Radiation Spectroscopy With Scintillators PDF

CHAPTER 10: RADIATION SPECTROSCOPY WITH SCINTILLATORS: I. General Considerations in Gamma-Ray Spectroscopy - The detection of gamma rays is dependent on causing the gamma-ray photon to undergo an interaction that transfers all or part of the photon energy to an electron in the absorbing material....

CHAPTER 10: RADIATION SPECTROSCOPY WITH SCINTILLATORS: I. General Considerations in Gamma-Ray Spectroscopy - The detection of gamma rays is dependent on causing the gamma-ray photon to undergo an interaction that transfers all or part of the photon energy to an electron in the absorbing material. - These electrons have a maximum energy equal to the energy of the incident gamma-ray photon and will slow down and lose their energy in the same manner as any other fast electron, such as a beta particle. - Energy loss is therefore through ionization and excitation of atoms within the absorber material and through bremsstrahlung emission. - In order for a detector to serve as a gamma-ray spectrometer, it must carry out two distinct functions: - first, it must act as a conversion medium in which incident gamma rays have a reasonable probability of interacting to yield one or more fast electrons; - second, it must function as a conventional detector for these secondary electrons. II. Gamma-ray Interactions: - Three gamma-ray interaction mechanisms are significant in gamma-ray spectroscopy: - photoelectric absorption: predominates for low energy gamma rays (up to several hundred keV), - pair production: predominates for high-energy gamma rays (above 5-10 MeV), - Compton scattering: is the most probable process over the range of energies between these extremes. - The photoelectric absorption (which varies approximately as Z4·5) is the preferred mode of interaction in gamma-ray spectroscopy 1 - Therefore, detector materials for gamma-ray spectroscopy are selected from elements with high atomic number. A. Photoelectric Absorption: - Incident gamma-ray photon disappears and a photoelectron is produced mostly from the K shell. Photoelectric absorption - Electron rearrangement to refill the vacancy will result in the emission of a characteristic X-ray or Auger electron. - The Auger electrons have extremely short range because of their low energy. - The characteristic X-rays may travel a millimeter or less before being reabsorbed through photoelectric interactions with less tightly bound electron shells of the absorber atoms. - Thus, the effect of photoelectric absorption is: 1- the liberation of a photoelectron, which carries off most of the gamma- ray energy, 2- one or more low-energy electrons - If nothing escapes from the detector, then the sum of the kinetic energies of the electrons that are created must equal the original energy of the gamma- ray photon. 2 - Photoelectric absorption is therefore an ideal process for measuring the energy of the original gamma-ray. - The total electron kinetic energy equals the incident gamma-ray energy and will always be the same for monoenergetic gamma rays. - Under these conditions, the differential distribution of electron kinetic energy for a series of photoelectric absorption events would be a simple delta function as shown below. - The single peak appears at a total electron energy corresponding to the energy of the incident gamma rays. B. Compton Scattering: - The result of a Compton scattering interaction is the creation of a recoil electron and scattered gamma-ray photon. - The photon energy is divided between the two depending on the scattering angle. - The energy of the scattered gamma ray h' in terms of its scattering angle  is given by 3 - where m0c2 is the rest mass energy of the electron (=0.511 MeV). - The kinetic energy of the recoil electron is therefore: - Two extreme cases can be identified: 1. A grazing angle scattering, or one in which   0. - In this case, the above two equations predict that hv'  hv and Ee–  0. - This means that the recoil Compton electron has very little energy and the scattered gamma ray has nearly the same energy as the incident gamma ray. 2. A head-on collision in which  = π. - In this extreme, the incident gamma ray is backscattered toward its direction of origin, whereas the electron recoils along the direction of incidence. - This extreme represents the maximum energy that can be transferred to an electron in a single Compton interaction. - In this case: - Usually, all scattering angles will occur in the detector. - Therefore, a continuum of energies can be transferred to the electron, ranging from zero up to the maximum. - The figure below shows the electron energy distribution for a specific gamma photon energy. 