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  1. 1. c Copyright by Zachary Paul Meisel, 2010
  2. 2. Simulation of Silicon Detector Response for 69 Kr β-Delayed Proton Emission by Zachary Paul Meisel THESIS Submitted in partial fulfillment of the requirementsfor the degree of Bachelors of Science of Astrophysics in the College of Natural Science of Michigan State University, 2010 East Lansing, Michigan
  3. 3. Simulation of Silicon Detector Response for 69 Kr β-Delayed Proton Emission Zachary Paul Meisel Department of Physics and Astronomy Michigan State University, 2010 Hendrik Schatz, Director of Thesis Research Modern nuclear astrophysics experiments rely on simulations to ensure accurate andefficient data interpretation. Here Monte Carlo simulations have been performed usingthe simulation packages MCNPX, GEANT4, and CASINO to aid in the identification of 69decay branches in the β-delayed proton emission of Kr. Information regarding these 68branches will be used to determine a proton-capture Q-value for Se to determine itsimpact as a waiting point in the astrophysical rapid proton-capture (rp-)process. It is wellknown that waiting points in the rp-process, the dominant mechanism of nucleosynthesisin type-I x-ray bursts, dominate many of the features of the burst’s light curves. Thus 68information on Se will help advance our understanding of this cosmic phenomenon. iii
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  5. 5. AcknowledgmentsThis work was completed with support from the Physics and Astronomy department atMichigan State University, and from the National Science Foundation grants PHY02-16783(JINA) and PHY01-10253(NSCL). Much thanks to my research advisor HendrikSchatz. He has provided me with many unique opportunities to present and discuss myresearch and has also connected me with a superior group of research scientists. I am alsogreatly indebted to Richard Cyburt and Karl Smith, each of whom have provided muchneeded mentoring over the last two years. Additional thanks are certainly due to Marcelodel Santo, Heather Crawford, and Giuseppe Lorusso for helping me with difficulties Iencountered in creating my simulations and to Ana Becerril, Fernando Montes, andSebastian George for useful discussions. v
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  7. 7. ContentsAcknowledgments vForeward xiii1 Introduction to the Study of Nuclear Reactions 1 1.1 The Study of Proton-Rich Nuclei . . . . . . . . . . . . . . . . . . . . . . 3 1.2 The Study of 69 Kr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Importance of Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Astrophysical Motivation 9 2.1 X-Ray Bursts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 RP-Process and Its Waiting Points . . . . . . . . . . . . . . . . . . . . . 133 Simulation Packages 15 3.1 MCNPX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.2 GEANT4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.3 CASINO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 Verification and Validation of Simulations 25 4.1 Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.2 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.2.1 Validation Experiment: 207 Bi Calibration Source . . . . . . . . . . 28 4.2.2 Replication via Simulation . . . . . . . . . . . . . . . . . . . . . . 29 4.2.3 Comparison Between Simulation and Experiment . . . . . . . . . 30 4.3 Potential Further Verification and Validation . . . . . . . . . . . . . . . . 315 Prediction of Experimental Results 35 5.1 69 Kr Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 5.2 Simulation and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 5.3 Future Use of Simulations for Data Analysis . . . . . . . . . . . . . . . . 38 vii
  8. 8. Bibliography 41Appendix: Code 45 5.4 MCNPX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 5.5 GEANT4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 5.5.1 Driver and Compact Macro . . . . . . . . . . . . . . . . . . . . . 47 5.5.2 Header Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 5.5.3 EventAction.hh . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 5.5.4 experimentalHall.hh . . . . . . . . . . . . . . . . . . . . . . . . . 49 5.5.5 experimentalhall Messenger.hh . . . . . . . . . . . . . . . . . . . . 49 5.5.6 Materials.hh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 5.5.7 ME2bDetectorConstruction.hh . . . . . . . . . . . . . . . . . . . . 51 5.5.8 ME2bPhysicsList.hh . . . . . . . . . . . . . . . . . . . . . . . . . 52 5.5.9 ME2bPrimaryGeneratorAction.hh . . . . . . . . . . . . . . . . . . 52 5.5.10 PixelParameterisation.hh . . . . . . . . . . . . . . . . . . . . . . . 53 5.5.11 Results.hh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 5.5.12 RunAction.hh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5.5.13 SiBlock.hh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 5.5.14 SiBlock Messenger.hh . . . . . . . . . . . . . . . . . . . . . . . . . 56 5.5.15 SourceData.hh . