X-RAY AND GAMMA RAY SPECTRA

Transcription

1 Experiment N3 X-RAY AND GAMMA RAY SPECTRA References: Handbook of Chemistry and Physics Nuclear Level Schemes, A=45 Through A=257, QC795.8.E5.N8 Background: As in case of atomic physics, much of what we know about the structure of nuclei is the result of studying the energy levels of their excited states. Here again energy levels cannot be measured directly but must be inferred from measurements of the differences in levels, either while energy is being absorbed or while it is being emitted. Nuclear energy levels, of the order of MeV rather than ev, require different experimental techniques. This being the case, you will use a long lived radioactive nucleus to produce a nucleus that is in an excited state. You will use a scintillation counter to measure the energies of photons radiated as that nucleus goes from the excited state to a lower energy level. These photon energies are determined by measuring the pulse heights, i.e., the peak voltage of the pulses produced, when the photon is absorbed in the scintillating material. To a good approximation the photon energy is proportional to the peak pulse height. A pulse height analyzer is used to measure the height of each pulse and keep track of the number of pulses of each pulse height detected. A complication of this type of spectroscopy is that photons with a single energy produce a rather complicated pulse height distribution, one that can be easily mistaken for a distribution with several different photon energies. This is because they are detected using several different mechanisms that can occur in the scintillator; the photoelectric effect, Compton scattering, and possibly pair production. The analysis becomes especially challenging when more than one photon energy is involved. We are helped in this to a certain extent since the nuclei produced by the beta decay of the long lived precursor are not usually left in highly excited states, so only one or two of the lowest energy levels are excited. (This is quite different from the case of atomic excitations in a discharge tube, for example.) The most prominent feature of a photon's pulse-height-distribution is the photopeak. This occurs when the photon has lost all of its energy in the detector, usually through a photoelectric interaction where the energy is transferred to an electron and the electron subsequently transfers its energy to the scintillator. Unfortunately, though the pulse heights that produce the photopeaks are proportional to the photon energy, we do not know the constant of proportionality. We will use a calibration procedure that depends on our use of a source that radiates at least one photon of known energy. Cesium-137 is commonly used for this purpose. It has a convenient 662 KeV photon. Object: The point of the experiment will be to record the pulse height spectra for several radioactive sources, analyze them to determine the energy of the photons being detected, and to make suggestions as to the nuclear energy levels in the nucleus or atomic energy levels that 1

2 could give rise to them. The Radioactive Sources: Radioactive decay, leading to the emission of photons, can proceed along several lines. The process usually begins with a weak interaction, since only the weak interactions are likely to have long enough half-lives to be convenient for us to use. Weak interactions can result in electron emission, positron emission, or electron capture as suggested by the following processes: -1 (1) Α Α + β + ν + Q (2) Α Α + β + ν + Q (3) Α + e Α + β + ν + Q 1 Here we have used A to represent the chemical symbol for a nucleus containing Z protons and N neutrons. A neutrino is symbolized by ν. Q is the energy of the reaction that is shared by all of the resulting particles. All decays will eventually end with the product nucleus in its ground state, but any one of these interactions can result in the product nucleus being in an excited state. The latter are the ones of interest to us as they tend to radiate photons, typically within seconds after the initiating weak interaction. Q is the energy difference between the original nucleus and the resulting nucleus in whatever energy level in which it ends up. Both process (1) and (2) result in three particles that share the energy of the reaction Q. This means that neither the β + nor the β - are monochromatic. They may end with nearly the entire energy Q, but on the average they will have somewhat less than half of the energy Q. The β + formed in process (2) will come to rest, find an electron and annihilate it. The result is two photons, each carrying the rest mass of an electron, 0.51 MeV. X-Rays from the Atoms: Several mechanisms may result in electrons being removed from the inner shells of either the parent or the product nucleus. When electrons return to fill these levels, X-rays may be produced. For higher Z nuclei they may be several KeV in energy, comparable to the photons from the nucleus which are commonly referred to as Gamma-rays. One such mechanism occurs when the product nuclei lose energy by transferring it to an atomic electron. The reaction goes as follows: (4) Α Α + e + Q This is called internal conversion. It appears as though it might be the result of an interaction between a gamma ray, produced through the normal photon emission process, which undergoes the photoelectric effect with an atomic electron before it gets out of the atom. However, 2

