the endpoint energies for Sr-90. By looking at the graph,
with the corresponding absorption coefficient, an endpoint energy for Sr-90 was found to be
approximately 0.6 MeV.
4.4 Dead Time and Recovery Time
The dead time was determined in two ways, both with a Thorium source. The first
method involved physically holding the source inside the G-M tube as close as possible to
the end window without touching it to maximize the counting rate. Using the oscilloscope’s
autostore feature, the envelope of secondary events were mapped following the original pulse.
The result was a graph identical to that of Figure 3.15. Using the oscilloscope’s time cursors,
a change in time Δt was found for both the recovery and dead time:
Dead time τ1 380 μs
Recovery time 1.020 ms
Table 4.2 Dead time and recovery time as determined by the oscilloscope for the first method outlined above
The second method involved the two source method discussed in section 3.14. Two
metallic thorium sources were used. One was measured m1, then the other m2, and then
both combined m12 in such a way to minimize solid angle problems, as shown in Figure 4.5
36
Figure 4.6 Source placement in the tray of the Geiger tube to minimize solid angle issues. A circular indented center is present in the center of the tray for a source to be fit into it.
The figure outlines how the solid angle issues are resolved. Source 1 is place so that only
half of its edge protudes onto the indented center (restricting the radiation that enters the G-
M tube window). The same is done with source 2. Then, when these two are measured
together, they are arranged so as both sources have the same solid angle window they had
when measured in isolation of the other thereby limited problems due to solid angles.
Before measuring, both sources were found to have approximately the same dead and
recovery time as the one used in the first method so that a fair analysis of dead and recovery
time may be made. Additional to the sources being measured, the sources were removed
and a background radiation count mb was taken. This is all the data necessary to compute
the dead time according to Eq. 3.12:
t =X (1 K 1 K Z )
Z(3.12)
Where X =3902313
100
Y =9984640683161692005194441
Z =998464068316
1692005194441
m1 = 196.6 s-1
m2 = 199.15 s-1
37
m12 = 324.4 s-1
mb = 0.4 s-1
explicit values of X, Y, and Z were calculated using Maple 10 given these measured count
rates. Putting these values into Eq. 3.12, the dead time τ2 was found to be:
Dead time τ2 ≈ 325.59 µs
Compared with the dead time yielded through the first method, this time is significantly
lower, a difference of around 13.17%. The disagreement between both sources may have
been caused due to their counting rates not being identical.
V. Conclusions
The theoretical basis for the G-M tube was shown to accurately hold up to
experiment. Through the use of different sources, it was found that the output amplitudes
were independent of the type of ionization at a constant high voltage. In part 2, this
examination was taken further by looking at the amplitude change for differing voltages.
This was accomplished using a single source, varying the voltage, and observing the average
output amplitude. As expected, as the high voltage was increased, the amount of positive
ion density in the G-M tube needed to be greater than at a lower voltage lending itself
towards a larger accumulation of charge and therefore a larger output pulse.
Counting rates were examined under the same conditions. Counts were unable to be
detected below a certain voltage, and soon after manifesting themselves they rapidly
approached a flat plateau region, the region of proper detection for a Geiger tube. This
region established a one-to-one correspondence between pulses and counting. Increasing
the voltage further contributed to damaging the tube in that an onset of continuous
discharge caused for a sharp increase of count rates. This increase is due to quench gas
failure, and irregularities in the form of spurious pulses that arise from polymerization
reactions affecting the anode.
Beta attenuation was examined by using a Beta source (Sr-90), and measuring the
fraction of particles that were detected under varying aluminum thicknesses acting as an
38
absorber. The resulting curve was found to be approximately exponential, and that the
greater the thickness, the fewer beta particles could be detected.
Dead time was measured using two methods. First, utilizing the oscilloscope in
tandem with holding a metallic thorium source as close as possible to the G-M tube window,
the dead time was calculated. Then using the two-source method: measuring the count rates
of one thorium source, then another, and then the two together and assuming a
nonparalyzable model the dead time was also calculated. These values were found to be
within approximately 13% of each other, and gives a good idea of what the dead time of G-
M detector is. The theory accurately predicted experimental conclusions.
VI. Appendix
6.1 Bibliography
1. Knoll, Glenn F. Radiation Detection and Measurement: Third Edition. Hoboken: John
Wiley & Sons, 2000.
2. Knoll’s Atomic Power Laboratory. Revised by Edward M. Baum, Harold D. Knox, and
Thomas R. Miller. Nuclides and Isotopes: Chart of Nuclides. Lockheed Martin
Distribution Services. 2002.
6.2 Tables
Al thickness(g/cm^2) Count rate (1/s)
0 3650.0007 353.30.0001 340.7
0.02 148.40.025 1280.032 103.360.04 87.540.05 61.28
0.063 35.30.08 18.33750.09 10.5420.1 7.175
0.125 1.228Table A.1 Count rate was recorded with differing aluminum thickness
39
High V (V) Count Rate (1/s)
Avg Amplitude (mV)
671 0 0672 0.2 3.125680 43.3 3.906690 228.9 6.406700 253.9 6.25710 276.2 9.062730 283.1 35.62760 303.7 25.62800 329.7 33.75830 331.7 71.88860 339.5 31.88890 347.7 31.88930 362.7 76.56960 362.8 82.811000 394.4 96.88674 5.1 0
Table A.2 Count rates and average output amplitude of varying high voltages