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 5.5.16 SteppingAction.hh . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.5.17 SteppingVerbose.hh . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.5.18 TrackerIonHit.hh . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.5.19 TrackerIonSD.hh . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.5.20 TrackerIonSD Messenger.hh . . . . . . . . . . . . . . . . . . . . . 59 5.5.21 VisManager.hh . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 5.5.22 Source Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 5.5.23 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 5.5.24 . . . . . . . . . . . . . . . . . . . . . . . . . . 61 5.5.25 exerimentalHall . . . . . . . . . . . . . . . . . . . . 61 5.5.26 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 5.5.27 . . . . . . . . . . . . . . . . . . . . 62 5.5.28 . . . . . . . . . . . . . . . . . . . . . . . . . . 64 5.5.29 . . . . . . . . . . . . . . . . . . 66 5.5.30 . . . . . . . . . . . . . . . . . . . . . . . 69 5.5.31 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 5.5.32 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.5.33 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.5.34 SiBlock . . . . . . . . . . . . . . . . . . . . . . . . . 74 5.5.35 . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 viii
  9. 9. 5.5.36 . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.5.37 . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5.5.38 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 5.5.39 TrackerIonSD . . . . . . . . . . . . . . . . . . . . . 79 5.5.40 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5.5.41 Sort to Root . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81Curriculum Vitae 89 ix
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  11. 11. List of Figures 1.1 Chart of nuclides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Proposed level scheme 69 Br. . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 NSCL Cyclotrons and A1900 Fragment Separator. . . . . . . . . . . . . . 6 1.4 Produced nuclei expected to reach the detector setup. . . . . . . . . . . . 7 2.1 The Crab Nebula as seen from the Hubble Space Telescope. . . . . . . . 10 2.2 Stellar evolution possibilities. . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3 Artist’s conception of an accreting binary system. . . . . . . . . . . . . . 12 3.1 A minimalistic MCNPX simulation input file. . . . . . . . . . . . . . . . 16 4.1 Near identical initial conditions used for verification simulations. . . . . . 27 4.2 General agreement between MCNPX and GEANT4 verification simulations. 28 4.3 Evidence 976MeV e− can be stopped in 500µm of Si. . . . . . . . . . . . 29 4.4 Engineering drawing of Beta Counting Station[52] . . . . . . . . . . . . . . 30 4.5 Formula and schematic for Compton scattering. . . . . . . . . . . . . . . 31 4.6 Experimental data and GEANT4 simulation comparison for validation. . 32 4.7 Unphysical behavior by MCNPX when simulating an e− in a single Si strip. 33 5.1 Experimental set up for experiment 07025 at the NSCL. . . . . . . . . . 36 5.2 Characteristics of a 14MeV Q-value β + -decay. . . . . . . . . . . . . . . . 38 69 5.3 Summing effect for IAS and proposed ground state decay branch for Kr β-delayed proton emission (blue=proton, red=sum). . . . . . . . . . . . . 39 5.4 Closeup of the summing effect for simulated decay branches. . . . . . . . 40 xi
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  13. 13. Foreward This paper is likely to have readers with various backgrounds in nuclear astrophysics,thus some of the following chapters may be of more interest to a given reader than others.It is the author’s belief that these readers will be of three types: the non-physicist lookingfor an example of an undergraduate’s contribution to the field of nuclear astrophysics,the undergraduate or early graduate student in physics whose task it may be to simulatesilicon detector response, and the specialist who requires information on the simulationsperformed for the NSCL’s experiment 07025. Chapters 1 and 2 are aimed at the firstclass of reader, though the remaining chapters should still be comprehensible. The secondclass of reader may use the first two chapters as a refresher and pay more attention tothe remaining text, where the most valuable sections will likely be chapter 3 and theappendix. The third class of reader will most likely be interested only in chapters 4 and5 as well as the appendix. However these are only suggestions and each section shouldhopefully be comprehensible and perhaps enlightening to the majority of readers. xiii
  14. 14. xiv
