Positron Annihilation - Essay Example

?Positron Annihilation When a low energy positron collides with a low energy electron, there is an emittance of two gamma rays in the opposite direction. This phenomenon, also called positron annihilation, results in two gamma rays at 180° and with 0.511 MeV of energy moving in opposite directions. The gamma rays released can be detected and measured. A source of positrons and a detector for gamma radiation is required to study positron annihilation. The positron annihilation experiment involves the use of two detectors placed at an angle anywhere between 160-200°. 22Na and 60Co are used in the experiment. The scintillation detectors are used not only for the detection but also measurement of gamma radiation. Electronic counters are used for investigating the annihilation events. The observations made regarding the annihilation events in case of 22Na were found to be in agreement with theoretical considerations. The angular distribution of gamma rays from a 60Co source was also investigated. This part of the experiment provided rather convoluted information. The gamma rays resulting from annihilation events were found to be more spread rather than peaked. Such a behavior can be attributed to the changes in the angular momentum of the 60Co nucleus as it progresses through its unstable, excited state. Observations made in this experiment are in agreement with theoretical observations. The experiment demonstrates back-to-back emission of annihilation photons, peaking at 180°. The coincidence events for 22Na were found to be more reliable than for 60Co. 2. Introduction Collision of a low energy positron by an electron of low energy results in their annihilation, causing the production of gamma ray photons. They are responsible for carrying away the momentum and energy of the pair. e? + e+ > ? + ? These photon rays do not have enough mass and energy to result in the production of heavier particles. The process of positron annihilation satisfies certain laws of conservation such as the conservation of electric charge, conservation of total energy, and conservation of momentum (both linear and angular). The conservation of linear momentum and energy does not accommodate the creation of one photon but rather two gamma rays. The two gamma rays ensuing from the positron annihilation move in the opposite direction. The energy possessed by these two gamma rays is approximately 0.511 MeV (Mega electron Volts). Figure 1: Feynman diagram of positron annihilation (Booklet, 2012) The two gamma rays are created because there is no momentum in the system during annihilation as both the electron and the positron come to rest for a short moment. The momentum of the system cannot be conserved if only one proton is created in the process. The collective amount of 1.022 MeV energy of the two gamma rays that are moving in opposite directions satisfies the conservation of the momentum and energy. The positron used in the annihilation process is often obtained from the decay of a proton into a neutron, resulting in the release of a positron and a neutrino. Figure 2: Emission of positron and its annihilation (PET, 2007) The gamma rays released in the process of positron annihilation are both detectable and measurable. Time coincidence counting is a technique that is employed for studying radioactive materials. With this technique, radioactive materials can be detected and identified. The disintegration rates of the radioactive materials can also be calibrated with this technique. The absolute activity of the materials can be measured by counting the radiation events occurring in the radioactive material. The radiation could comprise of beta and gamma rays and can be easily measured using the technique. During the decay of an unstable nucleus, several photons may be emitted in a cascade. 60Co nucleus is one such example. In 22Na, the decay product, which is a positron, annihilates in the source itself. To induce positron annihilation or study it, there is a need for a positron emitter. Various materials have been used as positron sources. Commonly employed positron emitting nuclei include 18F, 15O, 13N, and 11C. These are commonly used in PET (Positron Emission Tomography). PET is a practical application of positron emitters and positron annihilation. It is a very sensitive method for imaging molecules in vivo. In this technique, the positron is allowed to travel in the tissue for a short distance after which it is annihilated with an electron, resulting in the release of photons or gamma rays having 0.511 MeV of energy. Physics experiments on positron annihilation usually employ 60Co and 22Na as positron sources. 3. Theory 22Na releases a positron followed by a gamma ray. It is a radioactive isotope and undergoes beta decay. It has a half-life of 2.6 years. The release of a positron from a 22Na nucleus results in the formation of a stable Ne nucleus: 22Na ? 22Ne + ? + ?