Measurement of Krypton Fission Product Yields from 14 Mev Neutrons on 238U

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Measurement of Krypton Fission Product Yields from 14 MeV Neutrons on 238U

Ellen Edwards

A dissertation submitted in partial satisfaction of the

requirements for the degree of

Doctor of Philosophy

Engineering – Nuclear Engineering

in the

Graduate Division

of the

University of California, Berkeley

Committee in charge:

Professor Edward Morse, Chair Professor Lee Bernstein Professor Yasunori Nomura Dr. Charles Yeamans

Summer 2018 Measurement of Krypton Fission Product Yields from 14 MeV Neutrons on 238U

Abstract

Measurement of Krypton Fission Product Yields from 14 MeV Neutrons on 238U by Ellen Edwards Doctor of Philosophy in Engineering – Nuclear Engineering University of California, Berkeley Professor Edward Morse, Chair

Precisely-known fission yield distributions are used to determine a fissioning isotope and the incident neutron energies in nuclear security applications. 14 MeV neutrons from DT fusion at the National Ignition Facility (NIF) induced fission in depleted uranium (DU) contained in the target assembly hohlraum. The fission yields of Kr isotopes (85m, 87, 88, 89, and 90) were measured relative to the cumulative yield of 88Kr. The fission gas was pumped from the target chamber, collected, and analyzed in the Radiochemical Analysis of Gaseous Samples (RAGS) diagnostic. Isotopes with half-lives ranging 8 s-9 hr can be measured. Kr fission yields have been measured both from the fission of DU in the hohlraum and DU doped into the capsule ablator. Since the mass of U was not known, the relative amounts of Kr isotopes were calculated and compared to existing fission product distribution tables. It was found that measurements can be performed with high precision for isotopes with half lives longer than 4 minutes. A more precise quantification of gas transport needs to be achieved to quantify isotopes with shorter half lives to a precision of the published tables. i

To my family: Debbie, Ken, and Rachel Edwards. ii

Contents

Contents ii

List of Figures iv

List of Tables vi

1 Fission 1 1.1 Motivation ...... 1 1.2 Background ...... 2 1.3 Fission Theory ...... 5

2 Nuclear Forensics 10 2.1 Fission Product Yields ...... 10 2.2 Comprehensive Test Ban Treaty ...... 11 2.3 Debris Analysis ...... 13 2.4 Chronometry ...... 13

3 National Ignition Facility 17 3.1 NIF Basics ...... 17 3.2 Capsules ...... 18 3.3 Diagnostics ...... 20 3.4 Neutron Spectrum ...... 21 3.5 NIF for Fission Experiments ...... 23

4 Measurements of Gaseous Fission Products 24 4.1 Radiochemistry Experiments ...... 24 4.2 On-Line Isotope Separation ...... 24 4.3 This Experiment: NIF Radiochemical Analysis of Gaseous Samples . . . . . 25

5 Data Analysis 31 5.1 Data ...... 31 5.2 Energy and Eﬃciency Calibration ...... 37 5.3 Peak Fitting ...... 39 iii

5.4 Determination of Isotope Activity as Function of Time ...... 41 5.5 Fit Exponential Decay and Extrapolate to Shot Time ...... 44 5.6 Ratios ...... 45 5.7 Correction for Pumping Speed and Time ...... 47

6 Model Analysis and Fission Yield Determination 51 6.1 Distribution of Independent Yields ...... 51 6.2 Pumping Time Constant ...... 52 6.3 Delayed Neutrons ...... 53 6.4 85mSe...... 54

7 Results 56 7.1 Overall Results ...... 56 7.2 85mKr ...... 57 7.3 87Kr ...... 58 7.4 89Kr ...... 59 7.5 90Kr ...... 61 7.6 Uranium-Doped Capsules ...... 62 7.7 Comparison to SRCs ...... 63 7.8 Conclusions and Future Work ...... 64

Appendix A Gamma Ray Data 65 A.1 85mKr ...... 66 A.2 87Kr ...... 67 A.3 88Kr ...... 68 A.4 89Kr ...... 71 A.5 90Kr ...... 79 A.6 138Cs...... 82 A.7 138Xe...... 85

Bibliography 88 iv

List of Figures

1.1 Independent and cumulative yields...... 3 1.2 Fission Process. From [8]...... 4 1.3 Potential energy barrier of fission as a function of deformation...... 6 1.4 Diagram showing the splitting of nuclear energy levels with deformation. . . . . 7 1.5 Mass of the two fission products for different fissioning masses...... 8

2.1 Fission product distributions change based on neutron energy and fissioning mass. 11 2.2 Kalinowski diagram showing ratios of Xe isotopes for different sources of Xe. . . 12 2.3 4n+2 nuclides ...... 14 2.4 Time since 238Pu separation using different isotopes in its decay series. From [12]. 15 2.5 Spontaneous fission products from 240Pu. From [12]...... 16

3.1 NIF target. Figure from [24]...... 18 3.2 Cross section view of the outer edge of a lined depleted uranium hohlraum. From [25]...... 18 3.3 A typical CH capsule. From [25]...... 19 3.4 X-ray radiographs of capsules with and without DU dopant. Photos courtesy of General Atomics...... 20 3.5 NIF target chamber. From [32]...... 21 3.6 Simulated neutron spectrum from NIF...... 22

4.1 Schematic of RAGS...... 25 4.2 RAGS diagnostic...... 26 4.3 Coldhead with vacuum housing removed. The copper heat strap was originally aluminum. From [62]...... 28 4.4 Comparison of activity in collector with and without a translating detector. . . . 30

5.1 List mode data using 5 minute time bins...... 32 5.2 A histogram created by taking a time slice from Figure 5.1...... 33 5.3 Plotting the intensity of the photopeak at 402 keV vs time. This peak can also be observed in Figure 5.1. Error bars omitted for clarity...... 34 5.4 List mode data using 1 second time bins...... 35 v

5.5 A section of the Chart of the Nuclides [63]. Small squares indicate metastable states. Kr isotopes decay to Rb isotopes of the same mass...... 36 5.6 A typical measured efficiency curve for HPGe detectors...... 37 5.7 Fitting a photopeak from 87Kr...... 39 5.8 Similar to Figure 5.7 but for 89Kr. The photopeak at 586 keV is not fully resolved so instead of a single Gaussian fit, a double Gaussian is fit to the background- subtracted data...... 40 5.9 Relative activity of 87Kr vs time. This is the area calculated from the Gaus- sian peaks (Figure 5.7) at each time step, corrected for dead time and relative efficiency. It decays with the half life of 87Kr, 1.2 hr...... 42 5.10 Converting activity from Figure 5.9 to atoms and extrapolated to shot time. The detector moves from 11.5” to 5” from the sample after 5 hrs...... 45 5.11 Ratio of 87Kr / 88Kr atoms extrapolated to shot time...... 46 5.12 Decay chain for mass 87 ...... 48 5.13 Illustration of the effect pumping speed and duration has on 85mKr collected in RAGS. Because the half life of 85Br is non-negligible compared to pumping time, not all 85mKr is transferred to RAGS from the target chamber...... 50

6.2 Amount of 89Kr collected for 3 different pump speeds. The difference is most pronounced during pumping but the final amount differs by only 2.61% at the end of the collection period...... 53

7.1 Cumulative yield ratios from RAGS experiments and evaluations...... 57 7.2 Cumulative yield ratios (relative to 88Kr) measured by RAGS for individual shots. The weighted average is shown in black and JEFF value in red. The 1% error bar for the RAGS value is too small to see on this scale...... 58 7.3 Cumulative yield ratios (relative to 88Kr) measured by RAGS for individual shots. The weighted average is shown in black and JEFF value in red...... 59 7.4 Cumulative yield ratios (relative to 88Kr) measured by RAGS for individual shots. The weighted average is shown in black and JEFF value in red...... 60 7.5 Example of a shot with a corroded Ge detector. Low-energy channels do not have data for approximately an hour, preventing the measurement of 89Kr and 90Kr. . 61 7.6 Cumulative yield ratios (relative to 88Kr) measured by RAGS for individual shots. The weighted average is shown in black and JEFF value in red...... 62 7.7 Measurement of surface roughness in a U-doped capsule. Courtesy General Atomics. 63 vi

List of Tables

5.1 Energies used for energy and efficiency calibrations...... 38 5.2 Coefficients at two different times for a Gaussian fit to the 577 keV and 586 keV photopeaks of 89Kr...... 41 5.3 Nuclear data for the isotopes measured in this work. Additional nuclear data is listed in the appendix. Data from [66], [64], [65], [67], [69]...... 41 5.4 Contributions to uncertainty for an individual data point in Figure 5.11. . . . . 46 5.5 Factors to account for pumping speed and duration on Kr collected in RAGS. . 50

6.1 Errors of independent yields of Br isotopes [3] ...... 51 6.2 Change in amount of Kr collected by varying the pump time constant from 160- 200 s. A * indicates an average is taken from 780-900 s for 89Kr and 120-200 s for 90Kr...... 53 6.3 Probability of decaying to another element of the same mass. If the value is 100%, the isotope decays only by β− decay. If the value is less than 100% it partially decays by β− and neutron emission. Data from [7]...... 54 6.4 Diﬀerence from including delayed neutrons as part of independent yields vs throughout pumping interval. The correction is less than 1% for all Kr isotopes studied. 54 6.5 Independent and cumulative yields from England and Rider [3] and JEFF 3.1 [1]. 55

7.1 NIF shots with DU doped into the capsule ablator...... 63 vii

Acknowledgments

Thanks to:

RAGS Engineers: Don Jedlovec, Allen Riddle, Jaben Root, and Tony Golod. For keeping RAGS running during data collection even if it meant going to work at 2 am.

Bill Cassata and Carol Velsko: For all your help with familiarizing me with RAGS.

Dawn Shaughnessy: For your mentorship and being my adopted lab mentor at the last minute.

Ed Morse, my advisor: For getting me involved in this work.

Charles Yeamans, my lab mentor: For putting up with me for 4 years, doing (lots of) extra paperwork because of me, making fun of me for being a grad student, teaching various life skills and that throwing heavy objects at pins is a good way to let oﬀ frustration. I may still want your shed.

This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. 1

Chapter 1

Fission

1.1 Motivation

Stimulated fission is the process where a neutron is absorbed by a heavy nucleus, subsequently forming a compound nucleus that splits into two fragments and 2-3 neutrons. The amounts of the resulting fragment nuclides are usually distributed with masses roughly 1/3 and 2/3 of the mass of the original compound nucleus. The exact distribution is a function of neutron energy and fissioning isotope. After a nuclear explosion, debris is collected and nuclides are measured. Using nuclear data, including fission product yields, information about the event such as neutron spectrum or fissioning material, can be deduced. The conclusions drawn from the measurements rely on nuclear data on fission product yields. Yields are readily available in evaluations, for example JEFF [1] and ENDF [2], which is based on the work of England and Rider [3]. The fission-inducing neutrons may have several energies, or there may be more than one fuel material, or the presence of other materials may moderate the neutron spectrum. Models must be made to incorporate these complications. These models rely on precise fission product yield data. Even if a nuclide is not directly observed in the debris, it could still be important if it decays to other isotopes. The Radiochemical Analysis of Gaseous Samples (RAGS) is a diagnostic at the National Ignition Facility (NIF) capable of measuring fission-product noble gasses. In this work 238U is fissioned by 14 MeV neutrons (created from fusion at NIF) and the noble gas (Xe and Kr) is collected in RAGS. This work will focus on the measurement of Kr isotopes produced from fission. Even though the data for the products of this particular combination of neutron energy and fuel is well known, in the future RAGS could be used to study different materials with poorly-known fission product yields, thus improving the data used in nuclear forensic investigation. CHAPTER 1. FISSION 2

1.2 Background

In the 1930’s Fermi investigated beta decays of the products of neutron-induced reactions. It was known that β− decay produced an isotope of the same mass but one higher atomic number. When he hit U with neutrons he assumed transuranic elements were produced. A variety of half lives were observed, which were explained by successive neutron captures [4]. Hahn and Straussman repeated the experiments and observed isotopes of known elements such as Ba and La [5]. Meitner and Frisch hypothesized that U split into roughly equal parts [6], conserving the number of protons in the original U nucleus. Fission is often caused by a neutron hitting a heavy nucleus (certain nuclei also sponta- neously fission), causing it to split into two (occasionally 3) smaller fragments with roughly 1/3 and 2/3 of the original nuclear mass, and 2-3 neutrons. There is a probability distribution of the fragment masses, which results in many elements observed after fission. A probability distribution for 238U is shown in the lower left of Figure 1.1. The total number of protons and neutrons are conserved. The resulting fission products lie on the neutron-rich side of the line of stability, and beta decay to stable isotopes. Two important measurements are the independent yields and cumulative yields of the fission products, illustrated in Figure 1.1. The 88 mass chain is used as an example. The elements Sr, Rb, Kr, Br, and Se are all produced directly from fission. The fraction produced of each isotope per starting nucleus is called the independent yield. These isotopes are radioactive and undergo β− decay. 88Se decays to 88Br. The sum of the amount of 88Br produced from its independent yield and the decay from 88Se is called the cumulative yield. 88Br decays to 88Kr. The cumulative yield of 88Kr is composed of its independent yield as well as the cumulative yield of 88Br (which includes 88Br from the decay of 88Se). The independent and cumulative yields from fission are important for nuclear forensic analysis, discussed in the next chapter. Figure 1.2 shows the progression of a fissioning nucleus. First an incoming particle such as a neutron is absorbed by a nucleus. The excited nucleus deforms and eventually splits into two fragments that travel away from each other. Neutrons and gamma rays are also released. The fragments are heavy relative to the line of stability and beta decay to stable products. CHAPTER 1. FISSION 3

