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Gamma Interactions and Gamma Spectroscopy with Scintillation Detectors

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Gamma Interactions and Gamma Spectroscopy with Scintillation Detectors

Gamma Interactions and Gamma Spectroscopy with Scintillation Detectors


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  • 1. Gamma Interactions and Gamma Spectroscopy with Scintillation Detectors By Dan Maierhafer EES611 March 14, 2001
  • 2. Table of Contents I. ABSTRACT.....................................................................................................................4 II. INTRODUCTION..........................................................................................................4 III. THEORY......................................................................................................................5 A. GAMMA RAY INTERACTIONS IN MATTER...............................................................................5 1. Photoelectric Absorption...........................................................................................5 2. Compton Scattering...................................................................................................5 3. Pair Production........................................................................................................7 B. ENERGY SPECTRA.............................................................................................................7 1. Photoelectric Absorption...........................................................................................7 2. Compton Scattering...................................................................................................8 a) Compton Edge......................................................................................................9 b) Backscatter............................................................................................................9 3. Pair Production........................................................................................................9 C. RESPONSE FUNCTIONS.......................................................................................................10 1. Small Detectors.......................................................................................................10 2. Very Large Detectors..............................................................................................10 3. Intermediate Size Detectors.....................................................................................10 D. ENERGY RESOLUTION......................................................................................................12 IV. EXPERIMENTAL DESIGN AND PROCEDURE...................................................13 A. 2” X 2” NAI:TL SCINTILLATOR SETUP AND PROCEDURE...........................................................13 B. 5” X 5” NAI:TL SCINTILLATOR SETUP AND PROCEDURE...........................................................14 C. EQUIPMENT USED...........................................................................................................15 V. RESULTS AND DISCUSSION...................................................................................16 A. SINGLE CHANNEL ANALYZER............................................................................................16 1. Identify Peaks in Cs-137 Pulse Height Spectrum taken by SCA................................16 2. Determine Detector Resolution................................................................................16 3. Compare SCA Spectra with MCA Spectra................................................................17 B. MULTI-CHANNEL ANALYZER............................................................................................17 1. Detector Resolution using Cs-137............................................................................17 2. Detector Resolution using Na-22.............................................................................17 3. Unknown Identification...........................................................................................19 4. Determine the Activity of the Cs-137........................................................................19 VI. CONCLUSIONS.........................................................................................................19 A. 2” X 2” SCINTILLATOR COMPARED TO 5” X 5” SCINTILLATOR...................................................19 B. METHOD OF DETERMINING UNKNOWN.................................................................................20 2
