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Junior Physics Laboratory
Particle Counting Methods
Counting of individual particles is common in nuclear and high energy physics, and increasingly important for other areas such as atomic physics. Here we consider some devices capable of detecting particles and the electronics used to process their output.
A. Detectors As the name implies, particle detectors are devices used to sense the presence and perhaps energy of incident particles, including photons. Many physical phenomena have been harnessed for this job, including the photoelectric effect, Compton scattering, nuclear reactions, photochemical reactions, bubble nucleation and etching of damage tracks. Each method has some combination of characteristics to recommend it, but detectors which produce electrical outputs have proven most flexible and are the most commonly used. After mentioning some general considerations, we will examine two electronic detectors in more detail. Electronic detectors generally signal the arrival of a particle by producing a pulse of voltage or current in response to the energy deposited by the particle. Several parameters are needed to characterize the detector response for a particular application. These include: Sensitivity: Whether or not the device can detect the desired particle. This may depend on size, noise levels and other factors as well as the basic detection method. Efficiency: The fraction of the incident particles that are actually counted. Response function: The relation between energy input and pulse output. In some cases the pulse height or area may increase linearly with deposited energy. Other devices produce the same pulse for any particle they detect. Energy resolution: The range of pulse strengths observed for a monoenergetic input beam, usually expressed as a fraction of the average. Response time: How long the detector requires to produce an output after the arrival of a particle. Dead time: How long the detector is unresponsive after the arrival of a particle. This is usually only an approximation, since the recovery is often smoothly time-dependent, rather than all-or-nothing. Typical values of these parameters are given in Table II for some common detectors.
- Ionization detectors The first group of detectors we want to examine is the ionization devices. These exploit the fact that charged particles and energetic photons create electron-ion pairs when passing through matter. In the presence of an electric field the pairs can be separated and made to induce a current in an external circuit. The working medium can be a gas, a semiconductor or, rarely, a liquid. Figure 1 shows two typical designs. The coaxial geometry is used for single counters, of the sort used in radiation monitoring instruments. The multi-wire geometry is employed when it is desirable to know where the particle hit the detector. An amplifier is connected to each wire, and the amount of charge collected is measured. By finding the wires with the maximum charge, one can localize the hit. Two such planes, with wires at right angles, give both coordinates. Ionization counters can be operated in several modes, as indicated in Fig. 2. At very low applied voltages the pairs recombine before they can be collected. Raising the voltage separates the pairs so they can be collected, making the collected charge exactly equal to that produced by the particle. In the proportional mode, the electrons are accelerated sufficiently to ionize some additional gas atoms. The collected charge is still proportional to the initial number of pairs, but larger by a factor of 10^4 - 10^6. Pushing the voltage still higher takes the device into the Geiger- Mueller region. The electrons gain enough energy to start a cascade of further ionization near the wire which must be quenched by molecular gases that can scavenge excess electrons. The
Table II. Summary of Detector Characteristics
Ionization Scintillation Charac. G-M Prop. Semicon. NaI:Tl Plastic Response Fixed Linear Linear Linear Linear Resolution None 10-15% 0.2-0.3% 5-10% 15-20% Time res. 100μs 30-50ns 100ns 100ns 1-2ns Dead time 300μs 100ns 1-10μs 1μs 10ns Effic. , >90% >90% ~100% ~100% ~100% MeV 1-2% 1-2% 20-80% 30-100% 5-15% keV ~10% ~10% 100% Low Low
cathode
anode
+ V
signal
thin end window
incident particle cathode planes
anode sense wires Fig. 1 Typical gas-filled ionization counter geometries
Table II. Because of their higher density the semiconductor detectors are better for gammas, which cause less ionization per unit distance than charged particles. Also, less energy is required to create an ion-electron pair in the semiconductor than in gas, so far more pairs are created, resulting in less statistical uncertainty in the pulse strength. Against these advantages, semiconductor detectors are necessarily much smaller than MWPCs, are not usually position sensitive, and are much more costly.