+ + ?e. The decay scheme of a 22Na is shown in figure 3. Figure 3: Decay scheme of 22Na (Inoyatov, 2007) From the decay scheme shown, it can be seen that the 22Na decay occurs through electron capture and positron emission. This happens 99.95% of the time. The 22Na has 1.273 MeV of energy. Positron emission comprises 90% of the decay events and these end in annihilation resulting in the production of opposite moving gamma photons having 511 KeV or 0.511 MeV of energy. The release of these gamma rays can be observed in the gamma spectrum. Detectors using Nai (TI) can detect even a point source of such radiation. The angular separation or angle at which the gamma rays for each positron move away from the source is equal to 180°. Two detectors are used to detect gamma rays in the present experiment. One detector is fixed while the other can be rotated around the radiation source. These can be used to detect and measure the gamma rays. Another source, namely the 60Co, results in the release of gamma rays. It is a radioactive isotope and results in beta decay. The decay scheme of this material is shown in figure 4. Figure 4: Decay scheme of 60Co (Jimoid, 2005) As is seen, in 99.9% of the decay events, a beta particle of energy equal to 318 KeV is released. The resulting nucleus is 60Ni which is in 4+ state. The release of another gamma particle of 1173.2 KeV of energy results in the formation of a 2+ state. This state is then further released by the emission of another gamma having 1332.5 KeV energy. This results in the production of a 60Ni nucleus, which is stable. The two gamma rays emitted by 60Co are coincident and a stable nucleus is formed. 4. Method This experiment is performed using a source and several other equipment including detectors and counter timers. The electronics block diagram used is shown in figure 5. Figure 5: Block diagram of equipment used Half-life (Years) Original Date Original Activity Nuclide Sources 2.60 01/12/2006 394.0 kBq 22Na S 305.PH 5.27 08/7/1972 196.0 MBq 60Co S 082.RG Detector II (Movable) - SCINIX 25-B-51 NaI (Tl) detector - Operating Voltage: 510 V - Crystal Diameter: 25mm - Source-Detector Distance: 145 mm Detector I (Fixed) - SCINIX 25-B-51 NaI (Tl) detector - Operating Voltage: 540 V - Crystal Diameter: 25mm - Source-Detector Distance: 145 mm - 1xCanbera 2071A Dual Converter Timer - 2x570 OPTIC AMPLIFIERS 2x550 OPTEC SCA - - 1xCanbera 2040 Coincidence Resolving Table 1: Apparatus and equipment used Truth table: The detectors received signals from a circuit that took a coincidence counting rate for each angle. The circuit has logic AND gate. The truth table using two inputs A and B AND gate output Q is shown in table 2. Input A Input B Output Q 0 0 0 0 1 0 1 0 0 1 1 1 Table 2: Truth table used for experiment A scale timer unit is used to count the number of output pulses from the unit. The output pulse Q will be produced by the coincidence unit if both input A and input B are simultaneously active. This will only occur when two photons interact simultaneously in each of the two detectors. The signals are detected in a short amount of time that could be taken as a coincidence. Firstly, the 22Na source is placed at the center of the two detectors. The two detectors are then aligned at an angle of 180? and the number of coincidences is recorded in a period of five minutes. The rotatable detector is rotated in increments of 1? up to 10? and then in increments of 5? up to 20?. The number of counts is recorded at each angle for a period of five minutes. The rotation of the detector is reversed and the measurements are taken again. The source (Na) is removed and the coincidence level is measure. In the present experiment, the background coincidence level obtained was zero. Measurements of the distance between the center of rotation and the detectors were also taken. The 60Co was also placed as a source at the center of the two detectors, which were aligned at an angle of 180?. Number of coincidence events over a period of ten minutes was recorded. After this, the detector is rotated in increments of 2? up to 10? and measurements were recorded. The detector is then rotated in increments of 5? up to 20? and the counts were recorded at each angle for a period of ten minutes. The same procedure was performed while reversing the rotation of the detector. The background coincidence level was then measured and the distance of the measurements of the distance between the center of rotation and the detectors were also taken. 5. Results The diagram of the apparatus arrangement is shown in figure 6. As already discussed, one of the detectors could be rotated at various angles relative to the source and to the fixed detector. Figure 6: Diagrammatic representation of apparatus (Booklet, 2012) Upon counting the number of coincidence events and taking the measurements at left angles for minutes, it is seen that the more the rotations, the lesser the counts. The plot of the coincidence counting rate measured for 22Na as a function of the angle is shown in figure 7. Figure 7: Measured coincidence counting rate for 22Na The coincidence counting rate was plotted as a function of the angle between the two detectors. If observed theoretically, there should not have been any coincidence events upon rotation and change in angles. However, this was not found to be so. This was because of the poor resolving time of the apparatus used and also because of coincidence of secondary photons of Na with annihilation photon. The emission of photons is not necessarily diametrical because of the conservation of momentum in case of positrons’ energy remaining after the process. Back to back photon pairs could be observed even at angles other than 180° because of the fixed size of the detectors. The overlapping area can be given by the formula shown below: ? Equation I (d= distance between two centers (-2r ? d ? 