3 theoretical calculations show that this reaction is actually an additional process by which the excited nucleus can go to a lower state. The internal conversion coefficient is the ratio of the number of electrons from process (4) to the number of photons actually emitted by the nucleus. This ratio is generally low, but it can become quite large. You should note that electrons from process (1) differ from those of process (4) in that the latter will be monochromatic and the former are not (because there are three particles to share the energy). Note is that both processes (3) and (4) remove an atomic electron from the atom. These are usually the innermost, K-shell electrons. Thus, you should expect also to find X-rays emitted as the outer electrons fall into the vacancy. That is, the new atoms formed by the initial decay have themselves to return to a ground state. Generally the rearrangement will produce many low energy photons, but there may be these occasional high energy X-rays. Finally, you should also take note of the fact that the high energy photons that we have been discussing may also interact with other atoms near the detector. This may result in the removal of their inner electrons. These will result in X-rays with energies characteristic of the atoms involved, of course. The Scintillation Counter: As noted above, the scintillation counter produces voltage pulses (duration of about one microsecond) whose height can be used to determine the energy of Gamma-rays. A pulse-height analyzer is used to measure this pulse height and store that information digitally in memory. Individual memory locations keep a count of the number of pulses detected that fell within a small voltage interval between V and V+ V. In the terminology of the pulse-height analyzer we say that there are a number of channels, where the number of the channel is proportional to the pulse height V, and the number stored in each channel is the number if pulses that have been counted that fell within that interval from V to V+ V. The analyzers constantly update the display of the information collected with a plot of the number of counts per channel as a function of the number of the channel. We have three pulse-height analyzers in the laboratory, a RIDL (Radiation Instrument Development Laboratory, ca 1965), a TRACOR-NORTHERN TN-1705 (ca 1978), and an ORTEC plug-in for a PC (ca 1990). The first analyzer, entirely of discrete transistors cost about $12,000. The second, using integrated circuits and housed in a module that slips into a Tektronix scope, cost about $3000. The plug-in unit cost about $1500 (exclusive of the PC). In each case the number of storage channels increased and the flexibility of the instrument increased. Details of the operation of these analyzers are provided on supplementary sheets. All of these analyzers can use the same sodium iodide scintillator. It is perhaps useful to describe in more detail just how the scintillator works. The photons transfer all or part of their energy to the scintillator, mostly sodium iodide. Let us assume that the photon has transferred an energy of 1200 KeV. This energy propagates through the crystal and some of it finds a thallium impurity, raising it to an excited state. When it falls back to its ground state, this impurity atom emits photons of visible light. The process is quite inefficient, requiring about 600 ev of Gamma-ray energy for each visible photon of about 3 ev that is produced. Our initiating event can then produce about 1,200,000/600 = 2000 visible photons. Although some are lost on the way, about 10 percent of these will knock photoelectrons out of the thin cathode inside the photomultiplier tube. Thus, we have about 200 3

4 photoelectrons produced. Since there are several random processes involved, the actual number of photoelectrons will fluctuate about this average with a standard deviation of ± 200 = ±14. From this point on, the photomultiplier simply amplifies the number of photoelectrons, to obtain a current pulse that will produce the voltage pulse when it passes through the photomultiplier's output resistor. (The photomultiplier's amplification factor is about ) Further amplification eventually produces pulses in the range from zero to ten volts, but we don't know precisely what the scaling factor is and thus need to calibrate the scintillator and its ancillary components. What we do learn from this is that we can expect the center of the pulse height distribution to be proportional to the energy that the initial photon deposits in the scintillator and that the resolution will be about ±14/200 = ±7 percent, or in energy units ±1200x0.07 = ±84 KeV. (The best way to improve the resolution is to improve the efficiency in the initial event from 3/600 to something closer to unity. This is what happens with solid state detectors where the resolution can be under ±10 KeV.) The photomultiplier requires a high voltage supply. In addition there is a preamplifier, attached to the photomultiplier, which needs a low voltage power supply. This power is taken from the unit that provides the final amplification stage. The amplifier and high voltage supply are housed in a 'NIM Bin', a standard unit developed to service a wide range of modular units used in nuclear and particle physics research. Each gamma ray with a unique energy does not necessarily produce the same pulse height. To understand this we need to look at the mechanisms by which photons can lose energy to the crystal. When the photon interacts in the scintillator via the photoelectric effect, it transfers all of its energy and the pulse appears in the photopeak. However, the photon may also undergo a Compton scattering: (5) γ + e - γ' + e - If the secondary gamma escapes from the crystal, only the kinetic energy of the recoiling electron will contribute to the height of the pulse produced. The lower energy region of the pulse height distribution is due to these electrons. It has a maximum energy T(max) which will depend on the energy of the gamma but extends all the way down to zero energy. The number of pulses in every energy interval from zero up to T(max) is roughly constant. The computer program SCATT on the lab PCs and the Unix account on Gerda, can be used to determine the possible electron recoil energies, including T(max). Occasionally a Compton scattering occurs, but the secondary gamma is detected before it escapes. (Through a photoelectric effect type interaction.) In this case the whole energy of the photon ends up in the scintillator and thus in the photopeak. This is the reasonwhy we pay good money for large scintillator crystals! Finally, the pulse height distribution frequently shows a smallish peak at low energies attributable to photons that are backscattered into the scintillator. They are artifacts of the Compton scattering process occurring outside the detector. As the program SCATT shows, the secondary gammas coming backwards from a nearly backward angle will have an energy very near [E(γ) - T(max)]. This is one way to check the identification of this peak. A check on this would be to place an absorber just below the source to increase the amount of backscattering. 4