4 - The gap between the maximum Compton recoil electron energy and the incident gamma-ray energy is given by - In the limit that the incident gamma-ray energy is large, or hv >> m0c2/2, this energy difference tends toward a constant value given by C. Pair Production: - The process occurs in the intense electric field near the protons in the nuclei of the absorbing material. - An electron-positron pair is created at the point of complete disappearance of the incident gamma-ray photon. - Because an energy of 2m0c2 is required to create the electron-positron pair, a minimum gamma-ray energy of 1.022 MeV is required to make the process energetically possible. - If the incident gamma-ray energy exceeds this value, the excess energy appears in the form of kinetic energy shared by the electron-positron pair. - Therefore, the process consists of converting the incident gamma-ray photon into electron and positron kinetic energies, which total - For typical energies, both the electron and positron travel a few millimeters at most before losing all their kinetic energy to the absorbing medium. - A plot of the total (electron + positron) charged particle kinetic energy created by the incident gamma ray is again a simple delta function, but it is now located 2m0e2 below the incident gamma-ray energy, as sketched below. 5 - This amount of energy will be deposited each time a pair production interaction occurs within the detector. - Once the positron’s kinetic energy becomes very low (comparable to the thermal energy of normal electrons in the absorbing material), it will annihilate with a normal electron in the absorbing medium. - The time required for the positron to slow down and annihilate is small, so that the annihilation radiation appears in virtual coincidence with the original pair production interaction. III. Predicted Response Functions: A. "Small" Detectors - As an example of one extreme in gamma-ray detector behavior, we first examine the expected response of detectors whose size is small (1 to 2 cm in dimension) compared with the mean free path of the secondary gamma radiations (few cm) produced in interactions of the original gamma rays. - These secondary radiations consist of: 1- Compton scattered gamma rays, 2- together with annihilation photons formed at the end of the tracks of positrons created in pair production. - Assuming that all charged particle energy (photoelectron, Compton electron, pair electron, and positron) is completely absorbed within the detector volume. - The predicted electron energy deposition spectra under these conditions are illustrated in the figure below. 6  The "small detector" extreme in gamma-ray spectroscopy. The processes of photoelectric absorption and single Compton scattering give rise to the low-energy spectrum at the left. At higher energies, the pair production process adds a double escape peak shown in the spectrum at the right. - If the incident gamma-ray energy is below the value at which pair production is significant, the spectrum results only from the combined effect of Compton scattering and photoelectric absorption. - The continuum of energies corresponding to Compton scattered electrons is called the Compton continuum. -The narrow peak corresponding to photoelectrons is designated as the photopeak. - The ratio of the area under the photopeak to the area under the Compton continuum is the same as the ratio of the photoelectric cross section to the Compton cross section in the detector material. 7 - If the incident gamma-ray energy is sufficiently high (several MeV), the results of pair production are also evident in the electron energy spectrum. - For a small detector, only the electron and positron kinetic energies are deposited, and the annihilation radiation escapes. - The net effect is to add a double escape peak to the spectrum located at an energy of 2m0c2 ( 1.022 MeV) below the photopeak. - The term double escape refers to the fact that both annihilation photons escape from the detector without further interaction. B. Very Large Detectors: - As an opposite extreme case, imagine that gamma rays could be introduced near the center of a very large detector (many tens of centimeters), as in figure. The "large detector" extreme in gamma-ray spectroscopy. All gamma-ray photons, no matter how complex their mode of interaction, ultimately deposit all their energy in the detector. 8 - The detector dimensions are now sufficiently large so that all secondary radiations, including Compton scattered gamma rays and annihilation photons, also interact within the detector active volume and none escape from the surface. - If the initial interaction is a Compton scattering event, the scattered gamma ray will subsequently interact at some other location within the detector. - This second interaction may also be a Compton scattering event, in which case a scattered photon of still lower energy is produced. - Eventually, a photoelectric absorption will occur and the history is terminated at that point. - If the average migration distance of the secondary gamma rays is of the order of 10 cm, then the total elapsed time from