2r)) The counting rate for each detector is given by the equation: ? Equation II (S = number of decays per second; ? = efficiency of the detector in recording the gamma ray, distance k between source and detector >> detector radius r (145 >> 12.5). The solid angle is given by ? = (if detector area A is a function of ?) and the intrinsic efficiency is expressed by – ? Equation III The intrinsic efficiency of the detectors can be calculated as around ten percent after taking the count rate at 180° as pulses recorded and the expected count rate as number of quanta. The activity of 22Na can be calculated as 98000Bq with the help of the decay formula. The expected counting rates can then be plotted again using the same angles. It appears from the figure 7 that the radiation was emitted back to back, with the peak being at 180°. Theoretically, expected delta function can be seen in the graph in figure 7. However, the function is spread and not a sharp peak. This could be due to fixed detector size, inappropriate resolving time, and false coincidence. A plot of the coincidence counting rate versus angle (both measured and expected) is shown in figure 8. Figure 8: Measured and Expected count rate for 22Na Figure 9: Coincidence counting rate for 60Co vs. angle between detectors In the figure 8, the measured and expected count rates have been compared. It is apparent that there is a peak at 180° for both, indicating the presence of back-to-back emission. In case of 60Co, as shown in figure 9, the measurements were made at intervals of 2° for angles between +10° and -10° for ten minutes. The counting for 60Co was done for a longer time to ensure accuracy. In this case too, the peak is at 180°. Although the peak is observed at 180°, getting perfect back-to-back radiation is not possible. Coincidence events in 60Co are observed because it decays to give 60Ni through beta decay. A cascade of gamma ray emission occurs at the 1.3325 MeV energy range. This state survives only for 0.7 picoseconds. The resolving time of the instrument used in this experiment is 1 µs, which is higher than the 0.7 picosecond limit. Thus, it appears that the two gamma rays are in coincidence. Based on the readings obtained, it can be said that the area of the detector does not influence the number of coincidence events occurring. Assuming that in the case of gamma emission from 60Co, simultaneous back-to-back coincidence has occurred would thus be wrong. The experiment is therefore limited by the accuracy of the equipment and the maximum resolution offered by it. Back-to-back emission of annihilation photons has however been demonstrated in this experiment. 6. Conclusion Positron annihilation is an interesting phenomenon that occurs when a low energy positron collides with a low energy electron, resulting in the release of two gamma ray photons of 0.511 MeV energy, moving in the direction opposite to one another, and geometrically placed at 180°. In this experiment, the coincidence events occurring during this phenomenon have been investigated. Furthermore, the experiment studied the angular dependence of the photons resulting from the decay of 22Na and 60Co. The decay of 60Co results in a cascade of events and subsequent release of gamma photons. The experiment shows the presence of the delta function, with the peak occurring at 180°, which is consistent with the theoretical expectations. The experiment demonstrates the back-to-back emission of photons resulting from annihilation events in the case of 22Na. Due to limitations in the resolving time of the equipment, coincidences were also observed in angles other than 180°. Gaussian distribution is not seen in the plot for 60Co. It can be assumed that random coincidences may have occurred by chance owing to the 0.7 picosecond survival period of the intermediate excited state of 60Co, which is very small, compared to the 1µs resolving time of the equipment. The area of detector is not found to have any impact on the number of coincidence events. Appendix Angle (degree) Counts/300sec and error ± Counts/sec and error ± 0 16899 ± 129.9961 56.33 ± 7.505331428 1 15787 ± 125.6463 52.623333 ±7.254194189 2 13857 ± 117.7157 46.6066667 ± 6.82690755 3 10984 ± 104.8045 36.6133333 ± 6.05089525 4 7824 ± 88.45337 26.08 ± 5.106858134 5 5135 ± 71.658914 17.1166666± 4.13722934 6 2965 ± 54.451813 9.8833333 ± 3.143776922 7 1422 ± 37.709415 4.74 ± 2.177154106 8 298 ± 17.262676 0.9933333 ± 0.31517905 9 160 ± 12.649110 0.53333333 ± 0.7302967 10 171 ± 13.0766968 0.57 ± 0.754983443 15 159 ± 12.609520 0.53 ± 0.728010988 20 151 ± 12.288205 0.50333333 ± 0.70945988 0 15744 ± 125.4750 52.48 ± 7.24430811 -1 14894 ± 122.0409 49.646666 ± 7.04603907 -2 12771 ± 113.0088 42.57 ± 6.52456895 -3 9798 ± 98.98484 32.66 ± 5.714892825 -4 6925 ± 83.21658 23.0833 ± 4.804511 -5 3989 ± 6315853 13.2966666 ± 3.646459 -6 2165 ± 46.52956 7.2166666 ± 2.686385 -7 878 ± 29.631064 2.92666 ± 1.71075032 -8 233 ± 15.264337 0.7766666 ± 0.8812869 -9 157 ± 12.529964 0.5233333 ± 0.72341758 -10 151 ± 12.288205 0.50333333 ± 0.70945988 -15 144 ± 12 0.48 ± 0.692820323 -20 149 ± 12.206555 0.4996666 ± 0.7047455 Table 3: Measured coincidence counts for 22Na Angle (degree) Counts/600sec and error ± Counts/sec and error ± 0 68 ± 8.24621125 0.11333333± 0.33665016 -2 81 ± 9 0.135 ± 0.3674234 -4 65 ± 8.0622577 0.10833333 ± 0.32914029 -6 51 ± 7.14142842 0.085 ± 0.29154759 -8 72 ± 8.48528137 0.12 ± 0.34641016 -10 83 ± 9.11043357 0.13833333 ± 0.37193189 -15 78 ± 8.83176086 0.13 ± 0.360555127 -20 82 ± 9.05538513 0.1366666 ± 0.36968 0 79 ± 8.88819441 0.13166666 ± 0.36285901 2 71 ± 8.42614977 0.11833333 ± 0.34399612 4 67 ± 8.18535277 0.11166666 ± 0.33416562 6 81 ± 9 0.135 ± 0.3674234 8 77 ± 8.774964387 0.12833333 ± 0.35823642 10 58 ± 7.61577310 0.09666666 ± 0.31091263 15 72 ± 8.48528137 0.12 ± 0.346410161 20 76 ± 8.71779788 0.12666666 ± 0.35590260 Table 4: Measured coincidence counts for 60Co Read More