  • 3. VII. REFERENCES..........................................................................................................21 VIII. APPENDIX III – ORIGINAL DATA.....................................................................22 IX. APPENDIX IV – OTHER..........................................................................................23 3
  • 4. I.Abstract This paper investigates the response of an NaI:Tl scintillator and photomultiplier tube combination Gamma Ray Detector. Two sizes of crystal were used in this experiment. The first size was a 5”x5”, and the second size was a 2”x2”. The solid crystalline detector was coupled with a photomultiplier tube and other conventional radiation detection electronics to measure pulse height, count rate, energy resolution, dead time, and background count rate using nominal radioactivity standard sources. Plots of Count Rate versus Channel Number were made for Cs-137, Co-60, and Na-22 known sources. The Full Energy Peak was calibrated on these graphs using data from the RADECA program. The Energy Location of important features of these nuclides were located and listed in a table in this report. A curvefit plot was made of Source Gamma Ray Energy vs. Channel Number in order to find the Full Energy Peak of two unknowns. This Full Energy Photon Peak was then used to identify the two unknowns. II.Introduction The subject of this report is the Spectroscopy of Gamma Rays using the NaI:Tl scintillator and photomultiplier tube detector combination. These devices became popular in the early 1950’s, because they were able to make high resolution, high efficiency measurements in a portable detector. Even after the discovery of a multitude of other scintillating materials, NaI:Tl still remains popular because of its efficient energy conversion from photons to electricity. In this laboratory exercise, we used a NaI:Tl scintillator-photomultiplier device to detect and differentiate between the gamma ray energies of various sources. We also differentiated between the features and the measurement anomalies of the gamma ray spectra and found the Full Energy Peaks described later. Next we used the curvefit of the Full Energy Peak vs. Channel Number from the known sources to identify two unknown source Full Energy Peaks of using Channel Number as the independent variable. 4
  • 5. III.Theory A.Gamma Ray Interactions in Matter Gamma Rays are a type of ionizing radiation emitted from the nucleus of an atom with energies in excess of 10 KeV (Fjeld). Gamma rays can interact with matter in three main ways depending on how much Incident Energy the Photon contains. The three main ways are: Photoelectric Absorption, Compton Scattering, and Pair Production. 1.Photoelectric Absorption Photoelectric Absorption is prevalent when photon energies are below 100’s of KeV (Knoll, pp.308). The mechanism is an inelastic collision in which the gamma ray collides with a bound electron and causes it to ionize. The electrons usually affected are in the K-shell. Because the collision is inelastic, the kinetic energy imparted to the ionized electron is equal to the incident energy of the gamma ray minus the binding energy of the electron. Equation 1 shows how to find the Kinetic Energy of the ionized electron. Equation 1: KE e − = Eγ − E binding The electron that escapes from the atom called a photoelectron. The vacancy created by the escapee electron is filled from one of the upper shell electrons. When this occurs, the difference in electron binding energy from the upper to the lower level is emitted as either an X-ray or an Auger electron. If an X-Ray carries away the binding energy, it typically travels about a millimeter before being reabsorbed through photoelectric interactions. If an Auger electron escapes carrying the energy, it will also have limited range because the energy is typically very low (in the eV range) (Auger). 2.Compton Scattering Compton Scattering is the main interaction when gamma ray energy is from the 100’s of KeV to about 5 MeV. This interaction occurs with an outer shell electron of very low binding energy. The mechanism is like that of an elastic collision between two particles. If the incident gamma ray strikes the electron at an angle, the electron scatters the incident 5
  • 6. gamma ray at another angle, Θ. At the same time, this electron is deflected by an equal angle in the other direction. Eγ’ Θ Eγ Figure 1. Diagram of Compton Scattering Event The angle Θ depends on the grazing angle between the electron and the incoming gamma ray. The energy of the scattered gamma ray photon is found by using Equation 2. The energy of the scattered recoil electron is found by using Equation 3. Eγ Eγ ' = 1 +  Eγ Equation 2:   511 KeV  ∗ (1 − cos Θ )     Eγ     511 KeV  * (1 − cos Θ )    Equation 3: E e − = Eγ *   1 +  Eγ   ∗ (1 − cos Θ )     511 KeV   There are two extreme cases in this type of gamma interaction. The first case happens when Θ = 0 degrees, or the gamma ray just barely grazes the electron. From Equation 2 and 3, it is known that the recoil electron has almost zero energy, while the scattered gamma ray has almost the same energy after and before the interaction. The second interaction of interest occurs when Θ = 180 degrees. This is a head on collision, where the incident gamma ray is scattered 6