start to finish of the history will be less than a nanosecond. - This time is substantially less than the inherent response time of virtually all practical detectors used in gamma-ray spectroscopy. - Therefore, the net effect is to create the Compton electrons at each scattering point and the final photoelectron in time coincidence. - The pulse produced by the detector will therefore be the sum of the responses due to each individual electron. - If the detector responds linearly to electron energy, then a pulse is produced that is proportional to the total energy of all the electrons produced along the history. - Because nothing escapes from the detector, this total electron energy must simply be the original energy of the gamma-ray photon, no matter how complex any specific history may be. - The detector response is the same as if the original gamma-ray photon had undergone a simple photoelectric absorption in a single step. - In the event of pair production, the annihilation photons formed when the positron is stopped are now assumed to interact through Compton scattering or photoelectric absorption elsewhere in the detector. 9 - Again, the detector is large enough to prevent any secondary radiation from escaping, and the sum of the kinetic energies of the electron-positron pair and subsequent Compton and photoelectrons produced by interaction of the annihilation radiation must equal the original gamma-ray photon energy. - Therefore, the detector response is again simply proportional to the original gamma-ray energy. - The conclusion to be reached is therefore very simple: If the detector is sufficiently large and its response linearly dependent on electron kinetic energy, then the signal pulse is identical for all gamma-ray photons of the same energy, regardless of the details of each individual history. - The detector response function now consists of the single peak, as in the figure above. - The ability to interpret complex gamma-ray spectra involving many different energies is obviously enhanced when the response function consists of a single peak. - This peak is often called the photopeak, just as in the case of the small detector. - However, a better name is the full-energy peak because it represents all histories in which all of the original gamma-ray energy is fully converted to electron kinetic energy. C. Intermediate Size Detectors: - Real detectors of the sizes in common use for gamma-ray spectroscopy are neither small nor large by the standards given above. - For usual geometries in which the gamma rays are incident externally on the surface of the detector, even large-volume detectors appear finite because some interactions will take place near the entrance surface. - Normal detector response functions therefore combine some of the properties for the two previous cases, as well as additional features related to partial recovery of the secondary gamma-ray energy. 10 - Some representative histories that illustrate these added possibilities are shown in the figure below, together with corresponding features in the response function. The case of intermediate detector size in gamma-ray spectroscopy. - The spectrum for low to medium gamma-ray energies (where pair production is not significant) again consists of a Compton continuum and photopeak. - Now, however, the ratio of the area under the photopeak to that under the Compton continuum is significantly enhanced over that for the very small detector due to the added contribution of multiple events to the photopeak. - The lower the incident gamma-ray energy, the lower will be the average energy of a Compton scattered photon and the corresponding average distance of migration. - Thus, even detectors of moderate size will appear to be large, and the relative area under the photopeak increases with decreasing incident photon energy. 11 - At very low energies (say, < 100 keV) the Compton continuum may effectively disappear. - At medium energies, the possibility of multiple Compton scattering followed by escape of the final scattered photon can lead to a total energy deposition that is greater than the maximum predicted by Eq. (10.4) for single scattering. - These multiple events can thus partially fill in the gap between the Compton edge and the photopeak, as well as distort the shape of the continuum predicted for single scattering. - If the gamma-ray energy is high enough to make pair production significant, a more complicated situation prevails. - The annihilation photons now may either escape or undergo further interaction within the detector. - These additional interactions may lead to either partial or full-energy absorption of either one or both of the annihilation photons. - If both annihilation photons escape without interaction, events occur that contribute to the double escape peak. - Another relatively frequent occurrence is a history in which one annihilation photon escapes but the other is totally absorbed. - These events contribute to a single escape peak, which now appears in the spectrum at an energy of m0c2 (0.511 Me V) below the photopeak. - A continuous range of other possibilities exists in which one or both of the annihilation photons are partially converted to electron energy through Compton scattering and subsequent escape of the scattered photon. - Such events accumulate in a broad continuum in the pulse height spectrum lying between the double escape peak and the photopeak. - The response function to be expected for a real gamma-ray detector will depend on the size, shape, and composition of the detector, and also the geometric details of the irradiation conditions. 