Figure 1.1: The plot on the bottom left shows the mass distribution of fission products for 238U fissioned by 14 MeV neutrons [3]. The most probable masses are roughly 1/3 and 2/3 of 239, the fissioning system’s mass. The blue arrows demonstrate independent and cumulative yields of mass 88. Independent yields are the amount of Sr, Rb, Kr, Br, and Se produced directly from fission. These isotopes decay. The cumulative yield is the integral over time of all of a particular isotope produced both by fission directly and by the decay of other isotopes. Data from [3] and [7]. CHAPTER 1. FISSION 4

Figure 1.2: Fission Process. From [8]. CHAPTER 1. FISSION 5

1.3 Fission Theory

There are many different models of fission. Macroscopic and macroscopic-microscopic models depend on assumptions about the coupling between individual nucleons and the collective nuclear excitations, and how excited states are calculated [9]. Fully quantum-mechanical models of fission have been developed which use different approximations for nuclear inter- actions and energy levels [10]. Here the liquid drop model will be described, which represents the forces on the nucleus in similar manner to those exerted on a drop of liquid as it deforms. The liquid drop model describes fission as a competition between the coulomb energy, which tries to rip the nucleus apart, and the surface energy, which holds it together [11]. The liquid drop model is related to the semiemperical mass formula below [9]:

BE = a A − a A2/3 − a Z2/A1/3 − a (A − 2Z)2/A ± δ v s c a (1.1) BE = volume − surface − coulomb − asymmetry ± pairing The volume and pairing terms are not important for fission because they depend on the number of protons and neutrons, which are conserved in fission. The second term is related to the surface area. The nucleons on the surface are bound to fewer other nucleons, so there is more reduction in binding energy when the nucleus is extremely deformed from spherical. Next is the Coulomb term which accounts for the repulsion between protons. If the nucleus is deformed, the protons are spread out so the Coulomb force is weaker, which increases the total binding energy. The final term, the pairing term, reflects the change in energy due to spin coupling between nucleons. In the liquid drop model the pairing term is ignored. The only terms left for fission are the surface term and the Coulomb term. If a nucleus becomes deformed, the Coulomb energy will become less negative and the surface energy will become more negative. The nuclear surface can be represented as a sum of Legendre polynomials, Pn(θ), that describe the axial deformation of a nucleus [11]. If the radius of the sphere is deformed by a factor of 1 + α0 + α2P2(θ) + ... (1.2) then the surface energy is 0 2 Es = Es (1 + 2/5α2 + ... ) (1.3) and the Coulomb energy is 0 2 Ec = Ec (1 − 1/5 α2 + ... ) (1.4) 0 0 where Ec and Es are the electrostatic and surface energies of a spherical nucleus and α2 is the quadrupole distortion. Substituting Equations 1.2-1.4, a nucleus becomes unstable when 0 0 0 ∆Ec/∆Es = (Ec − Ec )/(Es − Es ) = x = Ec /2Es = 1 (1.5) x is called the fissility parameter. Values of x for actinides are around 0.7-0.8. If x>1 the nucleus will split without added energy but if x<1 it will remain whole. x is proportional to Z2/A of the fissioning nucleus. CHAPTER 1. FISSION 6

Using the liquid drop model, it was possible to calculate the potential energy of the nucleus at different points on its path to fission. It predicted a potential energy barrier with 1 hump, which had to be overcome for fission to occur.

(a) Potential energy as fission progresses. In- duced fission occurs an energy above the potential energy barrier, but isomeric and spontaneous fission require tunnelling. The fission barrier is proportional to Z2/A. From (b) The effect of the shell model on the fis- [12]. sion barrier. The top picture shows the barrier using only the liquid drop model. When shell effects are added the two-humped fission barrier is produced. From [13].

Figure 1.3

The liquid drop model predicts a symmetric mass split to be most probable, but in reality most nuclei divide into a heavy and light nucleus, roughly 1/3 and 2/3 of the total mass. Strutinsky [14] had the idea to include shell effects into the liquid drop model by treating the shell effects as a small perturbation from the liquid drop energy. This model produced a fission barrier with 2 humps as shown in Figure 1.3. Figure 1.3a shows the progression of fission [12]. For induced fission, the energy of the incoming particle populates excited states that overcome the potential energy of the nucleus being held together. Spontaneous fission occurs when the nucleus tunnels through the fission barrier. In the liquid drop model (top of Figure 1.3b), there is only one potential well but when shell effects are included there are two wells. As shown in Figure 1.4, nuclear energy levels split as the nucleus deforms, which affects the shell correction. Spontaneous fission can result from states in either well, and are referred to as fission isomers. As shown in the top of figure 1.3a, nuclei in the second well are more deformed than those in the first. That is why they CHAPTER 1. FISSION 7

are sometimes called shape isomers. States in the ﬁrst well must tunnel through the entire ﬁssion barrier but states in the second well only have to tunnel through the second hump.

Figure 1.4: Diagram showing the splitting of nuclear energy levels with deformation. The vertical axis is the level energy. The horizontal axis is deformation. There is no deformation where η=0 and the nucleus becomes more prolate η increases. Oblate levels, which would have negative η, are not shown. The lines on the diagram represent the split levels from the spherical nucleus, with their spins and parities labelled. The numbers on the right are arbitrary and the circled numbers are magic numbers. From [15].

The model including shell effects resulted in a fission product distribution agreeing with experimental measurements of fission products. The heavy fragment mass peaks at a value independent of the mass of the fissioning nucleus because of shell effects (Figure 1.5 [16]). The lower edge of the heavy peak is at A=132, which is doubly magic when Z=50 and N=82 [17]. Also as neutron energy increases the shell correction becomes less important, so the mass split is more symmetric. Experiments showed that the mass distributions from fission change a lot, even when the nuclei are not at magic numbers. For example, 257Fm (Z=100, N=157) spontaneous fission is symmetric but neutron-induced fission of 257Fm is mostly asymmetric [18]. The CHAPTER 1. FISSION 8

Figure 1.5: Mass of the two fission products for different fissioning masses. The light element’s mass changes a lot but the heavy element’s mass does not change much because of nuclear shell effects. From [16]. reason is that magic numbers are different when nuclei are deformed instead of spherical [17]. Wilkins [19] developed a theory that takes into account only the energy and deformation of the fragments at scission instead of the complete nucleus. For the purpose of seeing if the theory was feasible and explained general trends, they assumed a value for the distance between fragments at scission. Later, other scientists, such as [20], built on their theory and used different values for the distance. However, the Wilkins model was not perfect and did not predict the mass split correctly for all isotopes. Panebianco [20] modified the Wilkins model by using a microscopic approach CHAPTER 1. FISSION 9 to describe the energy instead of the liquid drop model. They also used a different distance between the fragments at scission. If the distance between fragments is larger the Coulomb energy decreases, which leaves more total energy available. Structure effects become more important if this is the case. 10

Chapter 2

Nuclear Forensics

2.1 Fission Product Yields

Fission fragments measured following a nuclear explosion are used in nuclear forensics to shed light on the neutron spectrum that induced fission in the nuclear device. Three fuels (235U, 238U, 239Pu) likely to be present in a nuclear weapon and two energy groups (fast, high energy) result in six different combinations of fuel and neutron energy and result in the formation of different fission fragment distributions. The term “fission split” refers to the relative contribution of each of the 6 components [12]. Depending on the type of fissioning fuel and the energy of the incoming neutron, the resulting fission split will have a different distribution of fission product nuclei. One purpose of nuclear forensic analysis is to deduce the fission split based on the measurement of debris of a nuclear event. The fission product distribution depends on the fissioning mass and neutron energy. Figure 2.1a demonstrates fission yields for 235U for 3 different neutron energies. the values at the peaks do not change much because of the doubly magic nucleus Z=50, N=82, but the valley and wing products change orders of magnitude when neutron energy changes. Figure 2.1b is a plot of fission yields for the same neutron energy on different isotopes. The high-mass peak does not change (due to the shell effects discussed earlier) but the low-mass peak moves to the right to conserve mass. The wing products on the high-mass side have a large variation. By measuring the amounts of several fission product sensitive to the fission split, it can be determined. During a nuclear event, other neutron-induced reactions occur in the device’s structural materials and in the soil. Some of the isotopes produced form these reactions are also fission products, so the non-fission products have to be subtracted from the total amount measured in the soil after an event. A common way to find the non-fission signal is to measure an activation product that is not produced in fission to find the neutron flux. Then the flux and cross sections are applied to the soil sample to find activation of other elements in the soil that are not fission products [12]. CHAPTER 2. NUCLEAR FORENSICS 11

(a) (b)

Figure 2.1: Fission product distributions change based on neutron energy and fissioning mass number. Figure 2.1a shows that fission becomes more symmetric when the neutron energy increases. Figure 2.1b shows the left peak shifts to the right as the fissioning mass number increases. Each line in the graphs represents the fissioning nucleus and the neutron energy. t, f, and h are for thermal (0.025 eV, thermal reactors), fast (up to few MeV, fast reactors), and high energy (14 MeV, DT fusion) neutron energies. Data from [3].

2.2 Comprehensive Test Ban Treaty

The Comprehensive Test Ban Treaty (CTBT) is an international treaty banning nuclear testing. The International Monitoring System (IMS) is a network of 321 stations and six- teen laboratories throughout the world that detect nuclear events. Eighty of these stations monitor gases. Forty of them have equipment to measure noble gases [21]. Noble gases that are released travel as part of the atmosphere and remain there, which allows detection long after the nuclear event has occurred. Other elements such as Cs or I attach themselves to dust particles and are spread as aerosols. Large particles do not travel far but smaller particles travel in a plume. Sometimes they leave the atmosphere as precipitation but they can also be transported quickly by winds in the stratosphere. This allows earlier detection of an event far away [22]. Kalinowski [23] came up with a way to discriminate between fission occurring in nuclear reactors and nuclear weapons using Xe isotope ratios. Before his work, only one isotope ratio was used and it was assumed that nuclear reactors were operating at steady-state leading to an equilibrium concentration of Xe isotopes. The isotope ratio (with the shorter half life in numerator) for a nuclear explosion at the time of release is greater than that of a reactor. For non steady-state scenarios, some Xe isotope ratios are similar enough to weapons signatures that a single Xe ratio could not for certain say if Xe from a reactor or a weapon was detected. This analysis is further complicated by the Xe isotopes decaying at different rates. After a CHAPTER 2. NUCLEAR FORENSICS 12 few days the signature from an explosion looks like a reactor release. In [23], a method is described using two different Xe ratios, with each ratio plotted on an axis. A line can be drawn separating reactor and weapon releases that also accounts for Xe decaying with time [23]. A complication is the production of 99mMo via a small amount of HEU placed in a reactor for a short time. 99Mo produced in this method is used to create 99Tc, which is one of the most commonly used imaging radionuclides for medical applications. This can be confused with nuclear tests.

Figure 2.2: Ratios of Xe isotopes for diﬀerent sources of Xe. Any measured activity ratio to the left of the red dashed line is deﬁnitely not a nuclear explosion. LWR is light water reactor, which produces thermal energy neutrons. HEU is highly enriched uranium, which is uranium >20% 235U. From [23].

85Kr can be used in a similar manner. Xe is found in the high-mass side of the fission product distribution so its yield is not as sensitive to variations in fissioning mass. Kr is on the low-mass side of the fission product distribution and the amount produced changes significantly with mass. For example, in fast neutron fission, there is over a factor of two difference in the amount of 85Kr produced from 235U (0.275%) and 239Pu (0.128%) [3]. There are complications to using Kr. The only isotope with a long half life is 85Kr, with a half life of 10 years [7]. However, since the half life is so long the background due to it is relatively high. In comparison, the four Xe isotopes have half lives ranging from 9 hr to 12 days. 37Ar can also be detected as a result of a nuclear test even though it is not a fission product [22]. This nucleus is produced via the 40Ca(n,α)37Ar reaction on calcium in the soil. The CHAPTER 2. NUCLEAR FORENSICS 13 cross section is low at neutron energies less than 4 MeV, but rises from 4-15 MeV. Neutrons from fusion can produce large amounts of 37Ar, although there is production due to fast fission spectrum neutrons as well. Another complication of using 37Ar are neutron reactions with Ar in air. Ar makes up 0.98% of air. Thermal neutrons can undergo capture reactions with 36Ar (0.337% natural Ar), and high energy neutrons can undergo (n,2n) reactions on 38Ar (0.063% natural Ar).

