ADVANCED UNDERGRADUATE LABORATORY
EXPERIMENT 30
The Germanium Spectrometer
Revised: June 1998 by David Bailey
September 1994 by D. A. L. Paul
Outline
Germanium spectrometers are the highest resolution gamma-ray detectors in existence, and they are used extensively for both basic research and applied physics. The energy of gamma or beta rays can be measured with typical resolutions of 0.1%.
The goal of this experiment is to calibrate a germanium detector and to do one of several experiments. Possible measurements include (but are not limited to):
Basic Physics
Strong interactions
• Deuteron formation by neutron-proton strong interactions
• Nuclear interactions and excited nuclear states.
Electroweak interactions
• Beta decay spectra and searching for massive neutrinos.
• Energy loss of electrons in matter.
Applied Physics
Analyses of material composition and characteristics.
• Neutron activation analysis of unknown materials.
• Measurement of the thickness of thin films.
Measurements of environmental, geological, and industrial radioactivity
• Composition of uranium ore and the effect of refining.
• Radioactivity of dinner plates or air.
• Determination of the internal composition of a neutron source.
Detector Physics
• Physics of semiconductor radiation detectors.
(These measurements are discussed in more detail starting on Page .)
Introduction
Germanium spectrometers are small, but very precise, electromagnetic calorimeters, i.e. they measure the energy of photons or electrons. Calorimeters and tracking detectors (e.g. drift chambers or bubble chambers) are the two major types of subatomic physics detectors. Germanium spectrometers are commonly used for a wide variety of low energy measurements, but they are too expensive (~$1k/cm3) for high energy physics experiments which require very large calorimeters (~106 cm3). Semiconductor tracking detectors are, however, very common in high energy physics detectors.
In intrinsic (ultra-pure) Germanium detectors, the kinetic energy of an electron is measured by collecting the electric charge produced by ionization along the path of the electron. The energy required to produce one electron-hole pair in germanium has an average value of about 3 eV. For example, a single 1 MeV electron track produces about 3105 electron-hole pairs. It is possible to collect nearly all of these charges in a germanium detector if the impurities in the germanium have been essentially removed. The statistical variance in 3105 pairs is so small that noise from random thermally excited electron-hole pairs is a major concern and is reduced by cooling the germanium crystal.
The energy of gamma rays can be measured in
Germanium detectors because the energy of a photon can be transferred to
electrons. Low energy gamma rays may be
totally absorbed by the photoelectric effect producing a single electron with
almost all the energy of the initial photon. The predominant interaction of
gamma rays with germanium from about 100 keV to well above 1 MeV is through the
Compton effect, so transfer of all the photon energy to electrons requires one
or more
Gamma ray spectra
When a nucleus undergoes beta or alpha decay, the final state nucleus may be in an excited state which then decays to the ground state by emission of one or more photons with specific energies. For example, when Cobalt-60 decays it turns into Nickel-60 in an excited state which then decays to the ground state of 60Ni by the consecutive emission of 1333 and 1273 KeV gamma rays. (See the Table of Isotopes for information on the decay of all known isotopes.)
Although the radioactive sources produce gamma rays of specific energies, the spectrum observed in a real detector is not simply a series of well defined narrow lines. Figure 1 shows a typical spectrum for a single high energy gamma ray. There are several processes which contribute to the observed spectrum.
Figure 1: Sketch of a typical single gamma spectrum. A higher energy spectrum might include first and second escape peaks as well as a positron annihilation peak.
The sharp full energy peak in the spectrum
is due to gamma rays which have deposited all their energy in the germanium
crystal. Low energy gamma rays are can easily transfer all their energy to an atomic
electron in a single step by the photoelectric effect, but higher energy
photons usually require several steps possibly involving
For energies well above 1.022 MeV, the dominant photon scattering process in matter is pair production. Pair production only contributes to the full energy peak when both electron and positron stop in the sensitive volume of the Ge crystal and when the positron annihilation gamma rays are also totally absorbed. Since sometimes one or both of the (usual) two positron annihilation gamma rays escape the detector, high energy gamma rays typically have first and second “escape peaks” at 511 and 1022 kev lower than the main peak.
