Experiment 2

September 1999

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This experiment has three parts: the first deals with some of the physics of a Geiger-Mueller (GM) Tube and will acquaint you with some characteristics of this gas-filled detector. The second part utilizes those parts of statistical theory that apply particularly to all counting experiments. The third part examines a fundamental property of all detectors, namely the detection efficiency. This is not the simple experiment it appears to be at first glance; it contains subtleties that are not always immediately apparent. The measurement and analysis techniques encountered here are universally applicable to all other types of radiation detectors.

If a g - ray interacts with the GM tube (primarily with the wall by either the Photoelectric Effect or Compton scattering) it will produce an energetic electron that may pass through the interior of the tube.

Figure 1. The principal mechanism by which gas-filled counters are sensitive to g- rays involves ejection of electrons from the counter wall. Only those interactions that occur within an electron range of the wall's inner surface can result in an output pulse.

Ionization along the path of the primary electron results in low energy electrons that will be accelerated towards the center wire by the strong electric field. Collisions with the fill gas produce excited states (~11.6eV) that decay with the emission of a UV photon and electron-ion pairs (~26.4 eV for argon). The new electrons, plus the original, are accelerated to produce a cascade of ionization called "gas multiplication" or a Townsend avalanche. The multiplication factor for one avalanche is typically 10^{6} to 10^{8}. Photons emitted can either directly ionize gas molecules or strike the cathode wall, liberating additional electrons that quickly produce additional avalanches at sites removed from the original. Thus a dense sheath of ionization propagates along the central wire in both directions, away from the region of initial excitation, producing what is termed a Geiger-Mueller discharge.

Figure 2. The mechanism by which additional avalanches are triggered in a Geiger-Mueller discharge.

The intense electric field near the anode collects the electrons to the anode and repels the positive ions. Electron mobility is ~ 10^{4} m/s or 10^{4} times higher than that for positive ions. Electrons are collected within a few ms, while the sheath of massive positive ions (space charge) surrounding the center wire are accelerated much more slowly (ms) outward towards the cathode.

The temporary presence of a positive space charge surrounding the central anode terminates production of additional avalanches by reducing the field gradient near the center wire below the avalanche threshold. If ions reach the cathode with sufficient energy they can liberate new electrons, starting the process all over again, producing an endless continuous discharge that would render the detector useless. An early method for preventing this used external circuitry to "quench" the tube, but the introduction of organic or halogen vapors is now preferred. The complex molecule of the quenching vapor is selected to have a lower ionization potential ( < 10 eV) than that of the fill gas (26.4 eV). Upon collision with a vapor molecule the fill gas ion gives up ~ 10 eV to the quench vapor molecule which then quickly dissociates rather than losing its energy by radiative emission. The remainder of the partially neutralized vapor-atom energy (~ 4 eV) produces a UV photon that is strongly absorbed by the molecules and prevented from reaching the cathode. Any quench vapor that might be accelerated and impact the cathode dissociates on contact. Organic quench vapors, such as alcohols, are permanently altered by this process, limiting tube life to ~ 10^{9} counts. Halogen quench vapors dissociate in a reversible manner later recombining for an essentially infinite life.

Reference: (2) p. 96-102.

**{Exercise: Work out the necessary relationship. (Assume no background.)}**

Reference: (2) p. 225-226.

Sample Mean:

Sample Variance:

(Note the N - 1 in the definition of s^{2} makes s^{2} a correct estimator of s^{2}.)

Under the conditions that are thought to apply to all radioactive decays (i.e., all the nuclei are identical, independent, and each has a definite and constant probability of decay in a unit time interval), one can derive a distribution function P(x) that is the probability of observing x counts in one observation period.