2.3 Debris Analysis

When comparing the amount of fission products in a sample, it would be simple to assume the products are uniformly distributed throughout the area of sample collection. However, this is not the case due to geometric and chemical fractionation. Geometric fractionation occurs immediately after detonation. The debris physically does not mix due to the momentum of different parts of the device. Chemical fractionation occurs seconds to minutes afterward and is caused by the condensation of the vaporized debris. Elements are divided into two groups based on their cooling rates. Refractory elements condense first and are commonly found in glassy melt debris. Volatile elements take longer to condense, and the effects of chemical fractionation are more pronounced [12]. Some materials are considered volatile even if the material itself is refractory. An example is 140Ba. The chemical properties of Ba are such that it is a refractory element. However, 140Ba has a low independent yield compared to its cumulative yield. Most of it is formed from its precursors, rather than 140Ba itself. Based on their half lives, it takes around 70 s for the precursors to decay to 140Ba. Chemical fractionation occurs in this timeframe, and it is the properties of Xe and Cs, rather than Ba that dominate distribution in the debris. The distribution of refractory and volatile elements also depends on particle size. Refrac- tory elements tend to form salts, which are soluble in the liquid of debris droplets. Therefore they are found distributed throughout the volume of the particle. Volatile elements condense later when the particle droplets have solidified more, and so condense on the surface of the particles. Small particles have a higher surface area to volume ratio than large ones, so volatile elements are more abundant on them. For an explosion far from ground level, atmospheric conditions carry small particles away from the site and larger particles are more affected by gravity so do not travel as far. Therefore there are more volatile elements in the debris found far from the event site, and more debris with refractory materials close by.

2.4 Chronometry

Chronometry is the process of using the relative concentrations of a material’s decay products to determine the time the material was created or puriﬁed [12]. For example, in the decay series shown in Figure 2.3, if U is separated from Pu, all of the daughters observed are due to the presence of U, and there will be no 238Pu. Using Bateman equations and the half lives CHAPTER 2. NUCLEAR FORENSICS 14 of each species, the ratios of the “4n+2” isotopes shown in Figure 2.3 can give information about the time of puriﬁcation, as shown in Figure 2.4.

Figure 2.3: “4n+2” nuclides: when the mass number is divided by 4, there is a remainder of 2. 242Pu, 238U, and 234Th are not important for chronometry except for short (<6 months) times due to their chemical properties. From [12].

If a material contains 240Pu, its spontaneous fission (which is in addition to α decay) can give other information about its manufacture. Figure 2.5 lists some of the fission products of 240Pu. Short-lived fission products, such as 131I, can be used to infer the efficiency of Pu separation during analysis. For example, if there is a Pu sample, 129I can be measured by mass spectrometry. But the amount of 129I must be corrected for the efficiency of collecting I from the sample. Since 131I is short-lived, it was in equilibrium with 140Pu when it was separated. This information can be used to determine the efficiency of I recovery. Xe and Kr are useful in determining the time since 240Pu metal was cast. After purifica- tion, Pu is converted from a salt to a metal. In this process there are still trace amounts of most fission products, but noble gases are completely removed. Therefore the only Xe and Kr observed in a sample are the result of spontaneous fission of 240Pu. Using ratios of Xe and Kr isotopes, the time since the metal was formed can be determined. CHAPTER 2. NUCLEAR FORENSICS 15

Figure 2.4: Time since 238Pu separation using diﬀerent isotopes in its decay series. From [12]. CHAPTER 2. NUCLEAR FORENSICS 16

Figure 2.5: Spontaneous ﬁssion products from 240Pu. From [12]. 17

Chapter 3

National Ignition Facility

3.1 NIF Basics

The National Ignition Facility (NIF) is used for inertial confinement fusion experiments, where lasers are used to compress the fusion fuel (deuterium and tritium) [24]. NIF is an indirect-drive system where the lasers do not hit the fuel directly, but instead hit a gold or gold-lined uranium hohlraum, which converts laser light into x-rays that drive the ablation of the external layer of a capsule containing the DT fuel, thereby leading to the implosion. Figure 3.1 shows a typical fusion target. 192 laser beams, which can deliver a total energy of up to 2 MJ [25] hit the inside of the hohlraum, which is around 10 mm long and 6 mm in diameter [25][26] with slight variations in size depending on the experiment. The laser light is converted to x-rays, which ablate the capsule shell and compress the DT fuel inside. Hohlraums at NIF were originally pure gold but it was found that depleted uranium is more efficient at converting laser power to x-rays [25]. They were first made with a gold coating (Figure 3.2) to protect the U from oxidation and preserve the shock timing from pure Au experiments. CHAPTER 3. NATIONAL IGNITION FACILITY 18

Figure 3.1: NIF target. Figure from [24].

Figure 3.2: Cross section view of the outer edge of a lined depleted uranium hohlraum. From [25]. 3.2 Capsules

The two main types of capsules are made of CH plastic or HDC (high density carbon, a.k.a. diamond). A “wedge diagram” showing the composition of a typical CH capsule is shown in CHAPTER 3. NATIONAL IGNITION FACILITY 19

Figure 3.3. The capsule is approximately 2 mm in diameter with a wall thickness of 170-200 µm. HDC capsules are similar but with thicknesses in the range of 65-80µm. The ablator is doped with a higher-Z material to avoid x-ray preheat of the fuel. However, too much dopant results in a higher density gradient in the ablation front and the fuel/ablator interface becomes susceptible to Rayleigh-Taylor instabilities. Therefore the amount of dopant is graded so that there is no high-Z material adjacent to the DT ice layer [27]. Some targets have no DT ice layer and only have DT in gas form.

Figure 3.3: A typical CH capsule. From [25].

A campaign at NIF fielded 4 targets that had DU doped in a CH ablator, instead of using U in the hohlraum. This has the advantage of using much less fissionable material (4 µg instead of 25 mg) because it is much closer to the neutron source. The signal from fission products on these shots is comparable to the signal from when U is in the hohlraum. CHAPTER 3. NATIONAL IGNITION FACILITY 20

(a) A normal capsule with no DU layer. (b) A capsule with a DU layer.

Figure 3.4: X-ray radiographs of capsules with and without DU dopant. Photos courtesy of General Atomics.

3.3 Diagnostics

The NIF target chamber (Figure 3.5) is 10 m in diameter. It contains 121 diagnostic ports ranging in size from 15 cm to 160 cm. Two target positioners, three diagnostic instrument manipulators [28], and 2 multi-purpose target and diagnostic manipulators [29] that extend into the interior of the chamber are available for experiments. Experiments are diagnosed using a suite of measurement instruments [30] [31]. NIF diagnostics are fielded both inside and outside of the target chamber. Neutron time-of-flight instruments [33] measure the neutron yield and spectrum [34] [35]. Activation diagnostics measure yield [36]. Indium samples can be placed on DIMs 25-50 cm from the neutron source to measure DD neutrons. Copper and zirconium are placed outside the target chamber to measure DT neutron yield and measure the symmetry of the implosion [37]. Radiochemical diagnostics consist of RAGS, which is the focus of this report, and solid collectors. Solid radiochemical collection foils (SRCs) 5 cm in diameter made of V, Ta, or graphite, are mounted on DIMs 50 cm from target chamber center [38] [39]. Three different DIMS can hold SRCs, with 4 SRCs mounted on each DIM. Larger collectors can also be fielded. The Vast Area Detection for Experimental Radiochemistry (VADER) [40] consists of six trapezoidal and three circular collectors. The Large Area Solid Radiochemistry (LASR) diagnostic is a single 20 cm diameter collector [41]. Solid collectors are used to measure neutron scattering using the ratio of neutron capture and (n,2n) reactions on Au-197 collected from the hohlraum. CHAPTER 3. NATIONAL IGNITION FACILITY 21

Figure 3.5: NIF target chamber. From [32].

3.4 Neutron Spectrum

Neutrons from DT fusion at NIF are centered at 14.07 MeV [42]. Typical NIF experiments burn at a DT ion temperature around 3 keV [34] [35]. A simulated neutron spectrum is shown in Figure 3.6. The peak at 14.1 MeV is from DT fusion. The neutrons on the low- energy side of the peak (10-12 MeV) are DT neutrons that have scattered [43]. Another component of the spectrum is the DD peak near 2.5 MeV, which is two orders of magnitude lower in intensity than the DT peak. Backscatter peaks from neutrons scattering off of D and T occur around 3 and 5 MeV. Other features of the spectrum include a continuum from 0 to 9.4 MeV due to the T+T → α+2n reaction [44] [45] and a low-energy component consisting of multiply-scattered neutrons. From Figure 3.6, the 14 MeV component is over an order of magnitude more intense than the other neutron energies. During the implosion, most of the ablator is ablated away by the time the neutrons are produced, but the neutrons scatter off CHAPTER 3. NATIONAL IGNITION FACILITY 22 of any remaining ablator material as well as D and T remaining in the fuel. Other sources of neutron scattering are the target holder and thermal-mechanical package, which contain Al and Si [46]. Other room-return neutrons come from scattering off of diagnostics and target chamber walls. It has been shown [47] that room-return neutrons are negligible for distances farther than 1 cm from the target. Since the hohlraum is 6 mm in diameter the return flux is negligible compared to the capsule source flux.

Figure 3.6: Simulated neutron spectrum. The peak at 14.1 MeV is DT fusion neutrons. Neutrons with energies ranging 10-12 MeV are scattered DT neutrons and are used to calculate the downscattered ratio. Neutrons produced from TT fusion have energies ranging from 0-9.4 MeV. The low-energy tail is due to neutrons scattering oﬀ the target. The two peaks below 4 MeV are from 14 MeV neutrons backscattering from deuterium and tritium. The amount of 2.45 MeV neutrons from DD fusion are 2 orders of magnitude lower than the DT neutrons. From [47].

The Solid Radiochemsitry diagnostic (SRC) collects debris from the implosion, including gold from the hohlraum [47]. Au-197 is the only naturally occurring isotope of Au, and the ratio of neutron capture and (n,2n) reactions on it provides information on the neutron spectrum. These measurements show that the only neutron scattering affecting the hohlraum is from the capsule. The downscatter ratio is the ratio of 10-12 MeV neutrons to 13-15 MeV neutrons, and is typically 3-5%. Another source of non-14 MeV neutrons is DD fusion reactions, which produce 2.45 MeV neutrons. These are typically 1% or less of the DT neutron yield. Neutrons below 1 MeV CHAPTER 3. NATIONAL IGNITION FACILITY 23 will not fission 238U and 14 MeV neutrons dominate the the fission in 238U at NIF.

3.5 NIF for Fission Experiments

The motivation for using NIF is the duration of a shot is short and no correction needs to be made for the production and beta decay of fission fragments during irradiation. All of the neutrons are produced in 100s of picoseconds [47] which is an advantage for measuring products with a range of half lives. In a beam experiment with low flux but a long irradiation time, fission products are being continuously produced directly and via beta-decay of their parents. This means that fragment yields need to be corrected for simultaneous production and decay, which requires good knowledge of their independent yields, which are often not available. NIF does not have this problem. There is a high neutron flux (1015 neutrons per shot), which means a small amount of uranium can be used to obtain a measurable signal of fission products. NIF also has an apparatus (the Radiochemical Analysis of Gaseous Samples), to be described later, that collects fission gas in-situ. This allows for gas to quickly be transferred from the target chamber to a detection system and therefore measure products with short half lives (10s of seconds). Only noble gas and other chemically refractory species are collected, allowing the noble gas to be analyzed with relatively little background. 24

Chapter 4

Measurements of Gaseous Fission Products

There are several methods to measure gaseous ﬁssion fragments. In this chapter two common types of experiments used in ﬁssion product yield evaluations [3] [1] will be discussed. Then the NIF experiment will be described in detail.

4.1 Radiochemistry Experiments

An experiment used in ﬁssion yield evaluations for Kr and Xe was performed by Ballou et al [48] using 15 MeV neutrons produced by the Isolated Core Transformer (ICT) accelerator at LLNL. Xe and Kr yields were measured with a radiochemistry technique that can measure nuclides with half lives of a few seconds or more. The material of interest, in this study 239Pu, was placed in a sealed quartz ampoule. The Pu was irradiated for 2 min at the ICT and removed via pneumatic tube, then crushed in a chamber. The ﬁssion gas was swept into a counting cell which was equipped with a Ge(Li) gamma ray detector. This measurement was performed for 10 samples and the gas separation was deliberately delayed by 15 min for 4 of the samples to allow 85Br and 87Br to decay. Cumulative yield measurements of 85m,87,89Kr were made relative to the yield of 88Kr and 138Xe. The absolute yield of 88Kr and 138Xe were taken from calculations and evaluations [49] [50] [51].

