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