5 Procedure: Familiarize yourself with the operation of the pulse-height analyzer. There are quite a number of controls that you need to become familiar with, but you cannot do damage to anything except to the stored data. If you take the time to become familiar with the instrument, the experiment itself will go quite fast. 1) Get a good spectrum for the Cesium-137 source as it will be used to calibrate the energy scale of the analyzer. The photopeak is at 662 KeV. You can expect to measure energies in the range from 0 to 1500 Kev, so that gives you a clue how the high voltage on the photomultiplier and the amplifier gain should be set. If you are using the interface for the PC, use this to peak to calibrate the analyzer. After that you can simply read out the photon energies. 2) Now increase the amplifier gain by a factor of about ten and get a recording of the low energy portion of the spectrum. (Channel numbers then need to be divided by the ratio to get the effective channel number before converting to energy units.) This is where you will find the x-ray photopeaks. 3) Now reset the amplification back to that used in Step 1 and obtain the spectrum for Sodium-22, Cobalt-57 and Cobalt-60, Barium-133, and a Zinc-65, and Thallium-204 sources. Some of these sources may be quite weak. To get a good spectrum you should let the weaker sources go for a longer time -- as long as over night, if necessary. 4) Analyze each spectra obtained as best you can, trying to distinguish real photopeaks from those associated with backscattering and Compton scattering. You should use the program SCATT to help in this analysis. (A sample is found in the instruction manual.) Once you have assigned the energies to the photopeaks, you can use the table of critical x-ray absorption energies in the instruction manual to identify the photons originating in atomic transitions. The remaining photon energies can then be used to assign nuclear energy levels for the product nucleus resulting from the decay of the parent nucleus. Details of the nuclear energy levels for these nuclei can be found in the reference book in the library. Analysis of the Cesium-137 Spectrum: Following the beta-decay of Cesium-137 we find that: Cs 56 + β Ba + ν (Q = 1180 KeV) When the barium is left in an excited state there can be an electromagnetic transition to the ground state with the emission of a photon. This is the 662 KeV photon that we detect. The difference, = 520 KeV, is the energy that is shared by the barium recoil, the β -, and the ν. It represents the maximum energies that the - can receive. These - energies are not sufficient to penetrate into the scintillator, though they can be picked up by our Geiger counters. The neutrinos are not detected. If there were a transition directly to the barium ground state, there would be no photons to be detected. Maximum energies of the β - would now be 1180 KeV. From the output of the SCATT program, clearly the maximum energy that an electron in 5

6 the detector can receive from a Compton scattering is about 480 KeV. Thus, if the secondary photon escapes the detector, these 'Compton electrons' generate pulse heights from 0 up to the Compton edge at 480 KeV, well below the photopeak at 662 KeV. On the other hand, Compton scattering outside the detector through angles greater than 90 degrees, may result in photons that are absorbed in the Sodium Iodide crystal. The SCATT program shows that these will have energies between about 180 and 300 KeV, the so-called backscattered region. When electron capture occurs, there are also x-rays emitted by the resulting Barium atom. The K-shell energy is at KeV (using the critical x-ray absorption energy table) and the L-shell is at -5.2 KeV. (Of the three L-subshell energies I, II, and III, the transition L(III)-K is the more likely.) Thus an x-ray of = 32.2 KeV would be expected. Other transitions into the now emptied L subshells will follow but are of too low an energy to be seen. For this source there is only the one nuclear photon emission, thus we can conclude that the product nucleus, Barium-137, has an excited energy level at MeV above the ground state. This is shown in the figure below. 662 KeV 480 KeV 182 KeV Pulse Height Distribution for Cesium-137 6