  • 7. backwards where it came, and the electron recoils along the path of the incident gamma ray. 3.Pair Production Pair Production occurs with high-energy gamma rays between 5 and 10 MeV. It is a type of energy to matter conversion that occurs near the high electric field located in the vicinity of the protons of the absorbing material. In this interaction, the gamma ray is transformed into an electron-positron pair. Einstein’s equation describing energy to mass conversion is employed as shown in Equation 4 to determine the minimum energy required for this type of interaction. Equation 4: E = m * c 2 Since the mass of an electron and a positron are both equal to m0, then the minimum energy required to create the particles will be 2*E, which corresponds to 2*m0*c2. If the incident gamma ray has any additional energy, it will be imparted to the two particles as kinetic energy. This is shown symbolically in Equation 5. Equation 5: E e − + E e + = Eγ − 2 * m0 * c 2 After the electron-positron pair is created, the electron escapes and interacts with matter via an ionization, excitation, disassociation, or free radical formation. The positron is an antimatter particle, and once it slows down to the thermal energy of a normal electron in the absorber, it combines with an electron and creates two annihilation photons, each of energy m0*c2, or 511 KeV. Neither of the particles travel far, so all the different interactions are indistinguishable from each other. B.Energy Spectra 1.Photoelectric Absorption The energy spectrum of a photoelectric absorption is very simple. The spectrum is made up of the effects of the ejected photoelectron, and the effects of the energy hole it creates. Photoelectron kinetic energy is equal to the incident gamma ray energy minus its binding energy as described in Equation 1. The effects of the binding energy show up as 7
  • 8. an X-ray emitted as an outer shell electron deorbits or as an Auger electron is ejected. Therefore, the energy spectrum for monoenergetic gamma rays is an impulse function situated at the incident gamma ray energy. See Figure 2 for a drawing of this. Figure 2. Energy Spectra of Photoelectric Absorption for a Monoenergetic Gamma Ray. 2.Compton Scattering Normally all scattering angles will occur in the detector. This means that the energies from the recoil electron will be distributed randomly between 0 and Eγ. For one specific random gamma ray interaction, the electron energy distribution will fit the curve shown in Figure 3. Figure 3. Electron Energy Distribution of Compton Scattering from a Monoenergetic Gamma Ray. The point marked hν is the total energy of the original gamma ray (Eγ). This energy is distributed between a recoil electron and a scattered gamma ray photon. The energy Ec is the gap between the incident gamma ray energy and the maximum Electron recoil Energy at Θ=180 degrees. Equation 6 describes this energy. Eγ E C = Eγ − E e − ( Θ = Π ) = 1 + 2 *  Eγ Equation 6:  511KeV     8
  • 9. a)Compton Edge If the incident gamma ray energy is much larger than ½ * 511 KeV, then Equation 6 goes to a constant value of 256 KeV. Therefore the Compton edge is about 256 KeV less than the incident gamma ray energy (See Equation 7). Equation 7: ECE = Eγ − 256keV b)Backscatter The backscatter peak is from source gamma rays that have interacted by Compton scattering in the shielding material, and have been deflected back into the detector. The energy of the Compton scatter is described by Equation 2, and when the scattering angle is set to 180 degrees, Equation 2 simplifies to Equation 8. If the incident gamma ray energy is much greater than ½ * the energy of an electron or positron, then Equation 8 can be simplified into Equation 9. Eγ Eγ ' (Θ = 180) = 1 + 2 *  Eγ Equation 8:  511KeV     511KeV Equation 9: Eγ ' (Θ = 180) = = 256 KeV 2 3.Pair Production An ideal pair production energy spectrum is a delta function at the incident gamma ray energy minus the total energy of an electron and a positron. This difference is from the escape of the annihilation photons when the positron combines with another electron and releases their equivalent energy of 1.02 MeV. Figure 4. Pair Production Energy Distribution from Monoenergetic Gamma Ray Interaction 9