- Scintillation counters Scintillation counters constitute the other major class of particle detectors. In a scintillating material the incident particles excite some atoms to emit light, usually visible or near UV. The light was originally detected visually, as in the original Rutherford experiments, but electronic devices are now used. A common arrangement is shown in Fig.4. The scintillator is optically bonded to a light guide which conveys the light to a photomultiplier tube (PMT). The entire assembly is, of course, shielded to eliminate outside light. The light guide is used when it is necessary to locate the tube in a more favorable area, perhaps away from a large magnetic field or excessive temperature. Conversion of the weak burst of scintillation photons to a strong electrical signal is done by the PMT. A typical structure is shown in Fig. 4. An applied voltage of 1-2kV is divided so that the potential between adjacent dynodes is 50-100V, increasing from the negative cathode end to the anode output. Photons incident on the front plate cause emission of electrons (photoelectric effect) from the cathode. These electrons are accelerated to the closest dynode, where their impact releases additional electrons. This process is repeated at each of the 12- dynode stages in the tube, resulting in a pulse of 10^6 -10 7 electrons per incident photon at the anode. Very little noise is added in the process, so it is often possible to detect individual photons incident at the photocathode surface. Obviously, such a sensitive device should never see daylight when the high voltage is on. Efficiency for the desired radiation, timing characteristics, and cost usually dominate the choice of scintillator material. For example, plastic materials have good charged-particle
light PMT (^) base scintillator guide
cathode (^) dynodes anode Fig. 4 Schematic of a scintillator crystal coupled to a photomultiplier tube
efficiency, are fast, cheap and very easy to fabricate in large dimensions. Thallium-doped sodium iodide is a much better choice for gamma spectroscopy, but it is relatively slow so count rates are limited and it is hygroscopic so it must be carefully sealed. Bismuth germanium oxide is a good gamma counter with fewer problems, except that it costs an order of magnitude more than sodium iodide. The parameters in Table II provide some guidance in selecting a detector, but it must be realized that those are typical values only. The size and shape of the detector itself, and the electronics it drives may have major effects. Other characteristics may be important also. For example, germanium and sodium iodide have vastly different energy resolutions for gamma radiation, but also different low-energy backgrounds. Referring to Fig. 5, we see that sodium iodide has many more low-energy events. These are caused by photons which lose some energy through Compton scattering but then escape the crystal. In contrast, the photoelectric effect is much more likely in germanium, causing the incident photon to lose all its energy within the sensitive volume. This means that low-energy peaks would be clearly visible in a germanium counter, while they might be lost in a sodium iodide device even if the energy resolution is adequate.
B. Pulse Instrumentation The detector produces a pulse which contains, in general, both energy and time of occurrence information. This information will be analyzed by subsequent instruments to produce the physics data of interest. A number of different operations are commonly performed, the most important of which will be summarized here. The first decision to be made is whether to keep the energy information, select pulses
0 1000 2000 3000 4000 Channel
Ge
NaI
Counts [x10 ]
3
0
2
4
6
Fig. 5 Gamma spectra recorded with NaI and Ge detectors. The source is 60 Co, which produces two mono-energetic gamma rays.
Time to Amplitude Converter (TAC) or Time to Digital Converter (TDC): Devices to convert the time interval between two logic pulses to a pulse amplitude or directly to a digitized value. With the TAC a subsequent ADC converts the amplitude to digital form. The TDC is usable for intervals down to a few nanoseconds, while TACs may have picosecond resolution. Large-scale experiments may implement the required functions with computer-derived chips in a dedicated instrument. For typical laboratory work, however, it is more common to wire together general purpose modules to perform the desired operations. Nuclear Instrument Modules (NIM) are standardized units which obtain power and mechanical support by plugging into a NIM bin. As indicated in Table I, they provide for both slow and fast logical outputs, so they are quite flexible. Fast inputs provide proper termination for cables, so the user can generally just patch together the desired circuit without further fuss. For computer acquisition, the CAMAC and FASTBUS standards provide a convenient interface. Although not used in this lab, both are common in mid-scale experiments that do not require dedicated acquisition hardware. As an example of the use of pulse instrumentation, consider a scheme for measuring the lifetime of a muon at rest. These particles decay according to
μ +^ e +^ + μ + (^) e (1)
with a life of 2.2μs in their rest frame. Muons are produced in cosmic rays and as secondary particles at proton accelerators. They can be stopped in solid targets, from which the emitted decay positron readily escapes. To carry out the measurement we use an array of five counters, as shown in Fig. 6. Detectors A , B and C determine whether or not the incoming muon stopped in the target, as in our previous example. Counters E1 and E2 , safely outside the beam, count the
del
TAC MCA
START
STOP
veto
D
D
D
D
D
del
del
del
del
del
A
B
C
E
E
A B
C
E
E
Fig. 6 Counter geometry and logic for the muon decay experiment
decay positrons. All the detectors are plastic scintillator, since we want good time resolution and are not particularly concerned with energy information. We measure the time to decay by starting a TAC when the muon arrives, and stopping it when the decay positron appears. The output pulse from the TAC, with amplitude proportional to the individual lifetime, can be histogrammed in a MCA. Between the actual detectors and the TAC, we need logic to obtain the start and stop conditions, according to
START = A • B • C • E 1 • E 2 STOP = E 1 + E 2
The required logic is also shown in Fig. 6. Signals from each counter are first brought through delay lines, to compensate for different response times or cable lengths. Discriminators convert the detector pulses to logic pulses, eliminating small noise inputs in the process. From there the signals go to majority logic modules, configured as OR and AND (with veto on the AND). Note the use of DeMorgan's law to simplify the start condition. The stop signal is deliberately delayed, so that decays at very short time do not produce near-zero amplitude pulses that might be obscured by MCA noise. The output of this system is shown in Fig. 7. The exponential decay in the number of counts at increasing times (channel number) is clearly visible, as are the statistical fluctuations in the counts. At long times the plot flattens out at the background level.
Log counts
Channel Fig. 7 Spectrum of muon decay times. The exponential decay appears as a straight line on this semi-logarithmic plot