  15. 15. Chapter 1Introduction to the Study ofNuclear ReactionsNuclear physics strives to understand the nuclei of the elements that make up our uni-verse. The study of nuclear reactions strives to understand how these nuclei interact.A convenient context in which we speak of nuclei is the chart of nuclides, also knownas a Segr` chart, which is shown in Figure 1.1[1] . The x-axis denotes neutron number eN , the y-axis denotes proton number Z, and the combination of these two gives us theatomic mass A = Z + N . Using these numbers we refer to a nucleus with a given symbolS with the notation A SN . For example, the ultimate nucleus of interest in this study, ZSelenium-68 (A = 68, Z = 34, N = 34), is denoted by 68 Se34 . 34 To describe nuclear reactions, or interactions between nuclei and leptons, we incorpo-rate our notation for individual nuclei. In a nuclear reaction, the participating particlesthat interact are the reactants and the resultant particles after the reaction are theproducts. A convenient way to write the reaction is reactants −→ products.For this study we’ll deal with one or two reactants and two or three products, so insteadthe reaction looks something like A + B −→ C + D.Then, to save space, we condense this notation by placing the heavier reactant and theheavier product, i.e. the nuclei, on the outside of a set of parentheses and place thelighter reactant and product on the inside of these parentheses, separated by a comma.So, our fictitious equation above now looks like, A(B, C)D. Often times we will refer tothe outside reactant as the target and the inside reactant as the beam, but in the context 1
  16. 16. Figure 1.1: Chart of nuclidesof a stellar environment it does not really matter which reactant gets which label. Inthe physical process that occurs in an astrophysical environment, all that matters is thatthe reactants interact to produce the products. The main factors which control whether or not a nuclear reaction will occur arethe temperature of the environment and the density of reactants in the environment.A multitude of nuclear reactions are often possible in similar conditions, meaning thatthey can occur simultaneously. Thus, we could imagine a situation where our fictitiousreactants A and B can interact along side product C interacting with some other reactantE. A + B −→ C + D C + E −→ F + G It doesn’t take much of an extension of this idea to realize that whole networks canform, depleting nuclei of lower mass to build nuclei of higher mass, absorbing and re-leasing energy along the way. Many such networks exist in astrophysical environments.The reaction network of interest in this study is the rapid proton-capture (rp-)process.In the rp-process successively heavier nuclei capture protons (p), releasing energy inthe form of photons (γ). Whenever a nucleus is created that deviates too much fromstability (N = Z for light nuclei), indicated by the black squares in Figure 1.1, thisnucleus undergoes β + decay, where one of its protons changes to a neutron, a positron(e+ ), and an electron neutrino (νe ). One such piece of the rp-reaction chain looks like [33] 2
  17. 17. 34 Cl + p −→ 35 Ar + γ 35 Ar + p −→ 36 K + γ 36 K + p −→ 37 Ca + γ 37 Ca −→ 37 K + e+ + νe .If the above proton capture reactions are faster than decays on the respective nuclei thenthe process can create so called neutron deficient (a.k.a. proton-rich nuclei). Hence thename “rapid” proton-capture process.1.1 The Study of Proton-Rich NucleiWhen classifying nuclei each falls into one of three general classes: stable, proton-rich, orneutron-rich. As you might expect, proton-rich nuclei have more protons than a stablenucleus of the same mass A and neutron-rich nuclei have more neutrons than a stablenucleus of mass A. This begs the question, what makes a nucleus stable? While the nature of stability is much too complicated to be discussed here, it isworthwhile to briefly consider the simple model for a nucleus. In this model protonsand neutrons, generically known as nucleons, are bound together via the strong force,which is roughly 100 times stronger than the Coulomb force that causes protons to repeleach other. The bound nucleons must obey the Pauli principle. That is, since theyhave half-integer quantum spin, they cannot simultaneously occupy the same spatial andspin state[3] . Then if space were at a premium, as in a nucleus, it makes sense that itwould be highly efficient, i.e. energetically favorable, to pair protons and neutrons. Thispairing is observed as a tendency for the line of nuclear stability to stay near N = Z[4] . Keeping in mind that charged protons repel each other due to the Coulomb force,it would be expected that at large A more neutrons are added. As a consequence ofthe previously stated criterion for a bound nucleus, there are far fewer proton-rich nucleithan neutron-rich nuclei. But this does not mean proton-rich nuclei are not interesting. Proton-rich nuclei are the nuclei which are created in explosive hydrogen burningevents, as will be explained in Chapter 2. Hence, it is these nuclei that we must study ifwe are to understand the astrophysical events in which explosive hydrogen burning occurs.While many proton-rich nuclei are created and participate in the rp-process, it would beincredibly time consuming to study them all. So, given guidance from theoretical nuclearastrophysicists, experimental nuclear astrophysicists set out to measure the nuclei ofparticular importance. More information will be given in Chapter 2 as to which nuclei are important in therp-process, but for the moment we can just refer to these as waiting points. Waitingpoints, as the name indicates, are nuclei that delay the flow of the rp-process. Thisstudy will contribute information to the task of finding out how slow one of these waitingpoints, that of 68 Se, is. Though there are theoretical predictions, experiment is needed 3