  • 10. This energy peak is called a double escape peak, because both annihilation photons escape. It is described by Equation 10. Equation 10: E DE = Eγ − (2 * 511KeV ) C.Response functions 1.Small Detectors A gamma ray detector is considered “small”, if its size is less than the mean free path of the secondary gamma radiations produced in interactions of the original gamma rays. This dimension is often between 1 and 2 cm. The energy range due to the different angles of scattering is called the Compton continuum. The narrow peak corresponding to the photoelectrons from the incident gamma ray is called the photopeak. By definition, the small detector is sufficiently small that only single interactions take place. If the gamma energy is high enough (much greater than 1.02 MeV), pair production will occur. The electron and positron kinetic energies will be deposited, and both resulting 1.02 MeV annihilation photons will escape. 2.Very Large Detectors A gamma ray detector is considered “large” when all incident and secondary gamma rays interact inside the detector volume. In the real world, this is on the order of 10’s of centimeters. All the interactions from the incident gamma ray occur so fast that they are electronically indistinguishable. Therefore the spectrum that is detected looks like a perfect photopeak, just as if the incident gamma ray had undergone one photoelectric interaction. 3.Intermediate Size Detectors Realistically detectors fall into the intermediate size range. These detectors recover some of the secondary gamma ray energy that is produced. Figure 5 shows a picture of such a detector. 10
  • 11. Figure 5. Monoenergetic Gamma Ray Interactions in an Intermediate Size Detector The low to medium energy gamma rays consist of a Compton continuum and a Full Energy Peak. The relative area under the Full Energy Peak increases with decreasing gamma ray energy due to the high Photoelectric Cross Section (σpe) at low energies. At medium energies, multiple Compton scatters and the escape of the final scattered photon can fill in the gap between the Compton edge and the photopeak. If the gamma ray energy is high enough to cause pair production, one or both of the annihilation photons may escape without being detected. This is called a single escape, and double escape peak respectively. The energy of a single escape peak is described by Equation 11, while the energy of a double escape peak is described by Equation 10. 11
  • 12. Equation 11: E SE = Eγ − 511KeV D.Energy Resolution Equation 12 can be used to find the Energy Resolution of the detector, where FWHM is the Full Width at Half Maximum count rate of the Full Energy Peak, and Ho is the Mean Pulse Height of the same peak. FWHM Equation 12: R = Ho 12
  • 13. IV.Experimental Design and Procedure A.2” x 2” NaI:Tl scintillator setup and procedure The 2x2 NaI:Tl scintillator was connected to the MCA and support electronics as shown in Figure 6. HV 1000V Osc. 2” x 2” NaI:Tl p Am Pre- 32x p Am Scintillator MCA Figure 6. 2” x 2” NaI:Tl scintillator Experimental Setup First, the MCA was used to take a 5-minute background count in Live Time Mode. This data was saved as filename MCA_Bkgnd in Aptec .S0 and .CSV format. Second, a Cs-137 source was inserted in the detector and a 5-minute count was taken. This data was saved as filename MCA_CS137 in Aptec .S0 and .CSV format. Third, a Co-60 source was inserted into the detector and a 5-minute count was taken. This data was saved as filename MCA_Co60 in Aptec .S0 and .CSV format. Fourth, a Na-22 source was inserted into the detector and a 5-minute count was taken. This data was saved as filename MCA_Na22 in Aptec .S0 and .CSV format. Fifth, an unknown source was inserted into the detector and a 5-minute count was taken. This data was saved as filename MCA_Unknown#1 in Aptec .S0 and .CSV format. Sixth, a bonus source was inserted into the detector and a 5-minute count was taken. This data was saved as filename MCA_Bonus in Aptec .S0 and .CSV format. 13
  • 14. B.5” x 5” NaI:Tl scintillator setup and procedure The 5” x 5” NaI:Tl scintillator was connected to an SCA, MCA, and the associated electronics as shown in Figure 7. HV 1000V Osc. 5” x 5” NaI:Tl p Am Pre- 4x p Am SCA T/C Scintillator MCA Figure 7. 5” x 5” NaI:Tl scintillator Experimental Setup First, the SCA and the MCA were both used to take a 5-minute background count. The MCA data was saved as filename SCA_Bkgnd in Aptec .S0 and .CSV format. Second, a Cs-137 source was inserted in the detector and the SCA was used to take 1-minute counts of the source using an energy window of 0.05 Volts. The count was done until the spectrum flat lined after the Full Energy Peak. The ending point was 1.5 volts. This data was saved as filename SCA_Cesium-137.xls. 14