4.2 On-Line Isotope Separation

Several measurements have been made with the Isotope Separation On Line (ISOL) method [52]. In these experiments a sample of UO2 powder was placed behind the tritiated target of an accelerator-based neutron source with mean energy 14.5 MeV. Using a powder allowed gas to escape [53]. Gaseous products travelled 1 m to an ionization chamber. The ionized gas was separated by mass in a magnetic field. In this experiment the betas were counted CHAPTER 4. MEASUREMENTS OF GASEOUS FISSION PRODUCTS 25 but other facilities allowed counting gamma rays or neutrons [54]. When calculating the fission yield, corrections were made for gas transport and ionization efficiency. Cumulative yields for 87−93Kr were measured relative to 90Kr or 91Kr and 137−142Xe cumulative yields were measured relative to 137Xe. The ratio of the independent yield of Kr (or Xe) to the cumulative yield of Br (or I) was also measured. The absolute yield of the normalizing nuclide was obtained from an evaluation performed by a different group [55] to calculate absolute yields from the ISOL experiments.

4.3 This Experiment: NIF Radiochemical Analysis of Gaseous Samples

The Radiochemical Analysis of Gaseous Samples (RAGS) is an apparatus at NIF that trans- ports gas from the target chamber and collects it under a HPGe detector [56]. Figure 4.1 is a diagram of RAGS and Figure 4.2 is a photo of the system as installed. Thirty seconds before a shot the NIF cryopump valves close, leaving only 3 turbopumps open to the chamber, which pump gas into RAGS. RAGS runs for 15 min, and it takes 20 s for the gas to travel from the target chamber into RAGS. There are three main components: the ﬁlter cart, collector cart, and abort tank. There is also a tracer injection system on the target chamber capable of injecting radioactive and stable gas at shot time or as needed. Collection eﬃciency for Kr and Xe is measured to be >95% [56].

Figure 4.1: Schematic of RAGS.

Filter Cart The filter cart chemically filters out the non-noble gases and is designed to process 0.5 Torr L/s of gas [56]. A Pfeiffer HiPace 80 turbopump and an Adixen ACP40 rough pump CHAPTER 4. MEASUREMENTS OF GASEOUS FISSION PRODUCTS 26

Figure 4.2: RAGS diagnostic. create vacuum. The HiPace 80 [57] has turbomolecular pump stages, which are alternating rotors and stators, at the inlet of the pump. Gas molecules hit the angled rotors and gain momentum in the direction of the pump exit, which is a drag pump. In this stage, a tubular rotor spins at a speed approximately the speed of the gas molecules between cylindrical walls. The outer wall has grooves that guide the molecules, which are trapped between the rotor and the wall, toward the outlet. The drag pump stage allows pumping of gas at higher pressures than the turbo stage. The ACP40 [58] is a multi-stage Roots, or rotary-lobe, pump. In each stage two figure-eight shaped lobes mesh without touching rotate to transfer gas through the pump. Stainless steel components with ConFlat knife-edge sealing surfaces are used. An SRS RGA200 RGA (residual gas analyzer) is a quadrupole mass spectrometer that monitors gas composition. It works by first ionizing the gas [59]. Then a combination of RF and DC voltages is applied to four rods. The trajectory of ions in the field depends on the mass-to- charge ratios of the ions for a given magnitude and frequency of RF. First the gas from the target chamber enters the water trap. The water trap is custom fabricated and consists of a cylinder made of stacked Cu foam disks and a solid Cu core. The assembly is mounted on a single stage Oxford/Austin Scientific M1050 coldhead [56]. Gas flows through the foam, which is cooled to 175 K, freezing out the water and allowing the rest of the gas to continue to the next stages of filtration. As the sample passes through the water trap, a temperature gradient between the inlet and outlet of 20 K develops. The water CHAPTER 4. MEASUREMENTS OF GASEOUS FISSION PRODUCTS 27

vapor signal increases 10% in the RGA during sampling. An Ortec LaBr3(Ce) detector is placed on the water trap. After the water freezes the remaining gas continues to 2 hot and 2 cold getters. All four getters are composed of ST 707, an alloy of 70% Zr, 24.6% V, and 5.4% Fe [60]. Non-noble gases are sorbed onto the getter surface, then diffuse into the body of the getter. O, C, and N form strong bonds with the getter material and cannot be released, even at high temperature. The hot getters are SAES GP500 MK5 units [61], operated at 450oC starting 1 hr before until 30 min after the shot [56]. They remove N, O, and residual water from the gas stream. The cold getters are SAES GP100 MK5 units [61] at room temperature that are used to remove H isotopes. H isotopes diffuse faster than other gas in ST 707, even at low temperature. After H is captured, it can be released when heated [60]. After a shot, the cold getters are heated and the H is released to the NIF Tritium Processing System [56]. During a shot, the gas exiting the last getter is composed of Kr, Xe, Ar, and a few percent N, F, water vapor, and H. A second LaBr3 detector monitors the first hot getter for radioactive species. The gas travels 15 ft in a 1.5-inch diameter vacuum line to the collector cart.

Collector Cart Noble gases with a trace of hydrogen, N, and F remain to enter the collector cart. Xe and Kr are frozen onto a cryogenically cooled foam. Gas is pumped away from the foam with a Pfeiffer HiPace 80 and an Adixen ACP15 rough pump. Other gases continue to the abort tank (described in the next section). Near the end of the 15 min sample processing time the valves for 2 room temperature SAES GP100 MK5 getters and a SRS RGA200 are opened. The valves to the tubopump and abort tank are closed, isolating the collector cart. The foam is in the sampling line, where gas flows through it. It is composed of 1.5 inches of Cu foam brazed onto the vacuum sleeve and contained in a Cu block. The block is connected to a heat strap connected to the first stage of an Oxford/Austin Scientific Model 350 2-stage cryocooler (see Figure 4.3). Four 25 W cartridge heaters and 2 resistance temperature detectors to control and monitor the temperature are connected to the Cu block. In the original design the Cu foam was cooled to 60 K to trap Xe but allowed the other gases (mainly Kr with some Ar) to pass through to the abort tank. Originally an Al heat strap connected the Cu to the cryocooler, but was later upgraded to a Cu heat strap. This allows the Cu foam to be cooled to 44 K instead of 60 K. The lower temperature freezes Kr as well as Xe, so both can be counted in the collector cart [62]. At first the Ge detector on the collector cart was set a fixed distance (8-12”) away from the sample on the Cu foam. Later it was modified to be on a translatable stage controlled by a computer with a pre-selected translator recipe that depends on the expected shot yield. A common recipe is shown by the blue line in Figure 4.4. In the first 100 s of shot N160418 the detector is 0” from the sample, in contact with the outer housing of the coldhead. Because it is 8” closer the sample than red line (N140819, fixed at 8” from the sample), the detector reaches its saturated count rate (approximately 10000 cts/s) 10 s earlier than N140819. The CHAPTER 4. MEASUREMENTS OF GASEOUS FISSION PRODUCTS 28

Figure 4.3: Coldhead with vacuum housing removed. The copper heat strap was originally aluminum. From [62]. true count rate rises as gas arrives through the foreline and accumulates in the coldhead. The detector for N140819 saturates around 50 s. Because it is so close to the sample, the translating detector for N160418 not only saturates but also stops recording events due to CHAPTER 4. MEASUREMENTS OF GASEOUS FISSION PRODUCTS 29 pulse pileup, missing counts and resulting in a decreasing apparent count rate after 35 s until it reaches 0 cts/s around 100 s when it moves away from the sample. The green line, N170130, is for a shot with more than an order of magnitude lower yield and demonstrates how the signal should rise throughout the entire interval 0-100 s. After 100 s the translating detector moves 11.5” from the sample and begins counting again, with a dead time around 40%. At early times (<100 s) when gas is being pumped into the cart, there is not much activity so the detector is next to the Cu foam to improve signal and observe the short-lived isotopes. After 100 s enough gas has entered the cart that dead time becomes a problem if the detector is too close to the sample. Figure 4.4 shows two shots with similar yields, approximately 3-6e15 DT neutrons. Even though the yield for N160418 was about half of N140819, the amount of gas was similar for the two shots because both Kr and Xe were trapped in the collector for N160418. After some period of time (usually hours after the shot), the Cu foam is heated to 135 K, which allows the transfer of Xe and Kr to a 50 cm2 sample bottle with double valves to prevent air leakage into the sample. The getters maintain vacuum during the transfer. The RGA measures Xe, Ar, Kr, H, N, O, He, and CO2 released during heating. The sample bottle is taken to the Nuclear Counting Facility, located in another building at LLNL, where the longer-lived isotopes are transferred to gas sample counting cells and counted with HPGe detectors to obtain a calibrated measurement of long lived isotopes. This result is used to cross calibrate the RAGS counting system.

Abort Tank The remaining gases continue to the 11.4 L abort tank, where it is stored for several hours. Eventually the gas is released to the NIF Tritium Processing System. There is no measurable diﬀerence between Kr measurements taken in the collector vs the abort tank. Part of the analysis changes since it takes 20 s for the gas to reach the collector but 50 s for it to reach the abort tank. Figure 4.1 shows where radiation detectors (LaBr3 and HPGe) and RGAs are located to monitor various stages in the gas collection process. For this paper, the Ge detectors on the collector cart and abort tank are most important since that is where the ﬁssion gases are. CHAPTER 4. MEASUREMENTS OF GASEOUS FISSION PRODUCTS 30

Total Observed Count Rate (not corrected for dead time) 12000 detector is always 8" from sample 10000

8000

detector 11.5" from sample 6000 detector 0" from sample cts/s

4000

2000 N160418 N140819 N170130 0 0 50 100 150 200 250 300 time (s) Figure 4.4: Comparison of activity in collector with (N160418, blue) and without (N140819, red) translating detector, and an example of a non-moving detector at low yield (N170130, green). N140819 (yield 5.5e15) is saturated throughout the entire time 50-300 s, while moving the detector in N160418 (yield 2.8e15) allows counting, although with a 65% dead time. It should be noted that although the yield is lower for N160418, there is additional contribution to the count rate from Kr not present in N140819. N170130 shows how the count rate should rise throughout the entire interval 0-100 s. Kr was present for N170130 (yield 2.0e14) and had a maximum dead time around 40%. 31

Chapter 5

Data Analysis

The general method of analysis is as follows:

First, the energy and eﬃciency calibrations of detector are determined.

The amount of each isotope is calculated as a function of time.

An exponential decay is ﬁt for each isotope and extrapolated to shot time to calculate initial atoms produced.

The each the ratio for each isotope is taken the initial atoms of 88Kr.

Finally, this ratio is corrected for pumping speed and time

5.1 Data

Figure 5.1 is a typical gamma ray spectrum as a function of time from a shot. The horizontal axis is energy and time moves vertically. The data is collected in list mode, in which the detector stores the time and channel (energy) of each detected event. Events in a certain time range are summed to create histograms. For example, in the time 0-5 min events in each channel are summed to make a histogram. The next interval, from 5-10 min, creates another histogram in a similar manner. This continues every 5 min. A histogram from 70-75 min is shown in Figure 5.2. When the histograms are “stacked” on top of each other (to represent time), they create the plot in Figure 5.1. Photopeaks are selected based on their energy in the histograms. Photopeaks in a certain energy range are ﬁt with a Gaussian curve to calculate the area. Then the area can be plotted as a function of time to see the decay of the isotope, as demonstrated in Figure 5.3. Another feature of the data is the the movement of the detector is visible. In Figure 5.1 a horizontal line at 5 hr corresponds to the detector moving from 11.5” to 5” from the sample. The count rate increases immediately after the move and is also evident in Figure CHAPTER 5. DATA ANALYSIS 32

Figure 5.1: List mode data using 5 minute time bins. Energy is on the horizontal axis and time runs vertically. Each pixel in the plot is composed of 1 channel (roughly 0.4 keV) and 1 time interval (5 min). Looking at 1 time bin, for example 70-75 min, would result in a histogram of counts vs energy (Figure 5.2). Looking at 1 channel would ideally give the decay of a photopeak over time, but unfortunately a detector does not have perfect resolution so several channels must be summed to accurately calculate the decay of a photopeak. For example, the decay of the peak centered around 402 keV is shown in Figure 5.3.