  18. 18. 69 Figure 1.2: Proposed level scheme verify or falsify the theory. The experiment which this study simulates will add onepiece of the required experimental input. 691.2 The Study of Kr69 Kr (Kr is the symbol for Krypton) is not itself a waiting point nucleus for the rp-process, but it is key in studying the proton capture of 68 Se. It might then be surprisingthat a quick reference of the chart of nuclides, or the periodic table, reveals that thenucleus one unit of Z greater than Selenium’s Z = 34 is Bromine (Br) with Z = 35,and not Krypton (Z = 36). However, recalling that proton capture is a process whichtransforms nuclei as A SN −→ A+1 TN , it becomes apparent that proton-capture on 68 Se Z Z+1creates the (likely) proton-unbound 69 Br[5] . Note that proton capture by 68 Se is still ofinterest because reaction rate timescales are short enough in the explosive astrophysicalenvironments in which the rp-process occurs to allow 69 Br to capture a proton before itexpels the initially captured proton. Being that 69 Br is too short-lived to allow for study in the lab[6] , we instead exploita fortuitous characteristic of 69 Kr. To the advantage of experimental nuclear astrophysi-cists, 69 Kr undergoes β + -decay to become 69 Br. The decay product is so short-lived, thatthe entire decay chain, 69 Kr−→ e+ + νe + 69 Br−→ 68 Se+p is referred to as the β-delayedproton emission of 69 Kr. In a way that will be outlined in Chapter 5, the light chargedproducts of this decay chain, e+ and p, are detected with relative ease. When 69 Kr undergoes β + -decay, it does not necessarily populate the ground state of69 Br. The “state” refers to the total energy of nucleons within the nucleus. A higherstate has more energy. The binding energy, or energy per nucleon, varies from nucleus tonucleus. We can determine this energy from a level scheme and, consequently, determinepossible relevant decays. One possible level scheme for 69 Br is shown in Figure 1.2 [7] .Here the arrows from 69 Kr to levels in 69 Br represent positron emissions of different 4
  19. 19. energies and the arrows from 69 Br levels to 68 Se represent proton emissions of differentenergies. It should be noted that of the shown 69 Br levels, only that labeled IAS isconfirmed to exist[5] . In the experiment which this study (described in more detail in Chapter 5) simulates,the goal is to identify other levels in 69 Br. Due to experimental limitations, Xu et al.were only able to identify β-delayed proton emission involving 69 Br’s isobaric analog state(IAS). As the study was forced to look at a small range in proton energy, they chose tolook at energies that corresponded to the IAS. This is because the majority of β-decaystend to populate the IAS due to its similar level structure [8] , and indeed Xu et al.were able to determine 83% of 69 Kr decays populated the IAS. Therefore, other β-decaybranches, and consequently other proton emission branches, can be expected to occur inthe β-delayed proton emission of 69 Kr. Why not be satisfied with the known decay branch, since it is so dominant? This isanswered simply by relating the excitation energy E of the IAS to its respective tempera-ture T using the well known relation E ∼ kT , where k is Boltzmann’s constant. Insertingthe IAS energy of 4.07MeV (MeV = 1 million electron-volts) provides the rough astro-physical temperature necessary to populate this state: T ∼ 1 × 1010 Kelvin. This over 10times the typical temperature associated with expected rp-process sites[9] , as shown inChapter 2. Given the previously stated information about the levels in 69 Br it is appar-ent that the levels of interest will be at energies below the IAS and that these levels willscarcely be populated. More details on the experimental set-up are given in Chapter 5.1.3 Importance of SimulationsIf we could isolate a single 69 Kr nucleus, observe it decay to 69 Br, and then collectthe proton with our detector system, and repeat this process many times over, thenidentifying new proton branches would be somewhat trivial. However this simple pictureis far from reality. The first detail to be considered is the time between 69 Kr decayingto 69 Br and 69 Br emitting a proton. The second concerns the process by which 69 Kr isproduced and delivered to the detector system. As was stated in the previous subsection, 69 Br is proton-unbound. This means that,upon coming into existence, it almost immediately expels a proton. The only informationon the lifetime of 69 Br is its non-observation, so that its half-life has an upper limit oft 1 < 24 nanoseconds[10] . This means that a positron is emitted and detected in our 2detector system and, on average, less than 24ns later a proton is emitted and detected.However, the time for the electronics to process information on particles detected sothat the information (e.g. the energy they deposited) can be recorded is of the order ofmicroseconds[11] . So we must instead gather the information on the positron and theproton at the same time. This leads to a summing effect that effectively shifts the proton 5