  • 15. C.Equipment Used Table 1 details a list of equipment used in this lab. Table 2 details the manufacturer and activities of the sources used in the MCA portion of the lab, and the mixed SCA/MCA portion of the lab. Table 1: Equipment Type and Model Numbers used in Lab Equipment Name Manufacturer, Model # 2”x2” NaI:Tl Scintillator Bicron, #155415 5”x5” NaI:Tl Scintillator 5MT4/5L Preamplifier EG&G Ortec #113 High Voltage Supply (HV) Tennelec TC945 Amplifier (Amp) Canberra 2012 Single Channel Analyzer Canberra 2031 (SCA) Counter/Timer (C/T) Canberra 1772 Multi-Channel Analyzer (MCA) Aptec Model 5008 SCA Oscilloscope Tektronix 2205-40 MCA Oscilloscope Tektronix 250 Table 2: Table of Radioactive sources used for lab Source Activit Date of Manufacturer / Model# y Manufacture MCA Sources 137 Cs 1 uCi 4/96 Oxford Model S-13 60 Co 1 uCi 4/96 Oxford Model S-13 22 Na 1 uCi 4/96 Oxford Model S-13 Unknown ? 4/96 ? Extra Credit ? 4/96 ? SCA Sources 137 Cs 1 uCi 12/17/1980 New England Nuclear 15
  • 16. V.Results and Discussion A.Single Channel Analyzer 1.Identify Peaks in Cs-137 Pulse Height Spectrum taken by SCA From Table 4 in Appendix 4, it can be seen that the 662 KeV full energy peak of Cs-137 is actually one of the gamma ray emissions from its decay product Ba-137m. Looking at the plot of Cs-137 Source+Background Count Rate vs. Mean Window Voltage in Appendix 3, this peak appears at around 1 Volt. It is known that this is the Full Energy Peak, because it is the highest peak, and very well defined. The next lowest peak appears at about 0.4 Volts, and is a backscatter peak because it is poorly defined and is at 0.25 MeV or less. The next lowest peak appears at around 0.15 Volts and is an X- Ray peak from interaction of a primary gamma ray with the shielding material. Finally the lowest peak is at about 0.1 volts, and is due to instrumentation error. 2.Determine Detector Resolution SCA Detector Resolution was determined from a plot of Source+Background (S+B) Count rate vs. Mean Window Voltage for Cs-137. The measured SCA count of B could not be subtracted from S+B, because the B was from the entire energy spectrum of the detector, while the S+B spectrum was binned in increments of 0.05 volts. Instead, the B count rate under the full energy peak was visually estimated as 9.9167 cps. Since the S+B Maximum Height was 210.05 cps, the Full Width, Half Maximum S+B level was found by dividing the Maximum S+B by two. This yielded 105.025 cps. Next a slope and y-intercept was found for each of the two lines that defined either side of the S+B peak. The S+B (y value) of these two equations were set to Ho/2, and a corresponding Mean Window Voltage (x value) was calculated. Finally, the two Mean Window Voltages were subtracted to find the FWHM. This value was used in Equation 12 to calculate an energy resolution (R) of 0.05%. The natural log of this Energy Resolution is –2.99. The FWHM found by using the automated function on the Multi-Channel Analyzer was 7.89%, whose natural log R = 2.07. Per Knoll, page 331, the average 16
  • 17. NaI(Tl) scintillator energy resolution for a sampling of several units of the same design was between 10-11% (Knoll). The experimentally measured Energy Resolution in Knoll, Table 10.17 is –2.1 for Cs-137 (Knoll). 3.Compare SCA Spectra with MCA Spectra The SCA spectrum has far less resolution than the MCA spectrum. The SCA spectrum completely missed one of the peaks at 27.96 KeV or 4.93 KeV. It may have blended the two peaks into one peak because our resolution was much lower with the SCA windowing technique. B.Multi-Channel Analyzer 1.Detector Resolution using Cs-137 From the MCA Paint Function, the detector resolution can be calculated. For Cs-137, the Centroid (Ho) can be defined as 661.65 KeV (Hacker), while the FWHM is 52.48 KeV. Using Equation 12, this gives an energy resolution of 7.93%. See Appendix 3 for plots and denotation of peaks. 52.48 KeV % Energy Re solution = *100% 661.65 KeV 2.Detector Resolution using Na-22 Using the MCA Paint function again, the detector resolution can be calculated. For Na-22 Full Energy Peak, Ho is equal to 1274.5 Kev (Hacker), and the FWHM is 37.34 KeV. Using Equation 12, this gives an energy resolution of 2.93%. See Appendix 3 for plots and denotation of peaks. 37.34 KeV % Energy Re solution = * 100% 1274.5KeV Table 3 is a summary of all the known and unknown feature energies and channel numbers. The source plots with the features labeled can be found in Appendix 3. 17
  • 18. Table 3: Radionuclide Peak Definitions, Channel Numbers and Energies Radionuclid Peak Name Energy Channel Number e (KeV) Cs-137 Full Energy 661.65 688 Compton Edge 462.28 481 Backscatter 224.9 234 X-Ray 148.01 154 Instrumentation 19.22 20 Na-22 Full Energy 1274.5 1284.58 Annihilation 529.81 534 Compton Edge 1141.97 1151 Backscatter 200.42 202 Instrumentation# 19.84 20 1 Instrumentation# 9.92 10 2 Co-60 Full Energy #1 1332.5 1348 Full Energy #2 1173.9 1188 Compton Edge 946.98 940 Backscatter #1 217.49 167 Backscatter #2 321.3 277 Instrumentation# 69.32 10 1 Instrumentation# 78.76 20 2 Unknown Full Energy#1 385.2965 377.28 Full Energy#1 95.4458 93.46 Compton Edge Backscatter 190.97 187 Compton Edge Bonus Full Energy#1 2644.5831 2589.56 18