The rest of the spectrum is due to scattered and partially absorbed gammas as well as thermal noise and background radioactivity and cosmic rays.
General description of Germanium detectors
The set-up of a typical germanium detector is illustrated in Figure 2. The detector itself is sealed within a vacuum system and is attached to a cold finger which is in thermal contact with liquid nitrogen. Intrinsic Ge detectors are operated at liquid nitrogen temperatures for low noise performance, but they do not necessarily suffer if they are allowed to warm up slowly to room temperature. The detector is often shielded by lead to reduce the background from the natural radioactivity present in the air, walls, and floor.
To collect the charge liberated in a germanium detector a voltage must be applied. The detector is equivalent to a p-n junction having a thick layer of pure germanium at the position of the junction. For operation as a detector it is back-biased in the sense of an ordinary diode and is a good insulator at liquid N2 temperatures. The charges released by the ionizing radiation drift rapidly to the electrodes, typically in times from 0.1–3 µs (mobility ~4-7 m2/V•s @ 77 K). A low noise charge-sensitive preamplifier is connected to the detector output. The input stage of the preamplifier must generally be cooled to amplify such small pulses without introducing too much noise. (For a 1 MeV pulse and a total capacitance of 510–11 F, only 2µV noise would be greater than the rms intrinsic resolution of about 0.1%.) The output of the preamplifier is then fed to a linear amplifier of high quality for pulse shaping and further amplification. The choices of the time constants in the amplifier are important for best results.
Figure 2: Germanium spectrometer. The crystal sits on a “cold finger” the other end of which is in direct contact with liquid N2.
The amplifier output is fed into a Analogue-to-Digital Converter (ADC) which sends digitized pulse amplitudes to a computer based multichannel analyzer (MCA) for sorting. The ADC may be a separate device in a Nuclear Instrument Module (NIM) crate, or be installed on the computer backplane.
The preamplifier attached to the detector should not require any adjustment, but the high voltage, amplifier settings and multichannel analyzer system may all need setting. Each of our germanium detectors is different, so you should match your detector to the physics you wish to investigate (see the experiments starting on Page ).
Setting the high voltage
The sign of the applied high voltage for a detector depends on the way in which it is connected inside the vacuum system and must be known before any voltage is applied. If you apply the wrong sign voltage, you may fry the detector.[2] If you think the high voltage has the wrong polarity, check with the supervising professor or the lab technician, DO NOT CHANGE IT YOURSELF! The maximum allowed voltage (and polarity) are indicated on a label on the preamplifier. The detectors are not too sensitive to voltage, as long as most of the electron-hole pairs released by primary ionizing radiation can be collected. A voltage about 90% of the maximum is typically a good choice.
Germanium detectors have been found in practice to adjust slowly to applied voltages. Therefore it is wise to switch on the voltage well in advance of making measurements whenever precision is desired; an hour should be sufficient for stabilization. The full voltage should not be turned on or off all at once. Nevertheless, a few seconds after the operating voltage is switched on it should be possible to make preliminary measurements.
Adjusting the amplifier and ADC
Look at the input and output pulses of the spectroscopy amplifier. This amplifier converts the long-tailed (~50µs) pulse from the preamplifier into a unipolar (or bipolar) pulse of a few microseconds total duration suitable for analysis in the multichannel analyzer. The gain of the amplifier can be adjusted by controls on the amplifier. The conversion gain and discriminator threshold (minimum allowed pulse size) for the ADC have either external controls or in some cases can be controlled by the APTEC program. The amplifier may also have a discriminator setting which can be adjusted to reject small pulses. For very precise measurements you may need to adjust the integrating time-constant and the pole-zero cancellation of the amplifier. (See the amplifier manual for more information.)
The resolution and degree of symmetry in the measured peaks are likely be somewhat worse at very high counting rates. A useful rule-of-thumb is not to exceed 10% deadtime according to the APTEC program. (The “deadtime” is the fraction of time that the system is processing data and is not available to record new data.)
APTEC MCA software
Our APTEC multichannel analyzer system has software for data acquisition and a wide range of analysis and display options. For example, energies and counts of gamma ray peaks should be measured using Regions-Of-Interest, NOT by reading the pointer on the screen. The bin spacings for the MCA should be such that any gamma ray peaks of interest are spread over at least 3 bins, and the full range covers the energy range of interest.