The distribution of the values x about the true average m is called the Poisson distribution and has the form:

References: (1) p. 750-753 (3) p. 34-35 (4) p. 36-42

If the mean of a Poisson distribution becomes ~20, the distribution becomes symmetrical, assuming the characteristics of a Normal, or bell-shaped Gaussian distribution. This displays the characteristic that 68% of the total area of the distribution lies within ± s of the mean. For a Poisson distribution s=sqrt(m) , so that a counting measurement is 68% likely to be within ± s of the true population mean m Since x is probably close to m, we may take s = sqrt(x), and say that a single measurement is 68% likely to be within ± sqrt(x) of the true mean. Similarly the values for ± 2 s and ± 3 s are 95% and 99.7%, respectively. When plotting experimental results, it is customary to include error bars of length s_{1} on each point x_{i}.

**{Exercise: Express the uncertainty in X+Y, X-Y, XY, X/Y, and ln(X) in terms of s _{x} and of s_{y}. Write the uncertainties in XY and X/Y to show the fractional uncertainty in terms of the fractional uncertainties in X and Y. Do you see the mnemonic value of this?}**

References: (1) p. 768-769, (4) Chap. 4, (3) p. 51-55.

The apparatus consists of a halogen quenched Geiger-Mueller tube (TGM Model N106/3P) that may be used in or out of a lead shielded "house", a Counter/Timer/High-voltage Power Supply (Nucleus Model 550), and various radioactive sources. Be certain you understand the correct procedures for handling radioactive sources. See the Primer On The Effects Of Exposure To Ionizing Radiation that also contains an inventory of the radioactive sources available in the laboratory.

**1: Finding the best operating point for the GM tube.**

Apply 500V to the tube with a moderate strength ^{137}Cs source (50 mCi) nearby. Increase the HV until counts begin to appear, then record the count rate as a function of voltage for a few points up to ll00 V. Do you see the end of the flat region of counts *vs.* voltage? This flat region is called the plateau. DO NOT EXCEED ll00 V AT ANY TIME, as this will cause a continuous arc that destroys the tube by permanently dissociating the quenching gas. Estimate (just roughly) the %/V slope of the count rate curve near the middle of the plateau. Formerly this slope was important because HV power supplies were much less stable than they are today. Set an operating point that is near the middle of the plateau for your measurements.

**2. Measuring the dead time. (Two source and CRO Method)**

A high count rate is required to produce a significant dead time and to achieve sufficiently small statistical uncertainties in a reasonable time, as well as produce a usably visible CRO trace. Use one of the 250 mCi ^{137}Cs sources. Observe the dead time directly on the CRO by attaching a l0x probe to one of the 550 connectors labeled "COUNTS". Consult the 550 circuit diagram for details.

A vertical sensitivity of 2 V/div and a sweep speed of about 20 ms/div are suggested. When measuring a dead time from the recovery envelope be aware that the counting circuits contain a threshold discriminator (See 550 Manual).

When you attach anything to the "COUNTS" connector, what is done to the capacitance that must be charged by the GM tube? Attach a cable (48-60 inch RG-58/U, 30 pF/ft) to the second "COUNTS" connector. Compare the signal amplitude with and without the cable attached. Why use a l0x probe to make the connection rather than a coax cable? How much charge is contained in a full amplitude pulse? Can you estimate the total capacitance that the GM tube must charge up to produce its output pulses?

Use two similar strong sources (each 250 mCi). It is best to secure the GM tube to a thick bed of plastic foam to minimize any scattering from nearby material. Place Source 1 at the midpoint of the bare detector very nearly touching it. Take a counting run and measure the dead time on the CRO. Place Source 2 similarly on the other side of the tube, count and measure this dead time on the CRO. Remove Source 1, count and measure this dead time with the CRO. Count for times long enough for statistical uncertainties in N_{1}, N_{l}+N_{2}, and N_{2} that are small compared to the differences (N_{l}+N_{2}) - N_{l}, etc.

Calculate the dead time. Compare your CRO data to the corresponding counting data. Are they consistent? Explain any differences. What is the approximate uncertainty in the calculated dead time? Is this detector paralysable, or non-paralysable? Explain. (Reference (2), p.96-102.)