5.3. In Figure 5.4 the detector moves from 0” to 11.5” at 100 s, which is why the count rate decreases suddenly. Data collected while the detector is moving is not used in analysis. Because data is stored as single events, they can be binned into histograms of any length of time. This is useful for observing both long and short lived species. An isotope such as 88Kr has a half life of 2.84 hours meaning that its activity would be too low to be observed with 1-second time intervals. But isotopes with half lives of 10s of seconds such as 90Kr have completely decayed away in the ﬁrst 5 minutes and using 30-minute time bins would be pointless. Figure 5.4 shows the ﬁrst 2 minutes after a shot along with a few of the short-lived isotopes: 90Kr (32 s), 139Xe (40 s), and 137Xe (3.8 min). In Figure 5.1 both Xe and Kr are observed. Cs and Rb are also labelled on the plot. Xe beta decays to Cs and Kr beta decays to Rb (Figure 5.5). When looking at the decay of Cs and Rb, they do not appear to decay with their half lives because they are being produced from Xe and Kr. Since RAGS only collects the noble gas, the independent yields of Cs and Rb are not observed and the only activity from these species is due to Xe and Kr decaying. CHAPTER 5. DATA ANALYSIS 33

N160223 Ge-Collect time step=5 min, step #15 (70-75 min after shot) 104 Cs-138 3 Cs-138

10 Kr-87 Cs-138 Xe-138 Kr-88 Cs-138 Xe-138 Cs-138 Kr-85m Kr-85m Kr-88 Cs-138 Rb-88 Rb-89 Cs-138 Kr-87, Kr-88 Xe-138 2 Kr-88, Rb-89 10 Kr-88 Xe-138 counts

101

500 1000 1500 2000 2500 energy (keV) Figure 5.2: A histogram created by taking a time slice from Figure 5.1. CHAPTER 5. DATA ANALYSIS 34

N160223 Ge-Collect counts in 402 keV peak (87Kr) 1200

1000

800 detector moved from 11.5" to 5" from collection foam 600 cts/5 min 400

200

0 0 2 4 6 8 10 12 time (hr) Figure 5.3: Plotting the intensity of the photopeak at 402 keV vs time. This peak can also be observed in Figure 5.1. Error bars omitted for clarity. CHAPTER 5. DATA ANALYSIS 35

Figure 5.4: List mode data using 1 second time bins plotted in the same manner as Figure 5.1 with energy on the x axis and time increasing vertically. With short time bins it is possible to observe the short-lived isotopes. At 100 s the detector moves from 0” to 11.5” from the sample, resulting in a decreased count rate. CHAPTER 5. DATA ANALYSIS 36

Figure 5.5: A section of the Chart of the Nuclides [63]. Small squares indicate metastable states. Kr isotopes decay to Rb isotopes of the same mass. CHAPTER 5. DATA ANALYSIS 37

5.2 Energy and Eﬃciency Calibration

The energy and efficiency calibrations are done with Xe and Kr along with their daughters. The peaks used for the collector cart efficiency calibration are marked in Table 5.1 and consist of gamma rays from 88Kr with intensity greater than 3% and are not close in energy to other gamma rays. For example, the 2195.84 keV gamma ray from 88Kr has an intensity of 13%. However, it cannot be used because it is unresolved from the 2195.95 keV gamma ray of 89Rb, the decay product of 89Kr, with an intensity of 15%. An efficiency curve is generated and either a 4th order polynomial, 5th order polynomial, or power fit is selected based on the residuals of the fit and conforms to a typical HPGe efficiency curve shape (i.e. if the function continues to decrease at high energy (Figure 5.6)). If Kr is in the collector, 138Cs is also used and scaled to the 88Kr result to obtain data at lower energies. If Kr is collected in the abort tank, the above procedure is performed but without 138Cs.

1.0e-4 Kr Cs Xe fit 7.5e-05 Kr excluded from fit not part of fit efficiency 5.0e-05

2.5e-05 0 500 1000 1500 2000 2500 3000 energy (keV) Figure 5.6: A typical measured eﬃciency curve for HPGe detectors.

Usually the detector is 11.5 inches from the sample from 100 s-5 hr, then moves to 5 inches after 5 hr. Since some isotopes are shorter-lived than others, the analysis is done from 85m 100 s- 5 hr, even for isotopes such as Kr (t1/2=4.5 hr) that are observable for both the <5 hr and >5 hr portions of the counting period. This is also the time when the detector is CHAPTER 5. DATA ANALYSIS 38

Table 5.1: Energies used for energy and eﬃciency calibrations. Every gamma ray listed in this table was used for energy calibrations. If a gamma ray was also used for eﬃciency calibrations its intensity is also listed. Data from [64], [65], [66], [67], and [68].

Intensity Energy Isotope Half Life Measured Eﬃciency (if used for eﬃciency) 138.1 138Cs 33.41 min 227.8 138Cs 33.41 min 462.8 138Cs 30.8 ± 0.7 33.41 min 7.72e-5 ± 1.69e-6 547.0 138Cs 10.76 ± 0.3 33.41 min 7.07e-5 ± 2.00e-6 871.8 138Cs 5.11 ± 0.15 33.41 min 5.87e-5 ± 2.84e-6 1009.8 138Cs 29.8 ± 0.6 33.41 min 5.40e-5 ± 1.20e-6 1343.6 138Cs 33.41 min 1435.8 138Cs 76.3 ± 0.5 33.41 min 4.51e-5 ± 9.31e-7 1445.0 138Cs 33.41 min 2218.0 138Cs 15.2 ± 0.4 33.41 min 3.51e-5 ± 8.71e-7 2639.6 138Cs 7.63 ± 0.25 33.41 min 3.07e-5 ± 8.41e-7 151 85mKr 4.480 hr 166.0 88Kr 2.825 hr 196.3 88Kr 2.825 hr 402 87Kr 1.272 hr 834.8 88Kr 13.0 ± 0.6 2.825 hr 5.90e-5 ± 2.77e-6 845 87Kr 1.272 hr 1031 89Rb 15.32 min 1249 89Rb 15.32 min 1518.4 88Kr 2.825 hr 1530.0 88Kr 10.9 ± 0.5 2.825 hr 4.14e-5 ± 2.10e-6 1835 88Rb 17.773 min 2195.8 88Kr, 89Rb 2.825 hr, 15.32 min 2231.8 88Kr 3.39 ± 0.17 2.825 hr 3.44e-5 ± 3.71e-6 2392.1 88Kr 34.6 ± 1.6 2.825 hr 3.17e-5 ± 8.13e-7

11.5” from the sample, which means a correction for coincidence summing does not have to be performed. A detailed analysis will have to be done in the future to analyze data at the 0” position because coincident summing has a greater effect as the detector moves closer to the sample. Different time intervals are used for the Cs and Kr/Rb portions of the calibration. For Kr, time intervals of 1 hr are used. 138Cs uses 30 minute time intervals beginning after 1 138 hr to allow ingrowth from Xe (t1/2=14.1 min). Values at two different times are averaged. CHAPTER 5. DATA ANALYSIS 39

5.3 Peak Fitting

The first step of analyzing a single isotope is to identify its photopeak(s) and fit for each step in time. 87Kr will be used as an example. Its half life is 1.3 hr, which is comparable to that of 88Kr, so time bins of 30 min will be used for both of these isotopes. Because the background changes with time, Gaussian fits were used instead of a sum of the counts subtracted from background. At early times, isotopes with shorter half lives are present and the background region is not smooth. Figure 5.7 shows the 402 keV photopeak of 87Kr. A region on either side of each photopeak is chosen to use for subtracting the Compton scattering background. The number of channels in each background region is roughly a full width half maximum of the peak of interest. If the peak of interest is not fully resolved from another photopeak, the background region is chosen so that the other peak does not interfere, which could result in fewer background points used. For this example, the gray dashed line shows a few channels on either side of the background channels (solid black lines) so photopeaks that may be a problem can be observed. In this case, there are no other peaks in the region of interest.

402 keV (87Kr) timestep=30 min, step #4 8000 raw data line for background subtraction channels for background subtraction 6000 Gaussian fit to background-subtracted data data after background subtraction channels on either side (not used in analysis) 4000 counts

2000

395 400 405 energy (keV) Figure 5.7: Fitting a photopeak from 87Kr. The blue, black, and dashed gray lines are the raw data from the detector. The blue is the photopeak of interest, black is the region to use for background subtraction, and dashed gray is to see what other peaks may interfere with background subtraction. The green line is a ﬁt to the points on the black line and is subtracted from the raw data. The result is the blue points. Then a Gaussian is ﬁt to the background-subtracted photopeak to calculate the area.

The blue line in Figure 5.7 highlights the main portion of the peak and the black line is the background due to Compton scattering. A line (green) is fit to the background points (black). Then the fit is subtracted from the background and peak channels (black and blue), CHAPTER 5. DATA ANALYSIS 40 resulting in a Gaussian peak with its base at 0, represented by the blue dots. A Gaussian fit is performed (red line) and its area is calculated. The Gaussian fit is also used for the energy and efficiency calibrations. The centroid (one of the coefficients of the fit) is plotted as a function of channel for energy calibration. The area of the peak is used for the efficiency calibration.

586 keV (89Kr) timestep=30 s, step #19 raw data line for background subtraction 200 channels for background subtraction Gaussian fit to background-subtracted data 150 data after background subtraction channels on either side (not used in analysis) 100 counts

565 570 575 580 585 590 595 energy (keV) Figure 5.8: Similar to Figure 5.7 but for 89Kr. The photopeak at 586 keV is not fully resolved so instead of a single Gaussian ﬁt, a double Gaussian is ﬁt to the background-subtracted data.

Sometimes a photopeak of interest is not fully resolved from a neighboring one. The gamma ray energy used for 89Kr is 586 keV but it also has one at 577 keV, shown in Figure 5.8. There are around 20 channels between the centroids and they have widths around 5 channels, but there are only about 10 channels between the bases of the two peaks. The data is somewhat noisy and it is necessary to use more than 5 channels for background subtraction. Since the peaks are not fully resolved, two Gaussians are ﬁt to the peaks and the background channels are on either side of the combination of the two peaks. The equation used is

(x−b1) (x−b2) − c − c y = a1e 1 + a2e 2 (5.1)

a1 and a2 are the amplitudes of the two peaks, b1 and b2 are the centroids, and c1 and c2 are related to the widths. Table 5.2 lists the parameters of the ﬁt at two diﬀerent times. b1 was constrained to fall between 571-581 keV and b2 was constrained to fall between 581-590 keV. CHAPTER 5. DATA ANALYSIS 41

Table 5.2: Coefficients at two different times for a Gaussian fit to the 577 keV and 586 keV 89 photopeaks of Kr. The centroids b1 and b2 were constrained to be between 571-581 keV and 581-590 keV.

a1 b1 c1 a2 b2 c2 time 1 28.08±4.37 576.48±0.22 1.75±0.73 78.79±4.21 585.57±0.00 1.72±0.06 time 2 15.59±4.21 578.21±0.77 3.63±1.41 47.26±1.86 585.57±0.00 1.92±0.15

5.4 Determination of Isotope Activity as Function of Time

The coldhead was designed for trapping efficiency and not gamma counting geometry, and it is not known if the gas collects uniformly through the Cu foam. Because of this, instead of measuring absolute yields, they are all taken relative to 88Kr. 88Kr has the highest independent and cumulative yields of the isotopes with half lives greater than an hour. It also has many high-intensity gamma ray energies to choose from. Its precursor, 88Br, has a relatively short half life compared to other Br isotopes (see Figure 5.5), meaning more of its cumulative yield is collected. Because of these factors, it can be measured precisely and easily, so it was the Kr isotope chosen as the normalization standard. The gamma peak used to quantify each isotope is the highest intensity gamma ray that falls within the efficiency calibration of the detector and is well-resolved in energy to other photopeaks. For example, the 1530 keV photopeak of 88Kr is not the most intense peak of 88Kr. The one at 196 keV falls outside the calibration range. Photopeaks with intensities of a few percent are visible in the spectrum, so it was a concern that the 0.8% 836 keV peak from 87Kr would interfere with the 835 keV peak from 88Kr so both the 835 keV and 1530 keV photopeaks were compared for 88Kr analysis. They resulted in the same answer so it was not a concern, but either choice was valid. Gamma rays at 2196 keV are produced by 89Rb, a decay product of 89Kr and present the first few hours, so the 2196 keV peak for 88Kr was not used in analysis. Table 5.3 lists the energies used to determine the amount of each Kr isotope. Additional nuclear data is listed in the appendix.

Table 5.3: Nuclear data for the isotopes measured in this work. Additional nuclear data is listed in the appendix. Data from [66], [64], [65], [67], [69].

Krypton isotope Half life Energy (keV) Intensity (%) 88 2.84 hr 1529.8 10.9±0.5 85m 4.48 hr 304.9 14.0±0.3 87 1.27 hr 402.6 50±3 89 3.15 min 586.0 16.7±1.4 90 32.32 s 1118.7 39.0±3 CHAPTER 5. DATA ANALYSIS 42

Kr-87 Activity corrected for dead time, efficiency, gamma intensity ×105 3.5

2.5

cts/s 1.5

0.5

0 0 5 10 15 time (hr) Figure 5.9: Relative activity of 87Kr vs time. This is the area calculated from the Gaussian peaks (Figure 5.7) at each time step, corrected for dead time and relative eﬃciency. It decays with the half life of 87Kr, 1.2 hr.