Numerical analysis of the peaks
In exceptionally fine spectrometers the peaks are essentially gaussian, though this depends on the settings of the amplifier and on the count rates. Obtaining really symmetric peaks is more difficult at high count rates. The analysis below probably underlies the APTEC data analysis, but we do not have the full internal details.
For a gaussian peak superimposed upon a continuum bi, the count in channel i will be
ci = npeakexp{-(xi-<x>)2/2s2} + bi (1)
By simple counting statistics, the fractional uncertainty in the total number of counts (ci) in a bin is simply sci = ci -0.5. If the number of background counts (bi ) is known with relative accuracy sbi, then ni =ci- bi, the net count in channel i, is known with fractional accuracy
sni ={ci+ (bi sbi)2}0.5/(ci- bi ) (2)
The best estimate of the mean energy, _x_, of the peak is readily obtained from by weighting the bin contents by the reciprocals of their squared fractional error, i.e.
<x> = Si {xi /sni2}/Si {1/sni2) (3)
It is sometimes difficult to estimate bi under a peak, but luckily small errors of judgement in estimating sbi or bi are often insignificant.
The best estimate of the gaussian width, s, is given by the root mean square of xi-_x_:
s2 = Si {(xi-<x>)2 /si2}/Si{1/si2) (4)
The best estimate of the uncertainty in <x> is given by
s<x> = s/{Si (1/si2}0.5 (5)
If the spectral peaks are not gaussian, a careful centroid analysis (equation 4) is still called for, with weighting given by equation 3. The determination of widths must be based on scientific judgement as it will depend on the line shape.
Detector Calibration
The detector must be calibrated using known gamma ray sources, for example 137Cs, 60Co, 22Na, etc. (Note: The student must not use any radioactive material without receiving instructions on their safe use from the supervising professor. ) These sources produce gamma rays at well-known and precisely measured energies. It is important to use such sources to determine the energy scale for subsequent measurements. A number of gamma rays present in the ambient room radioactivity (e.g. from 208Tl, 214Pb , 214Bi, etc) also provide convenient calibration points. A smoke detector containing 241Am can be used for a low energy calibration point. Some calibration gamma ray energies are given in Table 1; the energies and intensities of other lines can be found in the CRC Handbook of Chemistry and Physics or in the Table of Isotopes. The APTEC spectrometer software allows you to calibrate the spectrometer using up to 16 known gamma rays, and allows automatic entry of values from regions of interest into its energy calibration table.
|
Source |
Energy (KeV) |
Intensity (%) |
|
22Na |
1274.53(2) |
99.944(14) |
|
40K |
1460.830(5) |
10.66(13) |
|
60Co |
1173.237(4) 1332.501(5) |
99.90(2) 99.9820(10) |
|
133Ba |
302.853(1) 356.017(2) |
18.33(6) 62.05(19) |
|
137Cs |
661.660(3) |
85.1(2) |
|
208Tl |
583.191(2) 860.564(5) 2614.533(13) |
85.2(7) 12.53(10) 99.16 |
|
214Pb |
295.213(8) 351.921(8) |
18.5(3) 35.8(5) |
|
214Bi |
609.312(7) 1120.287(10) 1238.110(12) 1764.494(14) 2204.21(4) |
44.8(5) 14.8(2) 5.86(8) 15.36(20) 4.86(9) |
|
241Am |
26.345(1) 59.537(1) |
2.4(1) 35.9(4) |
Table 1: Energies of some calibration gamma rays from the Table of Isotopes. The number in brackets is the error on the last digit(s), e.g. 122.0614(4) = 122.0614±0.0004, or 2614.533(13) = 2614.533±0.013. Only a few gamma rays are listed here for a each isotope; more may exist.
Linearity of the spectrometer
It is essential to measure the linearity of the spectrometer in order to know how much to trust the calibration. The “integral nonlinearity” of the spectrometer is the systematic deviation from the straight-line relationship
E = A0 + A1 xg (6)
where E is the gamma energy and xg is the channel number in the spectrum corresponding to the gamma peak centroid (see Page ). Note that xg is not generally an integer. The value of A0 is usually non-zero because the analyzer has a zero offset – one of the adjustments of the analyzer.