12 - For example, the response function will change somewhat if a point gamma- ray source is moved from a position close to the detector to one that is far away. - The variation is related to the differences in the spatial distribution of the primary interactions that occur within the detector as the source geometry is changed. - In general, the response function is too complicated to predict in detail other than through the use of Monte Carlo calculations, which simulate the histories actually taking place in a detector of the same size and composition. - Some properties of the response function are of general interest in gamma- ray spectroscopy. - The photofraction is defined as the ratio of the area under the photopeak (or full-energy peak) to that under the entire response function. - It is a direct measure of the probability that a gamma ray that undergoes interaction of any kind within the detector ultimately deposits its full energy. - Large values of the photofraction are obviously desirable to minimize the complicating effects of Compton continua and escape peaks in the spectrum. - At high gamma-ray energies, the single and double escape peaks are quite prominent parts of the response function and can, under some circumstances, become larger than the photopeak. - The ratio of the area under the single or double escape peak to the area under the photopeak is also a widely quoted property of the response function that can help in the interpretation of complex spectra. D. Complications in the Response Function: 1. Secondary Electron Escape: - If the detector is not large compared with typical secondary electron ranges, a significant fraction of the electrons may leak from the detector surface and their energy will not be fully collected. 13 - This effect is enhanced for high gamma-ray energies for which the average secondary electron energy is also high. - Electron leakage will tend to distort the response function by moving some events to a lower amplitude. - The shape of the Compton continuum will therefore be altered somewhat to favor lower amplitudes. - Because some events will be lost from the photopeak, the photofraction will be reduced as compared with the situation in which electron leakage is not important. 2. Bremsstrahlung Escape: - Secondary electrons can lose energy by the radiation of bremsstrahlung photons. - The fraction lost by this process increases sharply with electron energy and becomes the dominant process for electrons with energy over a few MeV. - Bremsstrahlung production scales approximately as Z2 of the absorber so its importance is greatest in detectors with high atomic number. - Even though the electron itself may be fully stopped within the detector, there is a possibility that some fraction of the bremsstrahlung photons may escape without being reabsorbed. - For both secondary electron or bremsstrahlung escape, the effects are to change the shape of the response function somewhat, but additional peaks or sharp features are not introduced. 3. Characteristic X-Ray Escape: - In the photoelectric absorption process, a characteristic X-ray often is emitted by the absorber atom. - In the majority of cases this X-ray energy is reabsorbed near the original interaction site. - If the photoelectric absorption occurs near a surface of the detector, however, the X-ray photon may escape as shown in the sketch below. 14 - In this event, the energy deposited in the detector is decreased by an amount equal to the X-ray photon energy. - Without the X-ray escape, the original gamma ray would have been fully absorbed and the resulting pulse would have contributed to the photopeak. - With escape, a new peak will appear in the response function and will be located at a distance equal to the energy of the characteristic X-ray below the photopeak. - These peaks are generally labelled "X-ray escape peaks" and tend to be most prominent at low incident gamma-ray energies and for detectors whose surface-to-volume ratio is large. 