  • 19. 3.Unknown Identification The Energy Calibration Plot in Appendix 3 was made of the known Photopeak Energies vs. MCA Channel number. The slope was calculated from the Least Squares Regression of these known data points. This slope, and a Y-Intercept of 0 were used to plot a best-fit line along these original data points. The Y-Intercept was set to 0 because at Channel #0 we should get 0 energy. Next, the unknown channels were put into the equation, and a corresponding energy was output. The range for this energy was defined as FWHM/2. See Appendix 3, Original Data for Plots. From the fit, the unknown should have gamma ray energy of 385.3 KeV and gamma ray energy of 95.45 KeV with FWHM of 33.93 KeV, and 22.7 KeV, respectively. Using the FWHM/2 search criteria, elements with gamma ray energy of 385.3 +/- 17 KeV and 95.45 +/- 12 KeV were searched. The fractional emissions were arbitrarily chosen to be greater than 0.01 for both of these gamma ray emissions. The next sieve involved looking at the half-lives. Half-lives of less than 1 yr were eliminated. After eliminations, the result was Cf-249, although upon closer inspection (See Appendix 4), the fraction of emission (fp) for a 104.6 KeV photon is 0.02, while the fp for a 387.95 KeV photon is 0.66. Looking at the unknown curve in Appendix 3, the lower energy peak has a higher count rate than the higher energy. If this were Cf-249, the Higher Energy peak would show more counts. 4.Determine the Activity of the Cs-137 Equation 13 gives decrease in Activity after a time if the initial activity is known. Equation 13: A = Ao * e − λ*t From Table 2, Cs-137 was 1 uCi (37KBq) on 4/96. At the date of the lab, which was 2/28/01, the activity is calculated in Appendix 3 as 33052 Bq. VI.Conclusions A.2” x 2” scintillator compared to 5” x 5” scintillator The instrumentation peak of the 5”x5” scintillator is almost non-existent when compared to the 2”x2” scintillator. The resolution of the 5”x5” plot is 19
  • 20. also finer. The photopeak shows many more counts were captured inside of the 5”x5” detector that must have escaped the 2”x2” detector, or must have undergone a Compton Scatter event instead of a Photoelectric event. This is in agreement with the theory, which states that in a larger detector, more of the interactions will look like Full Energy Peaks because they lose all their energy inside the larger scintillator. A perfect detector would have infinite size, and show only photoelectric peaks. B.Method of determining Unknown The plot of Photopeak Energy vs. Channel number yielded a strange curvefit. The y-intercept was equal to approximately –41 KeV. At Channel = 0, the Energy cannot be negative, so the Y-intercept was set to 0, which raised the entire curvefit off from the data points. This could be a source of error in the determination of the unknown source. The identification of the unknown through passing nuclides of interest through successive sieves is a good technique. It would be better to be able to do a logic query on the nuclides of interest to make sure the count rate of a high fractional emission photopeak was higher than a lower fraction of emission photopeak. The MCA Aptec program did not allow the subtraction of background. Hence, the data file was manipulated in Excel and MCA for the necessary results. 20
  • 21. VII.References Table of Authorities Knoll, Glenn F, (1999), Radiation Detection and Measurement, Third Edition. Hacker, Charles, (March 1997). Radiation Decay Software, Version 2. Fjeld, Robert, (8/24/2000), Clemson University EES610 Notes http://www.cea.com/cai/augtheo/process.htm, “Auger Process” 21
  • 22. VIII.Appendix III – Original Data 22
  • 23. IX.Appendix IV – Other Table 4: Ba-137m (Cs-137 daughter) Photon Emission Products (Hacker) Energy Emission Fraction (MeV) 0.004470 0.010381 0.031817 0.020703 0.032194 0.038197 0.036400 0.013900 0.661650 0.899800 Table 5: Na-22 Photon Emission Products (Hacker) Energy Emission Fraction (MeV) 0.000849 0.001250 1.274500 0.999400 0.511000 1.798000 Table 6: Co-60 Photon Emission Products (Hacker) Energy Emission Fraction (MeV) 1.173200 1.000000 1.332500 1.000000 0.693820 0.000163 23
  • 24. Table 7: Cf-249 Photon Emission Products (Hacker) Energy Emission Fraction (MeV) 0.015000 0.302620 0.054730 0.002112 0.092300 0.002970 0.104610 0.021944 0.109290 0.034998 0.123000 0.016627 0.241200 0.002244 0.252850 0.027324 0.266730 0.007458 0.295840 0.001426 0.333440 0.155100 0.387950 0.660000 0.283680 0.004336 24