A measurement of the integral nonlinearity can be made as follows. Three known gamma rays are chosen which are roughly equally spaced in energy. Preferably one chooses gammas which bracket the range of energies of relevance for your physics measurements, but this may not be possible. The spectrometer is calibrated using the high and low energy gamma rays of the three, and then the energy of the middle gamma is then measured. The integral nonlinearity is now defined as
|(Eg-E2)/(E3-E1)| (7)
Where E1 & E3 are the known energies of the low and high energy calibration gamma rays, and Eg is the measured energy of the middle gamma ray of known energy E2. In a modern gamma spectrometer the integral nonlinearity should not be greater than 0.07%. If your instrument is much worse than this, then you should draw this to the attention of the professor in charge.
Another way to measure the non-linearity is to calibrate your detector using a linear fit to the maximum number of gamma rays allowed by the program. The gamma rays should be well distributed over the maximum possible range of energies. The difference between the fit value and the input (true) value of every point should be less than about 0.1% of the highest energy calibration gamma. A long run on the natural room background is an easy way to get a wide range of calibration peaks, once you have identified the room background peaks.
Any significant electronic nonlinearities are most often found in the first 7% o and the last 20% of the spectrum, so it is a good idea to avoid using the highest and lowest channels.
A nonlinearity of 0.07% in the combined amplifier and ADC system can introduce systematic errors in your measurements exceeding ±1 KeV, compared to statistical uncertainties as small as ±10 eV, ro the use of a linear calibration formula can lead to systematic errors of more than 100 standard errors (statistical)! For high precision measurements of energies, one may have to use a non-linear fit, but one should then use the maximum number of calibration points possible, and the lowest order polynomial consistent with the calibration data. A nonlinear calibration can improve accuracy, but can also lead to big extrapolation errors, so only use a non-linear fit if you have to.
The energy calibration may need to be redone, and the detector settings adjusted for optimal performance, once you start working on your specific experiment. For some experiments the calibration needs only to be good enough to identify peaks, for other experiments the accuracy of your final results depend directly on the quality of your calibration and the resolution of your detector. If you are interested in specific energies, you should use calibration points as close to those energies as possible.
Efficiency
of the detector
For some experiments you may need the efficiency of the detector for specific gamma rays. This can be measured by using radioactive sources of known strength. The original activity and date of manufacture of such calibration sources are known, and the current activity can be calculated using the half-life. The efficiency depends on the gamma energy, the detector, and the geometry of the measurement. The efficiency for a specific energy gamma ray can be interpolated or extrapolated from the efficiencies for the calibration gamma rays. (Note: By combining measurements of calibrated low energy sources with measurements of an uncalibrated sources with both low and high energy gamma rays, it is sometimes possible to avoid risky extrapolations. For example, neutron activated sodium has gamma rays of equal intensity at 1.37 and 2.54 MeV.) See Leo for a further discussion and a typical germanium detector efficiency curve.
The efficiency for non-point geometries can be calculated using measurements of the point calibration sources in different positions simulating the geometry. If you cannot tell exactly where the radioactive material is located within the source holder, repeating the measurement after inverting the source allows an appropriate averaging to be made.
Some experiments using a germanium detector
You should do one of the following experiments or an equivalent experiment arranged with the supervising professor.
You should read the descriptions of all the experiments, since useful information is spread among all the descriptions.
Safety
Reminders
• Radiation safety rules must be strictly obeyed.
• Check with the supervising professor before using any radioactive material.
• No food or drink is allowed in any radiation laboratory.
• Radioactive sources should normally be shielded during use and storage, and must not be left unattended in an open room. Do not subject the sources to heat or excessive pressure, or do anything else that might damage them.
• Wear gloves when handling bare lead, and be careful not to drop it on your foot, your finger, or the equipment.
• Wash your hands with soap when you leave.
Note:You should
not do any measurement you have done as part of a previous lab. For example, if
you have done the Germanium Spectrometer experiment in the second year lab, it
may not be appropriate to do Experiments F or G here. Check with the
supervising professor .