4. Secondary Radiations Created Near the Source: a. Annihilation Radiation: - If the gamma-ray source consists of an isotope that decays by positron emission, an additional annihilation peak in the spectrum at 0.511 MeV is to be expected. - Most standard gamma-ray sources are encapsulated in a covering sufficiently thick to fully stop all the positrons, and thus they undergo annihilation in the region immediately surrounding the source. - This region therefore acts as a source of 0.511 MeV annihilation radiation, which is superimposed on the gamma-ray spectrum expected from decay of the source itself. 15 - For detector geometries in which it is possible to detect both annihilation photons from a single decay simultaneously (as in a well counter), then a peak at 1.022 MeV may also be observed in the recorded spectrum. b. Bremsstrahlung: - Most commonly-available gamma-ray sources decay by beta-minus emission, and the source encapsulation is usually also thick enough to stop these beta particles. - In other cases, an external absorber may be used to prevent the beta particles from reaching the detector where their energy deposition would needlessly complicate the gamma-ray spectrum. - In the absorption process, however, some secondary radiation in the form of bremsstrahlung will be generated and may reach the detector and contribute to the measured spectrum. - Bremsstrahlung spectra are continua, they do not lead to peaks in the recorded spectra but rather can add a significant continuum on which all other features of the gamma-ray spectra are superimposed. - To minimize the generation of bremsstrahlung, the use of beta absorbers made from low atomic number materials, such as beryllium, is often preferred. 5. Effects of Surrounding Materials: - Surrounding materials include: - Detector encapsulation to provide a barrier against moisture and light or vacuum enclosure. - Shielding structure to reduce natural background. - The gamma-ray source sample material or encapsulation. - All these materials are potential sources of secondary radiations that can be produced by interactions of the primary gamma rays emitted by the source. - If the secondary radiations reach the detector, they can influence the shape of the recorded spectrum to a noticeable extent. 16  Influence of surrounding materials on detector response. In addition to the expected spectrum (shown as a dashed line), the representative histories shown at the top lead to the indicated corresponding features in the response function. a. Backscattered Gamma Rays Pulse height spectra from gamma-ray detectors often show a peak in the vicinity of 0.2 – 0.25 MeV, called the backscatter peak. - The peak is caused by gamma rays from the source that have first interacted by Compton scattering in one of the materials surrounding the detector. - The next figure shows the energy dependence of these scattered gamma rays as a function of the scattering angle. 17 - From the shape of these curves, it can be seen that any scattering angle greater than about 110 - 120° results in scattered photons of nearly identical energy. - Therefore, a monoenergetic source will give rise to many scattered gamma rays whose energy is near this minimum value, and a peak will appear in the recorded spectrum. - The energy of the backscatter peak is given by: - If the primary gamma-ray energy is large (h >> m0c2/2), this expression reduces to - Thus, the backscatter peak always occurs at an energy of 0.25 MeV or less. b. Other Secondary Radiations In addition to Compton scattering, photoelectric absorption in the materials immediately surrounding the detector can lead to generation of a characteristic X-ray that may reach the detector. - If the atomic number of the material is high, the X-ray photon will be relatively energetic and can penetrate significant thicknesses of intervening material. 18 - Therefore, high-Z materials should be avoided in the immediate vicinity of the detector. - On the other hand, the most effective shielding materials are those with high atomic numbers such as lead. - A graded shield is one in which the bulk of the shield is made from high-Z materials, but the inner surface is lined with a material with lower atomic number. - This inner lining serves to absorb the characteristic X-ray emitted by the bulk of the shield, at the same time emitting only low-energy or weakly penetrating X-rays of its own. - If the energy of the primary gamma rays is high, pair production within high- Z surrounding materials can give a significant yield of annihilation radiation. - A peak can therefore appear at 0.511 MeV in the spectrum from the detection of these secondary photons. - This peak may be confused with that expected from annihilation radiation produced by radioactive sources that are positron emitters, and care must therefore be exercised in identifying the source of these annihilation photons. E. Summation Effects: - Additional peaks caused by the coincident detection of two (or more) gamma-ray photons may also appear in the recorded pulse height spectrum. - Some applications involve an isotope that emits multiple cascade gamma rays in its decay, as illustrated in figure. 