To calculate the amount of each Kr isotope, first the area of the photopeak was found at different points in time. The total time for each isotope (8 half lives) was divided into equally spaced time bins. For example, to calculate the peak area for 88Kr in the collector, an analysis time of 0-5 hr was selected. Although 5 hr is less than 8 half lives, the detector moves at 5 hr so anything greater than that would be invalid for the detector calibration for 100s-5 hr. Then the time range was divided into 10 30-min intervals. The peak area was calculated for each 30-min interval (Figure 5.9). 88Kr, 85mKr, and 87Kr have similar half lives so 30 min intervals were chosen. 89Kr had 30 s intervals and 90Kr had 5s intervals. Then the area was corrected for dead time, detection efficiency, intensity of the gamma ray energy used, and counting time. The counting time correction arises because the isotope decays exponentially throughout the time bin. The amount quoted for the time interval is the value at the beginning of the bin. The derivation for the decay correction factor is as follows: The number of counts observed in a time bin is C, which is the area of the peak at a given time interval. To convert to atoms, C must be divided by the time in the counting period, ∆t to get the activity Acalc. This is an average activity throughout the time interval without CHAPTER 5. DATA ANALYSIS 43 taking into account the decay of the atoms during this period. Activity can be converted to the number of atoms using the relation

A = λN (5.2) where A is activity, λ is the decay constant of the isotope, and N is the number of atoms present. Putting this all together, C = A = λN (5.3) ∆t calc calc Another way to write the counts in the time bin is to put it in terms of instantaneous activity. The change in number of atoms is the number of decays observed (C), which can then be converted to activity.

A (0) − A (∆t) C = N (0) − N (∆t) = inst inst (5.4) inst inst λ Ninst is the instantaneous umber of atoms and Ainst is the instantaneous activity. The number of atoms and activity at time 0 (start of time interval) and a time ∆t later are of interest. Since the activity is an exponential decay, the above equation can be rewritten as

A (0) · (1 − e−λ∆t) C = inst (5.5) λ Eq. 5.3 and Eq. 5.5 both contain the value C, the area of the photopeak. Setting C equal for both equations and solving for Ainst(0), the result is λ∆tA A (0) = calc (5.6) inst 1 − e−λ∆t This equation relates the activity at the beginning of the time bin to the activity calculated from an entire time interval by correcting for the decay throughout the counting time. If the time bin is short compared to the half life, the correction is small. The dead time correction assumes the detector is nonparalyzable and that events collected during the dead period of the detector following each detected event do not extend the period of dead time. From [70] the observed counts in a peak for each time interval is multiplied by the factor 1 (5.7) 1 − CR ∗ τ where CR is the observed total count rate in the time interval and τ is a system time constant. For the Ge detectors used in RAGS, the value of τ was measured to be 50 µs. In summary, after calculating the photopeak area there are adjustments for dead time, efficiency, gamma ray intensity, and the decay over the length of the time interval. Then the corrected peak area is divided by the amount of time in the interval, which is important because different time bins are used for different isotopes, to calculate the average activity in each time bin. Finally, using Eq. 5.2, the activity is converted to number of atoms. CHAPTER 5. DATA ANALYSIS 44

5.5 Fit Exponential Decay and Extrapolate to Shot Time

The next portion of the analysis is to ﬁnd the activity at shot time. Each isotope follows an exponential decay. The number of atoms at each time step extrapolated to shot time is

λti N(0) = N(ti)e (5.8)

The notation ti is a reminder that the time used is different for each time step. The turbo pump manifold is exhausted into the RAGS collection system for 15 min. After 15 min, the value for N(0) for each time step is constant because there is no more noble gas being added to the system. The only noble gas removal mechanism is radioactive decay. Figure 5.10 shows N(0) for 87Kr. Since time bins are 30 min, only the first one is affected by gas being introduced to RAGS. CHAPTER 5. DATA ANALYSIS 45

×109 Kr-87 Atoms at Shot Time 5

2 atoms at shot time 1

0 0 2 4 6 8 10 12 time (hr) Figure 5.10: Converting activity from Figure 5.9 to atoms and extrapolated to shot time. The detector moves from 11.5” to 5” from the sample after 5 hrs.

5.6 Ratios

In the preceding sections of this chapter, the amount of each isotope was calculated from the area of its corresponding photopeak and extrapolated to shot time using Equations 5.2-5.8 for time intervals of 30 min. Then, for 85mKr and 87Kr, the ratio of atoms (extrapolated to shot time) to 88Kr is taken at each 30 minute interval (Figure 5.11). Contributions to the uncertainty for the third data point in Figure 5.11 are shown in Table 5.4. As time progresses the statistical uncertainty increases. Finally, the average of these values for each isotope is taken to find the ratio for each shot. Since Kr is pumped into RAGS for the first 15 min, the first time bin 0-30 min is ignored in the average. 89Kr has a much shorter half life (3.15 min) so shorter (30 s) time bins are used. The average of 88Kr atoms at shot time is taken. Then an average of 89Kr atoms extrapolated to shot time, from 780-900 s is taken. 30 s time bins are used, which results in atoms at shot CHAPTER 5. DATA ANALYSIS 46

87Kr/88Kr Atom Ratio Calculated at Shot Time 1.1

0.9

0.8

0.7 atom ratio 0.6

0.5

0.4 0 1 2 3 4 5 6 7 8 9 10 time (hr) Figure 5.11: Ratio of 87Kr atoms extrapolated to shot time to 88Kr atoms at shot time. Each point is calculated using the half lives of 87Kr, 88Kr, and the time since shot time of each discrete time bin. After the 0-30 min interval, all ratios should be constant because the only transport of Kr is through decay, not by physical movement of gas in or out of the sample volume. For the purposes of this example, ratios are shown up to 10 hrs and include a different efficiency calibration for times after 5 hrs. As time passes, there is less signal and therefore poor statistics, leading to the fluctuation seen at late times.

Table 5.4: Contributions to uncertainty for an individual data point in Figure 5.11.

what error (%) eﬃciency calibration 2.59 gamma intensity 7.55 statistics 5.86 total 9.90 time appearing to increase during the ﬁrst 15 min, and then reaching an equilibrium value after 15 min. The half life of 90Kr is so short (32.32 s) it has completely decayed by the time pumping CHAPTER 5. DATA ANALYSIS 47 into RAGS is complete. As with 89Kr, the average of 88Kr atoms at shot time is taken. Then the average of 90Kr atoms at shot time is taken from 130-150 s and the ratio to 88Kr is calculated.

5.7 Correction for Pumping Speed and Time

The decay of Se and Br fission products in the target chamber contributes to the total production rate of their respective mass chain Kr isotopes. If the Se and Br isotopes have half lives sufficiently long compared to Kr, it will take a long time to observe the full cumulative yield of Kr. Since RAGS only pumps for 15 min, some Kr isotopes are still being produced inside the target chamber after the pump shuts off. Therefore, even if the pump is 100% efficient at collecting Kr, it is still expected that it will not collect the full cumulative yield of each Kr isotope. For example, 85Br has a 2.9 min half life (see Figure 5.5). After 15 min, only about 5 half lives have passed so there is still Br left in the target chamber to continue decaying after the pump has shut off. The amount of Kr observed in RAGS is the Kr independent yield plus some of the yield resulting from Br decay. To correct for this effect, a model was created based on the independent yields of Br and Kr and the cumulative yields of Se. Since the half lives of Se and its precursors are so short the cumulative yield of Se was used. Then a series of Bateman equations with terms for Se, Br, Kr, and the RAGS pump, which was modelled with an effective half life of 3 min. The transport of the first fission gas sample through the 100 feet of line to RAGS takes 19 s. In the model, isotopes start to decay in the target chamber at 0 s but the pump turns on at 19 s. Then the following equations are solved to find the amount of isotopes in the target chamber (not in RAGS). Figure 5.12 illustrates the isotopes decaying into and out of the 87 mass chain. Ni is the number of atoms for isotopes in each mass chain and Mi is the number of atoms in the A+1 mass chain. bij is the branching ratio for each isotope within a mass chain and aij is the branching ratio within the A+1 mass chain. The a and b terms account for isotopes that emit a neutron with their beta decays. λi is the decay constant for an isotopes in the mass chain and ki is the decay constant for an isotope in the A+1 mass chain. λp is the pump decay constant. The goal is to find NKr, which is Kr of a particular mass number in the target chamber. dN Se = −λ N (5.9) dt Se Se dM Se = −k M (5.10) dt Se Se dN Br = −λ N + b λ N + (1 − a )k M (5.11) dt Br Br SeBr Se Se SeBr Se Se dM Br = −k M + a k M (5.12) dt Br Br SeBr Se Se CHAPTER 5. DATA ANALYSIS 48

Figure 5.12: Decay chain for mass 87, shown in yellow. Each element of mass 87 decays either directly (by beta decay) to the next highest Z in the mass chain, or decays out of mass 87 and into mass 86 when a neutron follows the beta decay. Similarly, more of mass 87 is added when a species of mass 88 emits a neutron. The letters aij indicate branching ratios within the A+1 mass chain and bij are for the A mass chain, used in Equations 5.9- 5.14. Green arrows indicate yields entering the mass 87 chain, and red arrows indicate yields leaving the 87 mass chain. Data from [3], [65], and [66].

dN Kr = −(λ + λ )N + b λ N + (1 − a )k M (5.13) dt p Kr Kr BrKr Br Br BrKr Br Br

Note that the pump only removes noble gases so only NKr has the pumping term. The initial values of NBr and NKr are their independent yields. As mentioned before, anything decaying to Se has a very short half life so the initial values for Se (NSe and MSe) are cumulative yields. MBr (Br with mass A+1) is slightly more complicated. It is fed by the decay of A+1Se and A+2Se. However, the branching ratio for decaying by βn instead of regular β decay is up to 25%. So the A+2 chain is lumped in with the initial value of MBr. The CHAPTER 5. DATA ANALYSIS 49 initial value is NA+1Br(0) = CYA+1Br − bA+1SeA+1BrCYA+1Se (5.14) The Matlab function dsolve was used to solve the system of equations Eq. 5.9-5.14. dsolve solves differential equations analytically using matrices [71]. First it was performed with the pump turned on (λp=3 min). Then the equations were solved again but with no pump (λp=0), which is what would occur if everything stayed in the target chamber. The results of these two methods were subtracted to find how much Kr was expected to be in RAGS. The result of solving Eq. 5.9-5.14 is the expected amount of Kr observed in RAGS. The absolute number of toms in the RAGS experiments may not match the evaluations. The ratio of atoms from the model (which uses evaluated data) with and without the pumping was used to estimate the amount of Kr left in the target chamber due to Br not completely decaying after the 15 min pumping time. Table 5.5 lists the ratio of Kr (relative to 88Kr) expected to be observed with the effect of the pumping fractionation to the cumulative yield of Kr. To convert the values from Figure 5.11 to cumulative yield ratios, the average of the points in Figure 5.11 is divided by the correction factor for a given isotope listed in Table 5.5. Different evaluations have different independent yields so the model will have different results depending on the evaluation used. To compare the data with a specific evaluation, the pump correction factor must use that evaluation. The factors listed in Table 5.5 are the following ratios:

eqm /eqm CF = i 88 (5.15) CYi/CY88

where CF is the pump correction factor, eqmi is the amount (extrapolated to shot time) of 88 each isotope at time >15 min, eqm88 is the amount of Kr after 15 min, CYi is the cumulative 88 yield of each isotope, and CY88 is the cumulative yield of Kr, which has diﬀerent values depending on the evaluation used. All of the values in Eq. 5.15 are taken from the model and evaluated data. The measured results from RAGS are then divided by the correction factor CF. Most of the precursors for Kr decay quickly so the correction is close to 1, meaning the Br has a short half life and little Kr remains in the target chamber, with the exception of 85mKr. For other elements such as Xe the pumping has more of an impact [72]. Figure 5.13 shows the eﬀect of the precursors and pump on the amount of 85mKr delivered to RAGS. The red line represents the full cumulative yield of 85mKr. Because not all of the 85mKr arrives in RAGS only the blue line is observed. CHAPTER 5. DATA ANALYSIS 50

Table 5.5: Factors to account for pumping speed and duration on Kr collected in RAGS. Uncertainties in these numbers will be discussed in the next chapter. Values close to 1 indicate a short half life of Br.

Isotope E&R correction [3] JEFF 3.1 correction [1] 85m 0.604 0.898 87 1.004 0.996 89 1.017 1.021

Amount of 85mKr in RAGS (assuming no exponential decay of Kr) 1.2

1 Kr in RAGS 0.8 cumulative yield independent yield 0.6

0.4

0.2

0 number of atoms (% from fission) 0 200 400 600 800 1000 1200 time (s) Figure 5.13: Illustration of the eﬀect pumping speed and duration has on 85mKr collected in RAGS. Because the half life of 85Br is non-negligible compared to pumping time, not all 85mKr is transferred to RAGS from the target chamber. 51

Chapter 6

Model Analysis and Fission Yield Determination

The model used to take pumping speed into account is an important part of the analysis and it is necessary to quantify the sensitivity of the model to various parameters. Here the eﬀects of relative distribution of independent yields, pumping time constant, delayed neutrons, and 85mSe treatment will be discussed.

6.1 Distribution of Independent Yields

For this test the independent yields of Br were varied within their error bars so that the cumulative yield of Kr was held constant. This has the most eﬀect early in the sampling time so is most important for the shorter-lived 89Kr and 90Kr.