A. . Observation of deuteron formation by neutron-proton strong interactions
This experiment studies the binding of neutrons to protons by the strong nuclear force forming deuterons. The deuteron weighs less than the sum of its proton-neutron constituents, and the energy is released on formation by a single gamma ray.
The initial hydrogen target should be paraffin wax, which is basically carbon and hydrogen. A special intense radioactive source provides the neutrons (see Experiment B). The source, the target, and the detector should be arranged in an “L” shape and shielded such that the source does not directly irradiate the Ge detector or the student (i.e. you), but the neutrons can reach the target and gamma rays from the target can reach the detector. (Note that gamma rays interacting in the lead shielding can produce lead X-rays which can be observed.) The number of gamma rays produced is not large, so to see the signal you will want a lot of hydrogen and good shielding to reduce the very large gamma ray background produced by the neutron source. The experiment is best done with the large horizontal axial Ge detector.
The basic technique is to look for gamma rays which only appear when the target is present. Such gamma rays are most likely produced by neutron interactions in the target. Since the target is not pure hydrogen, it is necessary to also take data with a second target which contains hydrogen but not carbon, e.g. water. The gamma ray which is observed with both targets but not without a target is presumably from deuteron formation. The energy released in deuteron formation should be measured with the best accuracy possible. Taylor, Neff, & King give an example of a previous Toronto precision measurement.
A possible extension or variation of this experiment is to look for gamma rays produced by neutron capture by other nuclei. (If you used paraffin and water, you already have data in which you can look for carbon and oxygen capture. If you want to irradiate uranium, look at Experiment G.2.) Gamma rays will be produced if the capture of the neutron leaves the final state nucleus in an excited state; the excited state then decays to the ground state by emitting gamma rays. Gamma rays may also be produced if the final state nucleus is unstable and decays by beta or alpha emission. Such prompt neutron capture gamma rays have energies up to 10 MeV, e.g. 4443.0, 4710.2, 6759.3, and 7004.1 KeV for boron (e.g. in borax). You can increase the number of thermal neutrons by surrounding the source and target with a moderator such as paraffin. You should identify the nuclear transitions producing any gamma rays you observe. If you don’t see anything, quote an upper limit on prompt gamma production per nucleus compared to the rate for deuteron formation gammas from water in the same geometry and gamma energy.
B. The neutron source: Interactions, Excitations, and Decays
The portable neutron source is a powdered mixture of a heavy alpha emitter and a light target element. This mixture is permanently sealed inside a brass canister to stop the alphas, betas, and many of the photons produced, but most neutrons are not stopped. Even with the brass shielding, the source is still relatively intense, so make sure it is properly shielded with lead when using it or when it is temporarily on a desk in the lab.[3] The brass canister is pretty solid, but don’t drop it or try to open it.
Measure the gamma spectrum of the source, and identify the processes and excited states inside the source. The goal is to understand every peak in your spectrum. e.g. What are the isotopes? What decays and interactions are occurring? What excited states are involved? Draw any interaction and decay chains. You may see gammas produced by interactions in the brass or lead shielding.
Note: The portable neutron source to be used is the brass canister in the source cabinet, NOT the stronger source in the neutron bath used for neutron activation (see Experiment E). NEVER touch the source in the neutron bath.
C. Beta decay of 90Sr and the mass of the neutrino
In nuclear beta decays, the weak interaction transforms either an up quark into a down quark with the emission of a positron and an electron anti-neutrino, or a down quark into an up quark with the emission of an electron and an electron neutrino. Since the quarks are inside nucleons, this either transforms a proton into a neutron or vice versa. In this experiment the goal is to measure and understand the beta spectrum of Strontium-90, and to use this spectrum to set an upper limit on the mass of the electron neutrino. Current evidence suggests that at least some neutrinos have non-zero mass, e.g. see www.hep.anl.gov/NDK/Hypertext/nu_industry.html
This measurement should be done with the small, thin-windowed, planar Ge detector, so the electron does not lose too much energy before reaching the germanium. (The red plastic cover should be removed for measurements, but DO NOT TOUCH THE VERY THIN BERYLLIUM WINDOW. It is toxic, easy to break, and very expensive to fix.)