19 - If we assume that no isomeric states are involved, the lifetime of the intermediate state is generally so short that the two gamma rays are, in effect, emitted in coincidence. - Both gamma-ray photons from the single decay may interact and deposit all their energy within a time that is short compared with the response time of the detector or the resolving time of the electronics. - If enough of these events occur, a sum coincidence peak will be observable in the spectrum that occurs at a pulse height that corresponds to the sum of the two individual gamma-ray energies. - A continuum of sum events will also occur at lower amplitudes due to the summation of partial energy loss interactions. - The relative number of events expected in the sum peak depends on the branching ratio of the two gamma rays, the angular correlation that may exist between them, and the solid angle subtended by the detector. Gamma-ray interactions in NaI detector and lead shield 20 IV. Properties of Scintillation Gamma-Ray Spectrometers A. Response Function Pulse height spectrum from a NaI(Tl) scintillator for gamma rays emitted by 57Co at 122 and 136 keV. The iodine X-ray escape peak lies 28 keV below the corresponding full energy peak and is evident only for the more intense 122 keV gamma ray. Pulse height spectrum recorded from NaI(Tl) scintillation detectors for a 86Rb source (1.08 MeV gamma rays) showing the contribution at the lower end of the scale from bremsstrahlung generated in stopping the beta particles emitted by the source. 21  Spectrum from a 60Co source (1.17 and 1.33 MeV gamma rays emitted in coincidence) taken under conditions in which the solid angle subtended by the detector is relatively large, enhancing the intensity of the sum peak at 2.50 MeV. Pulse height spectrum from a NaI(Tl) scintillator for gamma rays emitted by 24Na at 1369 and 2754 keV. The single and double escape peaks corresponding to pair production interactions of the higher energy gamma rays are very apparent, as is the annihilation radiation peak at 511 keV due to pair production interactions in surrounding materials. B. Energy Resolution: where FWHM = full width at half maximum of the full-energy peak 22  H0 = mean pulse height corresponding to the same peak C. Energy Calibration - A detection system calibration curve is a plot of pulse position (or centroid channel number in a multichannel analyzer) for the full energy peak versus gamma-ray energy. - All scintillators have some degree of nonproportionality in their response to fast electrons, so such a calibration would be expected to show some nonlinearity. - Thus, a careful calibration of peak position versus energy for typical scintillators will show some degree of curvature that will in principle be specific to that detector. - For interpolation between narrowly spaced peaks of known energy, however, the assumption of linearity normally leads to negligible error. D. Detection Efficiency - There are more published data available on the detection efficiency of sodium iodide scintillators for gamma rays than for any other detector type or application. - The number of different sizes and shapes of NaI(Tl) crystals in routine use is relatively limited so that reasonably complete data can be compiled on each of the common configurations. Peak Area Determination: 23 - Nearly all peaks are superimposed on a continuum. - If the peak were a simple isolated one without any superimposed continuum, as shown in figure, its area could be determined by simple integration between the peak limits. - When the spectrum is recorded in a multichannel analyzer, the equivalent process is a simple addition of the content of each channel between the indicated limits. - If a continuum is present, as in figure below, some additional unwanted counts are included in this process and must be subtracted. - Some shape must therefore be assumed for the continuum within the region under the peak. - A linear interpolation between the continuum values on either side of the peak will give sufficient accuracy for many purposes. - At times, closely spaced or overlapping peaks do not allow the straightforward summation method to be applied. - More complex methods must then be used to separate the individual contributions of each of the closely lying peaks. 