Table 6.1: Errors of independent yields of Br isotopes [3]

isotope independent yield (%) error 85Br 0.1582 0.1013 87Br 0.9118 0.2918 88Br 1.0603 0.2439 89Br 1.3212 0.3039 90Br 0.9955 0.31857

Figure 6.1a shows the ingrowth of 85mKr as a function of time for different independent yield values of 85Br. In this figure the amount of Kr in RAGS is extrapolated back to t=0 to remove the effects of Kr decay. Because the cumulative yield of Kr is held constant, the final amount of Kr collected in RAGS should be constant if the collection time is long enough to let all Br decay to Kr before the pump shuts off. Since the half life of Br (2.90 min) is non-negligible compared to the collection time (15 min), a change in the amount of Br will affect the final amount of Kr collected. For 87Kr, the half life of Br is 55.65 s, which is shorter CHAPTER 6. MODEL ANALYSIS AND FISSION YIELD DETERMINATION 52

Effect of Varying Yield Distribution on 85mKr Collected in RAGS ) 0 0.6

0.5 Effect of Varying Yield Distribution on 87Kr Collected in RAGS 1.6

0.4 ) 0 1.4 Br IY=0.620 Br IY=0.912 Br IY=1.204 0.3 1.2

0.2 1

0.1 Br IY=0.057 0.8 Br IY=0.158 RAGS atoms Kr (extrapolated to t Br IY=0.259 0.6 0 0 200 400 600 800 1000 0.4 time (s) 0.2 (a) Eﬀect of varying the independent yield RAGS atoms Kr (extrapolated to t 85 85m 0 of Br on the amount of Kr collected 0 200 400 600 800 1000 1200 in RAGS. A change in Br independent yield time (s) is balanced by a change in Kr independent (b) Same as Figure 6.1a but for 87Kr. The yield so that the cumulative yield of Kr re- blue and yellow lines represent the maximum mains constant. The diﬀerent lines show uncertainty in Br independent yield. The the amount of Kr that would be collected in half life of 87Br is shorter than that of 85Br RAGS depending on the independent yields so the 87Kr is less sensitive to variations. of Br. The blue and yellow lines represent the maximum uncertainty in Br independent yield.

compared to the collection time and therefore makes the total Kr collected less sensitive to a change in Br independent yield (Figure 6.1b).

6.2 Pumping Time Constant

From the ingrowth of 135mXe, the pumping time constant was found to be 180±20 s [72]. The effect of pumping speed was determined by only varying the pumping constant (not the independent yield distribution) from 160-200 s. Because of the long-lived 85Br, the amount of 85mKr was most sensitive to variations in pumping speed, with a 5.15% difference from 160 s to 200 s (Table 6.2). As shown in Figure 6.2, the difference in pumping speed is most evident in early time but by the end of the collection period there is only a 2.61% difference between using a half life of 160 s and 200 s. This means that shorter-lived isotopes such as 90Kr (where it has all decayed away by the end of the collection period) are more sensitive to the pumping rate. CHAPTER 6. MODEL ANALYSIS AND FISSION YIELD DETERMINATION 53

Table 6.2: Change in amount of Kr collected by varying the pump time constant from 160-200 s. A * indicates an average is taken from 780-900 s for 89Kr and 120-200 s for 90Kr.

isotope % diﬀ 85m 5.15 87 3.18 88 2.67 89* 3.01 90* 17.22

Effect of Pumping Speed on Kr Collected in RAGS

1.2 Kr 88 1

0.8

0.6 Kr / equilibrium atoms

89 0.4

model t =160s 1/2,p atoms (number of atom extrapolated to t=0) 0.2 model t =180s 1/2,p model t =200s 1/2,p 0 0 200 400 600 800 1000 1200 time (s)

Figure 6.2: Amount of 89Kr collected for 3 different pump speeds. The difference is most pronounced during pumping but the final amount differs by only 2.61% at the end of the collection period.

6.3 Delayed Neutrons

Not all isotopes of Se and Br beta decay 100% to Br and Kr of the same mass, and instead decay via beta and neutron emission to Br or Kr of 1 mass unit smaller. Models with and without delayed neutrons were compared. For the model without delayed neutrons, it was CHAPTER 6. MODEL ANALYSIS AND FISSION YIELD DETERMINATION 54 assumed that every isotope decayed 100% by beta decay. To compare the amount of Kr without taking into account delayed neutrons as a function of time, the initial values of Kr, Br, and Se were adjusted so that the cumulative yield would remain the same whether or not delayed neutrons were taken into account during the decay process. For Br and Kr the new starting value was

IY + (1 − bA+1 ∗ CYA+1) (6.1)

For Kr, IY is the independent yield, bA+1 is the percent of time Kr decays to Br for the A+1 mass chain, and CYA+1 is the cumulative yield of Kr in the A+1 mass chain. The correction for delayed neutrons is a small one because the probability of not decaying by pure beta decay is small (Table 6.3). Table 6.4 shows the diﬀerence between taking the delayed neutrons into account during the entire pumping period vs taking it into account at the beginning and adjusting the independent yields.

Table 6.3: Probability of decaying to another element of the same mass. If the value is 100%, the isotope decays only by β− decay. If the value is less than 100% it partially decays by β− and neutron emission. Data from [7].

mass Se→Br Br→Kr 85 100 100 87 99.64 97.40 88 99.01 93.42 89 92.20 86.20 90 100 74.80

Table 6.4: Diﬀerence from including delayed neutrons as part of independent yields vs throughout pumping interval. The correction is less than 1% for all Kr isotopes studied.

Kr isotope diﬀerence (%) 85m 0 87 0.14 89 0.83

6.4 85mSe

The England and Rider [3] evaluation lists both 85Se and 85mSe as separate isomers with different half lives. In reality 85mSe is not listed in current nuclear data tables [7] and is not present in the JEFF 3.1 evaluation [1]. However, the sum of 85mSe and 85Se from England and Rider is roughly the same as the amount of 85Se quoted by JEFF 6.5. Since 85mSe does CHAPTER 6. MODEL ANALYSIS AND FISSION YIELD DETERMINATION 55 not exist, the England and Rider independent yields for 85mSe and 85Se were summed in the model. Its half life is short compared to its daughter, 85Br, and 9 half lives of 85mSe have passed in the time of one half life of 85Br. Therefore, adding the independent yield of 85mSe to that of 85Se should not have a significant effect on the amount of 85mKr observed in RAGS.

Table 6.5: Independent and cumulative yields from England and Rider [3] and JEFF 3.1 [1].

Isotope Half life IY E&R CY E&R IY JEFF CY JEFF 85mSe 19 s 0.329 ± 0.211 0.344 ± 0.220 0 0 85Se 39 s 0.336 ± 0.215 0.500 ± 0.320 0.601 ± 0.103 0.801 ± 0.103 85Br 2.87 min 0.158 ± 0.101 1.002 ± 4.009e-3 7.72e-4 ± 2.757e-4 0.847 ± 0.108 56

Chapter 7

Results

7.1 Overall Results

Figure 7.1 compares the cumulative yield ratio from this experiment to both the England and Rider and JEFF 3.1 databases. As described previously, an adjustment must be made to the measured ratio to calculate the cumulative yield ratio due to the pumping time. This adjustment is based on the independent yields of Kr and its precursors, which are different depending on which evaluation is used. Therefore a RAGS measurement results in different values of cumulative yield ratio depending on the evaluation used for the pumping correction. In Figure 7.1 RAGS data is shown in green and black. The green points rely on independent yield data from England and Rider, and should be compared to the blue points, which are the England and Rider values for cumulative yield ratios. Similarly, the black points use independent yield data from JEFF 3.1 and should be compared to the red points, which are the JEFF 3.1 evaluated cumulative yield ratios. All cumulative yields are normalized to the 88Kr yield and by definition the yield ratio for 88Kr is 1. As discussed earlier, the RAGS measurement for 85mKr is different from England and Rider because of the inclusion of 85mSe, which does not exist. JEFF 3.1 does not include it and agrees with the RAGS data within error bars. RAGS and the evaluations agree for 87Kr. The RAGS measurements for 89Kr and 90Kr disagree with the evaluations. These are the short-lived isotopes (3.15 min and 32.32 s) and are more sensitive to variations in pumping speed because more half-lives have decayed by the time the pumping period ends, as compared to the isotopes with several-hour half lives. CHAPTER 7. RESULTS 57

Kr Fission Yield Ratios to 88Kr 1.6 RAGS (E&R correction factor) RAGS (JEFF correction factor) 1.4 E&R JEFF 1.2 Kr 88 1

CY / 0.8

0.6

0.4 85mKr 87Kr 88Kr 89Kr 90Kr

Figure 7.1: Cumulative yield ratios from RAGS experiments and evaluations. Different pump correction factors are used to adjust the measured RAGS results to reflect the cumulative yield. The green RAGS results should be compared to the blue England and Rider [3] values. The black RAGS results should be compared to the red JEFF 3.1 [1] values. The small horizontal offsets between clusters of data is for readability.

7.2 85mKr

Figure 7.2 plots the RAGS measurement for each shot (with the pumping correction using JEFF 3.1 independent yields) along with the weighted average and the JEFF value for comparison. Because of the known nuclear data issue with England and Rider, the JEFF value is used for comparison. For the other isotopes in this study, JEFF will be continued to be used for consistency. Since [3] and [1] agree within their error bars, it is only necessary to compare against one evaluation. There is some spread in the data between shots, but with the exception of a few points, it is within error. Most of the uncertainty is due to counting statistics. Because 85Br, which decays to 85mKr, has a 2.9 minute half life, the amount of 85mKr is more sensitive to pumping variations than isotopes such as 87Kr whose precursors have half lives less than a minute. The JEFF value is 13% higher than the RAGS result. CHAPTER 7. RESULTS 58

RAGS results for CY 85mKr / CY 88Kr (JEFF) 0.55

0.5

0.45

0.4

0.35

0.3

0.25

JEFF N150115N150121N150211N150318N150401N150528N150610N150907N151020N151111N160120N160210N160223N160313N160411N160418N160509N160602N160807N160829N160908N161023N170130N170601N170730

RAGS average Figure 7.2: Cumulative yield ratios (relative to 88Kr) measured by RAGS for individual shots. The weighted average is shown in black and JEFF value in red. The 1% error bar for the RAGS value is too small to see on this scale.

7.3 87Kr

The RAGS result for each shot, including a pumping correction using JEFF 3.1 independent yields, is shown in Figure 7.3. The half life of 87Br is 55.65 s, so 87Kr is not as sensitive to variations in pumping speed as 85mKr. The RAGS result is in agreement with the JEFF evaluation and is 7% lower than JEFF. Because the mean is weighted, the error bars are not visible on the graph. Most of the RAGS measurements for individual shots are more precise than the JEFF value. For example, the RAGS value for N150115 has 3% uncertainty, while it is 9% for JEFF. CHAPTER 7. RESULTS 59

RAGS results for CY 87Kr / CY 88Kr (JEFF) 0.95

0.9

0.85

0.8

0.75

0.7

0.65

0.6

0.55

0.5

JEFF N150115N150121N150211N150318N150401N150528N150610N150907N151020N151111N160120N160210N160223N160313N160411N160418N160509N160602N160807N160829N160908N161023N170130N170601N170730

RAGS average Figure 7.3: Cumulative yield ratios (relative to 88Kr) measured by RAGS for individual shots. The weighted average is shown in black and JEFF value in red.

7.4 89Kr

The half life of 89Kr is 3.15 min. When the pump shuts off, 5 half lives have passed, which does not allow 89Kr to be measured easily when no more Kr is being introduced to the system. Therefore an average value is taken from 780-900 s. When time bins of 30 s are used, 5 points are used in the average. Figure 7.4 shows the cumulative yield ratios measured for individual shots, the average, and the JEFF value for comparison. Note there are fewer shots in this figure than in Figures 7.2 and 7.3. This is because certain shots were excluded based on poor-quality data at early times, caused by several factors. The main factor is high count rates at early times, resulting in saturation or high deadtime in the detector. This is either caused by the hardware malfunctioning during the shot, and the collector not moving back from the Cu foam, or a yield predicted to be lower than it was, resulting in the detector distance recipe positioning it too close to the sample. The detectors also had issues with corrosion on the coldhead. The Ge detectors look down on the sample. Condensation was trapped at the interface between the vacuum and room environment. The fittings were corroded, degrading the quality of the vacuum. When this problem was noticed, the detectors were shipped to the vendor for repair. The problem is evident in the spectrum, for example Figure 7.5. For approximately the first hour the low- CHAPTER 7. RESULTS 60 energy channels have no data. Additionally, gain, and thus energy, with the compromised vacuum is unstable. This is presumably related to count rate, and the detectors returned to normal behavior after an hour. This allowed measurement of the isotopes with half lives of several hours but not 89Kr or 90Kr.