**3. Examining a Poisson Distribution.**

Use only "natural room background" radiation as a source with the GM tube in its lead "house". Take 0.5 minute runs and plot them on a histogram until the shape of the distribution emerges, or you have 20 runs. Counting at low rates for short time intervals (x < 20) produces the characteristically skewed Poisson distribution.. Now calculate x-bar and s. How well does s match with sqrt(x) ? How many of the points fall within ± s of x-bar? What is the source of the background?

Reference (2) p. 774-780

**4. GM Tube Detection Efficiency.**

Estimate the efficiency of the GM tube using the attached plot of the total mass attenuation coefficient for aluminum and the energy of a ^{137}Cs g ray. Assume that the walls of the tube are thin enough so that any interaction that will scatter an electron in the proper direction will produce a count. Should you use the absorption or the attenuation coefficient? (see Evans, p. 686-689) Is the air between source and detector important? Is the mass attenuation coefficient for air comparable to that for aluminum? Consider the shape of the wall(s) of the tube. (See SUGGESTION below.)

**Relevant parameters are: Wall = 30 mg/cm ^{2} Aluminum, Fill Gas = Argon 95%/Halogen Quenching Vapor 5%, Total fill pressure ~5 cm Hg, Density of air ~1.3 mg/cm^{3}**

Now **measure** the efficiency. (SUGGESTION: Use the bare tube on a foam platform with as large a separation between the source and detector as permits a reasonable count rate.) Consider the effects of "background". To calculate the total emission from the source you will need an understanding of the ^{137}Cs decay scheme (See "'Internal Conversion", in any of References 1-3), the strength of the source, its half - life, and the calibration date. (Data on last page of the Primer On The Effects Of Exposure To Ionizing Radiation ) How well do the calculated and measured values agree? The decay schemes of several frequently used sources are provided in Appendix A. See also the Guide to the *TABLE OF ISOTOPES*. Would a correction for the shape of the wall be significant?

- Is it possible for a g - ray to interact with a free electron by means of the Photoelectric Effect?
- How does the avalanche phenomenon differ from gas multiplication?
- Which is more important in producing a signal - the collection of electrons at the anode or the less rapid increase in the diameter of the positive ion sheath?
- Which is more important in the operation of a Geiger tube - a large total potential drop or a large electric field gradient? What does the radial variation in electric field look like?
- Given a counter with a plateau threshold of 975 V, what changes in the design of the counter should be made to lower that threshold?
- How does the efficiency of a Geiger counter vary with photon energy? How does the choice of wall material and thickness affect the efficiency? How could you increase the efficiency of the GM tube that you used, without the use of any tools?

- * R. D, Evans,
*The Atomic Nucleus*, (McGraw-Hill, 1955). - * G. Knoll,
*Radiation Detection And Measurement*, (John Wiley & Sons, 1989). - * N. Tsoulfanidis,
*Measurement And Detection Of Radiation*, (McGraw-Hill, 1995). - * C. M. Lederer and V. S. Shirley,
*Table Of Isotopes*, 6th Edition, 1967; 7th Edition, 1978; or R. B. Firestone and V. S. Shirley 8th Edition, 1996 (Updated 1998), Wiley - Interscience. - * P. Bevington, D. K. Robinson,
*Data Reduction And Error Analysis For The Physical Sciences*, (CLAS), (McGraw-Hill, 1992). - S. A. Korff,
*Electron And Nuclear Counters*, (Van Nostrand Co., 1946). - W. Price,
*Nuclear Radiation Detection*, (McGraw-Hill, 1964). - E. Bleuler and G. Goldsmith,
*Experimental Nucleonics*, (Holt, Rinehart and Winston, 1952).

All of these are available in the lab. References with * are considered primary references.

Last updated 17 September, 1999.

Broken links fixed 31 March, 2000.