The energy spectrum should be measured for a thin walled Strontium-90 (90Sr) source and a Kurie plot made (see, for example, Perkins or Frauenfelder & Henley). Explain the shape of your spectrum. (Note: Any radioactive atom will keep on decaying until it reaches a stable isotope, so make sure you include all decays that occur.)
Set the best possible limit on the mass of the electron anti-neutrino by studying the beta spectrum near the endpoint (see, for example, Kofoed-Hansen or Robertson & Knapp). In order to do this analysis, you may need to transfer your data to another computer and use a spreadsheet or other mathematical analysis program.) Since the betas have to pass through the source container and the beryllium window, you may want to consider if the energy loss of electrons in matter may affect your conclusions (See Experiment D).
D. Energy loss of electrons in matter and thickness of thin films
Ionization energy loss is the primary mechanism underlying most particle physics detectors. (See, for example, our “High Energy Physics” experiment. )
The ionization energy loss of electrons can be measured by measuring the shift in the energy spectrum observed when thin sheets of material are placed between a 90Sr source and the planar detector. (Note: Read the cautions about the planar detector described in Experiment C - NEVER TOUCH THE BERYLLIUM WINDOW.) Thin sheets of aluminum, lead, various plastics, and other materials may be used. The Aptec software allows normalization and subtraction of different spectra. You should investigate how the energy loss depends on the electron energy and the type of material. Energy losses should be given in the standard units of MeV/gm/cm2. Are your results consistent with the Bethe-Bloch energy loss equation? (See, for example, Leo, Perkins, or Frauenfelder & Henley) You may need to consider the effects of multiple scattering or bremsstrahlung.
Energy loss, absorption, or scattering of alpha, beta, or gamma radiation are the basis for a wide range of gauges ranging from $10 home smoke detectors to $105 industrial thickness gauges. Now that you understand energy loss in matter, an interesting possible extension would be to measure the thickness of a piece of paper.[4] Devise and demonstrate the best scheme you can to measure the thickness of a typical piece of paper or similar material. Your scheme may not be very accurate or fast using our low intensity sources, but industrial thickness gauges use much more intense sources (e.g. 100 mCi) which improve any method and allow low rate techniques such as backscattering. A final production device using your scheme will be less expensive and more compact if it does not require high energy resolution and fancy analysis. e.g. A method that just depends on one or two count rates, with possible upper and lower energy thresholds. You can use a source (e.g. 22Na ) with a lower beta energy than 90Sr, although 90Sr has the advantage of having no gamma rays. Another possibility is to degrade the energy of the 90Sr electrons using an absorber. Make sure to measure the thickness of the paper, and to report the accuracy of your method.
E. Neutron activation analysis of materials
When thermal neutrons are captured by a nucleus, the new nucleus may be radioactive. If the new nucleus produces gamma rays when it decays, the original nucleus can be identified. Since gamma rays penetrate significant thicknesses of matter and they can be easily identified, neutron activation analysis is a powerful tool for materials analysis.
The goal of this experiment is to measure the composition of several materials. You should try both known and unknown samples. Not all elements can be identified using neutron activation, . Samples are irradiated in our neutron bath in the radioactive source room. Any activation gamma rays are best detected using an axial detector. Once the elements are identified, it is best to irradiate known samples of these elements to determine the sensitivity. If known samples are not available, you can calculate the needed efficiencies by measuring the detectors absolute efficiency and using known branching ratios.The composition of the samples should be measured with the best precision possible.
Before choosing your samples, it is a good idea to look at Erdtmann’s “Neutron Activation Tables” to get a feeling for what elements can be easily detected Do not irradiate anything you want back, since the samples will become very, very mildly radioactive. Samples should normally be small enough to fit in the end of the long plastic sample holders which can be inserted in the 4 irradiation slots.
Past samples studied have included stainless steel, coins, artist’s pigments, solder, clay, fruit seeds, teeth, small stones, ... . If you are looking for something specific, e.g. arsenic in fruit seeds, you should report an quantitative upper limit if you do not see the target element.
