How To Count A Gamma Ray Photon

Transcription

1 Chapter 7 Photon Counting and Spectroscopy in the Gamma Ray Energy Range 7.1 Objective Determine whether a radioactive source or set of sources obey Poisson statistics, and whether the radiation is isotropic. 7.2 Background Introduction A gamma ray photon can be emitted in an energy level transition in an atomic nucleus, a process which is usually referred to as radioactive decay. The energy level separations are very large so the photon is very energetic, with a typical energy on the order of 1 MeV or so compared to a few ev for visible photons. The radiation is usually isotropic, so that I 1 r 2 where I is the intensity of radiation and r is the distance from the source. The emission is a quantum mechanical process governed by statistical laws with which we can predict the behaviour of a large number of radioactive nuclei, but individual decays are randomly distributed in time. The

2 Photon Counting and Spectroscopy in the Gamma Ray Energy 7-2 Range separation of nuclear energy levels are unique to each nucleus (similar to the atomic energy levels which electrons occupy) and so the energy of the photon or photons released can be used to identify the nucleus which emitted it Detection Any photon detection system must rely on a physical interaction between the photon and the detector. In the gamma ray energy range, the probability of interaction per unit length is orders of magnitude lower than in the visible range, and the detection is done through three major processes: the photoelectric effect, the Compton effect and pair production. With a suitable material, the energy transferred to the electron involved in these processes can be measured. Our main interest is in the photoelectric effect since, in this interaction, all of the energy of the photon is deposited in the detector (there is not a range of possible energies as with the Compton effect). In our case, the detector is an insulating crystal of NaI (sodium iodide) doped with thallium atoms. This material will scintillate when one of the interactions mentioned above occurs in it releasing an energetic electron. The energy of the electron is dispersed in collisional processes which result in the emission of visible photons (these are the scintillations). One of these photons can be easily detected by a photomultiplier tube which is an evacuated tube with a phosphor coated window at one end which gives off an electron when hit by a photon (a TV set in reverse). This electron is accelerated in a large electric field through several stages, at each of which more electrons are released by collisions with metal accelerating plates (secondary electron emission at dynodes). At the final stage (anode) there should be enough electrons to be detectable as a current pulse, or as a voltage rise of a few microvolts on a capacitor. This pulse is amplified and the pulses can then be counted. Normally, the various scintillation photons from one gamma ray photon arrive at the phosphor within such a short time that they appear as part of one pulse. The size of the pulse (voltage) is determined by: 1. the energy of the gamma ray photon 2. the energy of the electron released in the scintillator crystal

3 7.2 Background the number of electrons in a cascade of electrons released by collisions with the first one 4. the number of scintillation photons produced (some of which impinge on the phosphor of the photomultiplier tube) 5. the number of primary electrons that are accelerated into the photomultiplier tube 6. the number of electrons which finally reach the anode of the photomultiplier tube 7. the size of the voltage pulse that is measured on a capacitor From this point on, the pulse is amplified in a pre amplifier, amplified again (and re shaped) in a main amplifier, electronically evaluated to measure its maximum height in an Analog to Digital Converter (ADC) and categorized and counted by a Multi Channel Analyser (MCA). Finally, the results of this process are displayed as a frequency distribution of pulse heights. It should come as no surprise that there is a fairly large uncertainty in the measurement of the energy of a gamma ray photon. The uncertainty is mainly random, however, so we can improve the measurement by doing the experiment several times. With the electronic system provided, only a short time is required to measure the energy of a few million photons. This will (at least for the photoelectric effect) produce a peak in the energy spectrum whose centroid (the mean of the energy distribution) is the best estimate of the energy of the detected photons and whose width (usually called the energy resolution of the system) indicates the size of the random variations in the signal processing chain described above. The upper limit of the energy distribution of a photon which undergoes a Compton interaction is smeared out for the same reason, and the position of the Compton edge in the energy spectrum is halfway up to the ledge that forms the Compton plateau.

4 Photon Counting and Spectroscopy in the Gamma Ray Energy 7-4 Range Start up Turn on the power switch on the right side of the nuclear instrumentation power supply and module cage (known in technotalk as a NIM bin). The detailed setting on the modules will already have been made for you and only a few changes will be required as you go along. You will have to turn on the power to the high voltage power supply separately, although it is located in the NIM bin also. The nearby cylindrical object is a housing containing a NaI(Tl) scintillator crystal, a photomultiplier tube, and a preamplifier. The connections to this detector are a high voltage line (use great care in handling or, better yet, do not move it at all) and a signal output. The signal runs to an amplifier where it is processed and then to the ADC. It is then fed to the MCA card in the PC and accessed by the Windows based program MCA.EXE in the directory S100. The sophistication of this system requires some training, so be prepared to take notes Pulse Counting The voltage pulses that are produced by the photomultiplier tube must be discharged through a resistor to allow the next pulse to be differentiated from the first. A trade off in time constant is made here between 1. the requirement for fast discharge so that pulses that are close together in time can be measured as separate pulses and 2. the requirement for large voltage signals so that pulse detection is easier and the pulse height has a larger dynamic range Counting Statistics Each measurement of radioactive decay counts is independent of all other such measurements because radioactive decay is a random process. However, for a large number of individual measurements, the count rates follow the Poisson statistical distribution with a well defined mean value and standard deviation. This is a special case of the binomial distribution where a simplification is achieved because the probability of success (decay of one radioactive nucleus) is very small. The mean value is found in the usual way,

5 7.2 Background 7-5 and the standard deviation is the square root of the mean. mean = variance = µ P (x, µ) = µx e µ x! This expression gives the Poisson probability that x events (counts) will be observed in a given time interval. Hint: To compare the observed and expected values, you will have to look up information on the standard error of the standard deviation in a statistics textbook Isotropy The intensity of isotropic radiation decreases with the square of the distance from the source. The mathematical expression for the count rate dependence for an isotropic source is given by I = I 0 4πr 2 where I is the intensity at a separation of r and I 0 is the total count rate. (Note that this is strictly only valid when the background radiation can be neglected. Also, due to the geometry of the detector, the effective source detector distance may be different than the measured source detector distance.)