24 VII. Specialized Detector Configurations Based on Scintillation: A. The Phoswich Detector: - The combination of two dissimilar scintillators optically coupled to a single PM tube is often called a phoswich (or phosphor sandwich) detector. - The scintillators are chosen to have different decay times so that the shape of the output pulse from the PM tube is dependent on the relative contribution of scintillation light from the two scintillators. - Most applications involve the use of this pulse shape difference to distinguish events that have occurred in only one scintillator from those that occur in both. - For example, lightly penetrating radiations can be made to stop fully in the first scintillator, but more penetrating particles may generate light in both. - Sodium iodide and cesium iodide are often chosen as the two materials because their decay times are quite different, and pulses arising from only one decay are easily distinguished from those with both components. B. Liquid Scintillation Counters - The liquid scintillation media are used when measuring low-energy beta particles or alpha particles. - The approach, sometimes called internal source liquid scintillation counting, involves dissolving the sample to be counted directly into the liquid scintillator. - Under these conditions, problems relating to sample self-absorption, attenuation of particles by detector windows, and beta backscattering from the detector are completely avoided. - These advantages are particularly important for low-energy radiations such 14 as the beta particles emitted by tritium and C. C. Position-Sensitive Scintillators 1. One-Dimensional Position Sensing: 25 - Because the light from a scintillator is generated along the track of the ionizing particle, it is possible to sense the position of interaction by localizing the source of the scintillation light. - For sensing position in one dimension, a long rod or bar of scintillation material can be used with PM tubes or photodiodes positioned at either end as in the sketch below: - In this type of geometry, it is generally observed that the intensity of the light measured at one end of the rod drops off exponentially with the distance at which the scintillation light is generated. - Therefore, by electronically deriving the logarithm of the ratio of the two PM tube signals, we obtain a linear indication of the position at which the scintillation occurs. 2. Two-Dimensional Position Sensing (Imaging Detectors): - In nuclear medicine, it is often necessary to form the image of the distribution of gamma-ray-emitting isotopes distributed throughout the patient. - The gamma-ray camera is a device that senses the two-dimensional coordinates of a gamma-ray photon as it interacts in a large-area detector and forms an image through the accumulation of many such events over the exposure time. - A lead pinhole or parallel hole collimator is used to restrict the gamma rays that strike the detector so that the image can be directly interpreted as the spatial distribution of the emitting isotope. - The most common type of gamma-ray camera is diagrammed in figure below: 26 Gamma-ray camera - The detection medium consists of a flat single scintillation crystal (generally sodium iodide) with length and width up to 50 cm and thickness of about 1 cm. - The light generated by gamma-ray interactions in this crystal is sensed by an array of PM tubes that completely cover one of its flat faces. - The two-dimensional position of each event across the area of the crystal is deduced from the relative size of the signals produced from these tubes. - Each scintillation event will generate output pulses of significant amplitude from all the PM tubes that are near the location of the interaction. - The largest signal will generally be from the tube nearest the position, with smaller pulses from tubes at a greater distance. - The "center of gravity" of the light can be electronically interpolated from these signals to form the image. 27  Example of a human bone scan produced by using a gamma camera to image the distribution of methylene diphosphonate labelled with 99mTc. The upper and lower halves of the image each were produced by recording approximately 106 counts over a 3-min period. Gamma-ray interactions: Energy dependence of the various gamma-ray interaction processes in sodium iodide. 28  K-edge Energy dependence of the various gamma-ray interaction processes in Lead. - In the low-energy region, discontinuities in the curve or "absorption edges" appear at gamma-ray energies that correspond to the binding energies of electrons in the various shells of the absorber atom. - The edge lying highest in energy therefore corresponds to the binding energy of the K-shell electron. - For gamma-ray energies slightly above the edge, the photon energy is just sufficient to undergo a photoelectric interaction in which a K-electron is ejected from the atom. - For gamma-ray energies slightly below the edge, this process is no longer energetically possible and therefore the interaction probability drops abruptly. - Similar absorption edges occur at lower energies for the L, M,... electron shells of the atom. - The total mass attenuation coefficient shows a minimum because as Ε increases, τ decreases, κ increases, and σ does not change appreciably. - For lead, μ shows a minimum at Eγ ~ 3.5 MeV; - for NaI, the minimum is at 5 MeV. - for aluminium, the minimum is at 20 MeV; 29 30