A useful compositional study is that of the antimonial (Sb) content of commercial lead. In the experiment “Measurement of the Compton total cross section” lead absorbers are used to study gamma ray absorption, but the Sb content of the lead is unknown. Lead is essentially invisible to neutron activation, so detectable impurities such as antimony can be seen with little background. (The reverse problem, detecting lead impurities in lighter elements, is easily done in the “X-ray Fluorescence” experiment.)
F. Radioactivity in the air.
Most atmospheric radioactivity is due to natural radon gas, but nuclear accidents anywhere in the world can produce observable radiation[5]. The radon level at any location depends on the amount of naturally occurring uranium and thorium in the local rocks and soil (see “Natural Radioactivity” in References), and on the local air flow. Radon levels in buildings (especially basements) vary by up to 5 orders of magnitude. The shortlived radon decay products are in secular equilibrium (see Chapter 1 of Leo or any book on radioactive dating).
This experiment involves filtering atmospheric air using an air blower (available from the first year lab wicket in room 126). A bit of thought about alpha or beta decays should convince you that radioactive decays will usually result in a charged ion, not a neutral atom. Such ions in the air will typically attach themselves to a dust particle, so by filtering the dust out of the air, a measure of the radioactivity can be made. (See, for example, Whyte and Taylor.)
Barring nuclear accidents, the observed radioactivity on the filter paper will be very similar to the natural room background radioactivity[6], so careful background shielding and monitoring is necessary. A background spectrum of at least 24 hours duration should be taken and all peaks in it should be understood.
The blower is usually hung outside from a window in the first year lab. The results, both amount and type of radioactivity, generally depend on the length of time for filtration, and on the weather conditions on a given day. As a comparison, you should also run the blower in a basement lab (consult the supervising professo for a good spot) or other interesting location, e.g. your home Do the radon levels differ? Are the different isotopes in the same ratios?
You will want to have run the blower about an hour, but the optimum time depends on the lifetimes of the radioactive isotopes observed. To see the short lived isotopes, your counting equipment should be ready to receive the sample when you turn off the sampler so that you minimize the time taken from when air sampling stops to when counting begins. All time intervals must be measured and your final results corrected for the finite lifetime of the observed isotopes. You should report the activity (Bq/m3) of the air for any isotopes observed.
G. Uranium
A plastic presentation case with Ontario uranium ore and uranium oxide powder is available. (Use only this sealed source; radioactive powder is dangerous if breathed in.)
Measure and explain the gamma spectra of the uranium ore and the uranium oxide. An axial detector is probably better, although some of the gammas are quite low energy. Can you estimate the percentage of uranium in the piece of ore? Can you measure both U235 and U238?
Try one of the following:
(1) Pitchblend
Compare the Ontario ore with the piece of Bohemian pitchblend. (This piece is fairly radioactive; leave it in the taped up glass fronted box and take care not to drop it.)
(2) MicroCandu?
Nuclear reactors work because neutrons can induce fission of uranium, so it may be interesting to measure the gamma spectrum of the uranium oxide when it is being irradiated by our portable neutron source. (See Experiment A for an explanation of how to arrange the source, target, and detector.) Use paraffin as a moderator. Do the neutrons have any observable effect, or do we have too little uranium and too few neutrons?
(3) Radioactive Dinner
Currently the most common radioactive consumer products are smoke detectors, but in the past, uranium was commonly used to make bright orange glazes for ceramics. We have several plates purchased before such glazes were banned. Measure the radioactivity of a plate and calculate the amount of uranium in the plate. (Please do not drop the plates.)
Estimate the annual gamma[7] dose received from the plate by someone who used the plate every day. The dose from gamma rays can be estimated from the formula:
D = 2 A*E/r2 (8)
where
D = Dose Rate (in µSv/hr)
A = the activity of the source (in MBq)
E = the total gamma energy emitted per disintegration (in MeV)
r = the distance from the source in metres
Note: To convert to traditional units (rem, Ci) to SI radiation units(Sv, Bq), use 1 Sievert (Sv)= 100 rem and 3.7 ´ 1010 Bequerels (Bq) = 1 Curie (Ci). Typical doses from natural radiation are a 1 or 2 mSv/year, but a few places have a natural background over 10 mSv/year.