RAGS results for CY 89Kr / CY 88Kr (JEFF) 2

1.8

1.6

1.4

1.2

JEFF N150115 N150121 N150401 N150528 N150610 N151020 N160418 N161023 N170601

RAGS average Figure 7.4: Cumulative yield ratios (relative to 88Kr) measured by RAGS for individual shots. The weighted average is shown in black and JEFF value in red.

The average of the shots is 14% higher than the JEFF value but there is a spread in the cumulative yield ratios between shots (p=0.01 calculated using σ dominated by counting statistics). This is not caused by varying collection efficiency because different isotopes of the same element have the same chemical properties and therefore pass through the filter cart and are deposited on the foam with the same efficiency. The pumping speed is the most likely cause of discrepancies between shots. Because the half life is short, the amount collected is sensitive both to variations in the average pumping speed and changes in speed during a single shot. CHAPTER 7. RESULTS 61

Figure 7.5: Example of a shot with a corroded Ge detector. Low-energy channels do not have data for approximately an hour, preventing the measurement of 89Kr and 90Kr.

7.5 90Kr

90Kr also has a short half life (32.32 s) and has completely decayed away by the time Kr is no longer being introduced in RAGS. An average is taken of the ratio from 130-150 s, which is 5 points when 5 second time bins are used. Figure 7.6 shows the cumulative yield ratios measured for individual shots, the average, and the JEFF 3.1 value for reference, which is the same as the England and Rider value within uncertainty. The RAGS result exceeds the JEFF 3.1 evaluation by 17% and the England and Rider evaluation by 15%. There is little data for experimental measurements used in the evaluation of 90Kr yields. For example there is only one independent and one cumulative yield measurement used in [3]. However, there is spread in the RAGS measurements resulting in p=0.003, which could be due to variations in pumping speed. CHAPTER 7. RESULTS 62

RAGS results for CY 90Kr / CY 88Kr (JEFF) 1.9

1.8

1.7

1.6

1.5

1.4

1.3

1.2

JEFF N150115 N150401 N151020 N160418 N160602 N161023 N170130

RAGS average Figure 7.6: Cumulative yield ratios (relative to 88Kr) measured by RAGS for individual shots. The weighted average is shown in black and JEFF value in red.

7.6 Uranium-Doped Capsules

Table 7.1 summarizes the 4 shots with U-doped capsules. The laser energy, recess of the DU layer, and DT neutron yield are listed. The fission yield compares the signal in RAGS of the fission products 137Xe, 138Xe, 139Xe, 87Kr, and 88Kr between shots. For each isotope, the activity (extrapolated to shot time) is calculated, then divided by the DT neutron yield. It is then normalized to a typical DU hohlraum shot. These values are averaged to calculate the fission yield in Table 7.1. The collection efficiency column gives a comparison to 97Zr solid fission products collected on the SRCs. The amount of 97Zr per cm2 collected per DT neutron is normalized to a typical DU hohlraum shot. Hohlraum geometry affects solid fission product collection and N170130 and N170723 had mass added to the hohlraum, which enhances solid collection efficiency. The yields of the U-doped capsules were lower than those of conventional capsules because of surface roughness issues. The U layer had visible microcracks and high low-mode roughness. Figure 7.7 is a plot of the surface height of the capsule at various locations. A normal capsule is over an order of magnitude smoother and is essentially represented by the CHAPTER 7. RESULTS 63

Table 7.1: NIF shots with DU doped into the capsule ablator [73]. Fission yield and collection eﬃciency are normalized to a typical DU hohlraum shot. Fission yield is 137,138,139Xe and 87,88Kr (from RAGS) per 1015 neutrons normalized to DU hohlraum shot. Collection eﬃciency is 97Zr atoms/cm2 (from SRC at 90-315) per 1015 neutrons, normalized to DU hohlraum shot.

laser energy DU recess shot DT yield ﬁssion yield solid collection eﬃciency (MJ) (µm) N150907-003 1.3 10 3.66e14 8.70 0.12 N160210-001 0.9 21 3.84e14 4.54 0.07 N170130-003 0.9 10 1.99e14 6.56 1.53 N170723-001 1.6 10 1.51e14 4-7 1-2 DU hohlraum 1.5 N/A 1e15 1 1

0 line. Even with laser delivery issues, the yield degradation due to laser performance made up 20% or less of the total yield degradation. The yield degradation was consistent with what would be predicted for an undoped capsule of similar surface quality, based on the results of a HYDRA [74] calculation.

Figure 7.7: Measurement of surface roughness in a U-doped capsule. Courtesy General Atomics.

7.7 Comparison to SRCs

SRCs are used to collect solid debris, which includes fission products in addition to target materials. Collection efficiency varies based on target configuration and location of the collector. Collectors can be fielded at 2 equatorial positions and the north pole. Equatorial collection is an order of magnitude more efficient than at the pole [39]. Foils of Nd or Tm CHAPTER 7. RESULTS 64

0.5 mm thick can be placed on the outside of the hohlraum to increase collection efficiency by another order of magnitude [75]. A fundamental difference between RAGS and the SRCs is RAGS measures the geometric average of fissions produced and there is no spatial information. Collection efficiency varies between SRC locations. An advantage to using RAGS is it has a collection efficiency of over 90% [56]. The SRCs have a collection efficiency up to 0.5%. Having larger-area collectors (VADER [40] and LASR [41]) has improved collection. The solid and gaseous fission product yields measured on the same shot are used to determine the 14 MeV fission product yield distribution for the isotope.

7.8 Conclusions and Future Work

From this study, and a similar study on Xe [72], RAGS is an effective high-precision measurement technique for fission product yields for species with half lives greater than 4 min. Measurement of shorter-lived isotopes will be possible with an accurate calibration of pumping speed. Fission product yields are relatively well known for 14 MeV neutrons on 238U. It would be possible to study lesser-known fission product yield distributions by introducing other materials into NIF, such as other isotopes of U, Pu, Th, or Np. If the target has only deuterium and no tritium, 2.45 MeV neutrons can also be used to acquire data at this energy. 65

Appendix A

Gamma Ray Data

Gamma ray data for isotopes used in energy and eﬃciency calibrations. A * indicates an x-ray. Uncertainties are shown after a space or % for the least signiﬁcant digit. For example, 37.2 22 is 37.2 ± 2.2. APPENDIX A. GAMMA RAY DATA 66

A.1 85mKr

85mKr data. From [64].

energy (keV) intensity (%) gammas from IT decay *1.59 0.170 % 6 *12.598 1.15 % 5 *12.651 2.24 % 9 *14.104 0.160 % 7 *14.111 0.311 % 13 *14.311 0.0411 % 17 304.87 2 14.0 % 3

gammas from β− decay *1.69 0.094 % 3 *13.336 0.632 % 25 *13.395 1.22 % 5 *14.952 0.089 % 3 *14.961 0.173 % 7 *15.185 0.0273 % 11 129.81 2 0.301 % 8 151.195 6 75.2 % 5 281.01 4 4E-4 % 4 451.0 1 0.011 % 4 580.6 1 4E-4 % 4 731.6 3 0.008 % 3 APPENDIX A. GAMMA RAY DATA 67

A.2 87Kr

87Kr data. From [65].

energy (keV) intensity (%) 402.588 12 50 % 3 582.32 21 0.035 % 10 673.83 8 1.89 % 10 814.25 6 0.164 % 13 836.38 5 0.77 % 4 845.44 4 7.3 % 4 894.02 13 0.046 % 4 946.69 13 0.129 % 8 976.14 12 0.056 % 5 1175.41 7 1.11 % 7 1338.00 7 0.63 % 5 1382.55 7 0.288 % 17 1389.87 12 0.119 % 8 1461.3 7 0.050 % 6 1531.2 4 ? 0.36 % 6 1578.03 14 0.129 % 12 1611.18 14 0.114 % 16 1740.51 7 2.04 % 11 2011.88 10 2.88 % 18 2378.5 3 0.094 % 7 2408.46 15 0.228 % 23 2554.75 25 9.2 % 6 2558.08 19 4.0 % 3 2652.48 38 0.023 % 4 2811.36 20 0.322 % 22 2961.2 8 0.069 % 20 3055.1 3 0.080 % 8 3308.5 2 0.45 % 3 APPENDIX A. GAMMA RAY DATA 68

A.3 88Kr

88Kr data. X-rays are marked with a *. From [66].

energy (keV) intensity (%) *1.69 0.36 % 3 *13.336 2.40 % 23 *13.395 4.6 % 4 *14.952 0.34 % 3 *14.961 0.66 % 6 *15.185 0.103 % 10 27.513 14 1.96 % 16 28.26 11 0.028 % 10 122.27 6 0.197 % 11 165.98 4 3.10 % 20 168.5 2 0.003 % 3 196.301 10 26.0 % 12 240.71 4 0.253 % 14 268.24 S 0.030 % 311.69 3 0.107 % 9 334.71 3 0.145 % 10 350.04 19 0.017 % 7 362.226 13 2.25 % 12 363.5 5 0.05 % 3 390.543 11 0.64 % 5 391.20 10 0.08 % 4 421.70 18 0.010 % 3 471.80 3 0.73 % 4 500.02 6 0.097 % 8 517.00 8 0.035 % 11 570.57 7 0.062 % 7 573.27 6 0.073 % 8 579.04 14 0.024 % 10 665.94 6 0.087 % 14 677.34 5 0.235 % 18 731.01 9 0.035 % 11 741.34 18 ? 0.035 % 11 774.14 6 0.097 % 15 779.12 8 0.097 % 21 788.28 4 0.53 % 3 790.32 7 0.125 % 12 798.65 21 0.028 % 10 APPENDIX A. GAMMA RAY DATA 69

88Kr data – continued from previous page

energy (keV) intensity (%) 822.01 12 0.090 % 11 834.83 1 13.0 % 6 850.34 5 0.173 % 13 862.327 19 0.67 % 4 879.51 19 0.024 % 7 883.06 14 ? 0.042 % 7 944.92 4 0.294 % 19 950.49 12 0.038 % 11 961.83 6 0.083 % 11 985.780 16 1.31 % 7 990.09 9 0.142 % 19 1039.59 3 0.48 % 3 1049.48 12 0.142 % 12 1090.53 12 0.062 % 14 1141.33 6 1.28 % 7 1179.51 3 1.00 % 5 1184.95 4 0.69 % 4 1209.84 8 0.14 % 3 1212.73 17 0.14 % 5 1245.22 4 0.363 % 24 1250.67 4 1.12 % 6 1298.78 15 0.093 % 21 1303.09 24 0.066 % 24 1324.98 4 0.16 % 4 1335.81 14 0.066 % 11 1352.32 11 0.159 % 22 1369.5 2 1.48 % 9 1406.94 10 0.218 % 20 1464.84 9 0.114 % 15 1518.39 3 2.15 % 11 1529.77 3 10.9 % 5 1603.79 5 0.46 % 3 1661.3 3 0.090 % 21 1685.6 4 0.66 % 8 1793.3 3 ? 0.035 % 14 1892.76 13 ? 0.14 % 3 1908.7 4 0.100 % 15 2029.84 3 4.53 % 23 2035.411 18 3.74 % 20 APPENDIX A. GAMMA RAY DATA 70

88Kr data – continued from previous page

energy (keV) intensity (%) 2186.5 3 0.29 % 6 2195.84 1 13.2 % 6 2231.772 21 3.39 % 17 2259.5 3 ? 0.031 % 14 2352.08 4 0.73 % 4 2364.7 3 0.031 % 14 2392.11 4 34.6 % 16 2408.91 7 0.104 % 11 2548.40 3 0.62 % 3 2771.02 5 0.149 % 10 APPENDIX A. GAMMA RAY DATA 71

A.4 89Kr

89Kr data. From [67].

energy (keV) intensity (%) 79.4 5 ? 0.028 % 4 83.4 6 ? 0.012 % 4 197.1 3 0.50 % 10 197.7 3 1.5 % 3 205.03 20 0.12 % 3 220.948 9 20.1 % 17 242.2 11 0.012 % 8 264.348 14 0.66 % 6 267.7 3 0.084 % 19 286.3 4 0.026 % 8 295.5 7 0.016 % 12 304.7 7 0.022 % 12 318.3 3 0.044 % 14 338.20 10 0.34 % 3 345.03 10 1.19 % 11 354.1 4 ? 0.13 % 3 356.16 9 4.2 % 3 364.88 10 0.90 % 8 369.30 10 1.39 % 12 380.7 3 0.046 % 12 402.25 20 0.32 % 4 411.42 10 2.57 % 21 419.2 3 0.038 % 10 428.5 4 ? 0.11 % 3 438.08 10 0.96 % 8 465.4 5 ? 0.24 % 4 466.13 10 0.80 % 8 468.4 6 ? 0.096 % 25 488.5 6 0.08 % 3 490.76 20 0.32 % 5 497.383 18 6.6 % 7 498.6 2 1.15 % 21 509.1 5 ? 0.15 % 4 523.5 4 0.034 % 12 542.2 5 0.030 % 12 546.9 5 0.030 % 12 557.30 20 0.161 % 19 APPENDIX A. GAMMA RAY DATA 72