The alpha and beta radiation from the plates is probably more dangerous than the gamma radiation since this radiation is mostly deposited internally from uranium leached out of the glaze by acidic foods and then eaten. The alpha and beta dose depends on the unknown leaching rate and is hard to calculate. It is not safe to try to measure the leaching rate.
H. Semiconductor detector physics
Semiconductor detectors are important for measuring both the energy and the positions of subatomic particles. Germanium and silicon detectors are the highest resolution calorimeters used in nuclear physics, and almost all high energy physics collider experiments have silicon vertex detectors. Continuing research includes room temperature operation (e.g. See Dusi, Perillo, &Siffert ) and radiation hard semiconductors such as diamond (e.g. W. Trischuk studies this in our department, see Borchelt et al.)
The observed width of a gamma ray peak comes from three sources:
(1) The natural line width, Gnat=S/t where t is the mean life of the state from which the radiation is emitted. For a mean life of 10-17 s, Gnat » 120 eV FWHM[8].
(2) Noise in the preamplifier and other electronics contributes a constant line broadening Gnoise which should be independent of energy.
(3) Counting statistics of electron-hole production in the semiconductor. It takes an average energy of e _ 2.96 eV to produce an electron-hole pair in a germanium crystal. The number of electron-hole pairs produced when a gamma ray is absorbed is
n=Eg / e (9)
and the standard deviation is
sstat = F (sn / n) Eg = F n–0.5 Eg = F (Eg e)0.5 (10)
Where the “Fano factor” F is a constant which corrects for the fact than e is only an average energy, and the correct quantum statistics are a too subtle to be easily calculated and must be measured. The Ge crystal typically contributes a full width at half maximum of very roughly
GGe = 1.3 Eg0.5 keV (11)
The total width is the quadratic sum of these contributions :
G2 = GGe2 + Gnoise2+ Gnat2 (12)
Gnat is usually small and can be neglected, so a plot of G2 against E should give F e0.5 and Gnoise.
Measure the gamma peak energy resolution as function of energy for either an axial or planar detector. What are F e0.5 and Gnoise. for your detector?
Measure the central value and width for several gamma rates at high and low rates. Are the central values or widths affected by the rate?
Measure the resolution, the calibration factor in channels/eV, and the efficiency for different voltages from almost zero up to the maximum allowed. What is the optimum voltage?
Measure
the efficiency for your detector as a function of energy when the source is
flush with the centre of the front face of the detector. (This maximizes the
geometrical acceptance of the detector.) If the count rate is too high for some
of your calibration sources, move the source back and use a weaker source to
measure the geometrical scaling factor.
References
F. Borchelt, et al., “First Measurements with a Diamond Microstrip Detector”, Nuclear Instruments and Methods A354 (1995) 318-327.
CRC Handbook of Chemistry and Physics, CRC Press. Yearly editions exist; the 68th edition was used for this writeup.
W. Dusi, E. Perillo, P. Siffert, (eds.), Proceedings of the 7th International Workshop on “Room Temperature Semiconductor X-Ray and Gamma Ray Detectors and Associated Electronics”, Ravello, Italy, September 23-28, 1991, published in Nuclear Instruments and Methods A322 (1992) 313-665.
G. Erdtmann, “Neutron Activation Tables”, Verlag Chemie (1976) QD/606/E7.
H. Fauenfelder, and Ernest M. Henley, “Subatomic Physics”, 2nd ed., Prentice Hall (1991) QC776.F723.
O. Kofoed-Hansen, “Maximum b Energies and the Mass of the Neutrino”, Physical Review 71 (1947) 451-452.
W.R. Leo, “Techniques for Nuclear and Particle Physics Experiments”, Springer-Verlag (1994 ) QC 793 .46 L46.
“Natural Radioactivity” at http://www.sph.umich.edu/group/eih/UMSCHPS/natural.htm
D. H. Perkins, “Introduction to High Energy Physics”, Adison-Wesley (1987) QC 793 .2 P47.
“Review of Particle Physics,” C. Caso et al, The European Physical Journal C3 (1998) 1. A World Wide Web version can be found at http://pdg.lbl.gov/.
R.G.H. Robertson & D.A. Knapp, “Direct Measurements of Neutrino Mass”, Annual Review of Nuclear and Particle Science 38 (1988) 185-215. QC 770 A52 v.38.