  20. 20. Figure 1.3: NSCL Cyclotrons and A1900 Fragment peak to higher energies. In order to correct for the β summing effect, simulationsare required to evaluate its impact. Once the shift in the energy distribution peak isdetermined, we will be able to more accurately determine the energy of protons emittedin various decay branches. Further complications arise due to the 69 Kr production process. Since 69 Kr has a half-life of 32ms[10] , it must be produced just prior to implantation in the detector system.The process in which it is produced is called fragmentation. In fragmentation a heavyisotope, here 72 Kr, is accelerated as the primary beam and collided into a productiontarget, here Beryllium. These collisions produce many different kinds of isotopes, occa-sionally producing our nucleus of interest. A series of magnets, here the A1900 FragmentSeparator (See Figure 1.3[30] ) then separates out the nucleus of interest, but often theprocess is imperfect and other nuclei make it to the detector system. The simulationwill only simulate the processes of interest, i.e. β-delayed proton emission, thus it shouldhelp in discerning relevant data from the whole. One may wonder how it can be known that simulations are accurately reproducingthe physical conditions of the experiment. This subject is discussed some in Chapter3 and at length in Chapter 4. The main simulation of this project and the experimentit simulates are detailed in Chapter 5. How this simulation will be used to aid in theinterpretation of the experimental results follows this in Chapter 6. 6
  21. 21. Figure 1.4: Produced nuclei expected to reach the detector setup. 7
  22. 22. 8
  23. 23. Chapter 2Astrophysical MotivationSince ancient times humans have been intrigued by the lights that illuminate their night’ssky. For those observing before the invention of telescope, these objects were simplyunchanging points that were static with respect to each other. Once in a very long whilea new light would appear, often shining throughout the day, and then slowly fade out ofexistence. The Crab Nebula (see Figure 2.1[15] ) is a well known example of one of thesetransient lights in the night sky that the Chinese observed in 1054AD. These occurrencesoffered the first clues that these lights were much more than decorations on the ceilingof the celestial sphere. With the invention of the telescope astronomers were able to analyze the lights ofour night sky more detail. The introduction of the fields of spectroscopy, the study oflight’s interaction with matter as a function of wavelength, and spectrometry, the studyof the creation and absorption of light due to atomic and nuclear structure, empoweredastronomers with the quantitative capabilities they have today. Applying these twodisciplines, Suess and Urey [16] were able to determine the relative abundances of thenuclei in our solar system. One year later Burbidge, Burbidge, Fowler, and Hoyle[17] ,and separately Cameron[18] , used this information and that from the then 20 year oldfield of nuclear physics to propose how all of the nuclei in the universe were synthesized.Thus nuclear astrophysicists were provided one of the major foundations of the field. Nuclear astrophysics studies the synthesis of elements in stars and stellar environ-ments and their dispersion into the interstellar medium. It provides us with uniqueinsight into the building blocks of nature, allowing us to study nuclei in environmentsthat are only marginally reproducible on earth. Volumes could be (and have been) filledon the many nucleosynthesis sites extant in our universe, but the remaining discussionwill focus on the main site that is pertinent to this study. This is the astrophysical siteknown as a type-I x-ray burst. 9
  24. 24. Figure 2.1: The Crab Nebula as seen from the Hubble Space Telescope.2.1 X-Ray BurstsType-I x-ray bursts are frequently recurring thermonuclear (driven by temperature de-pendent nuclear reactions) explosions on the surface of an accreting neutron star’s crust[19] .They were first observed in the early to mid-1970s [20][21] , characterized by a steady peakflux of light in the x-ray region (0.01nm ≤ λ ≤ 10nm) with an occasional sharp rise inluminosity followed by an exponential decay. Astrophysics theorist produced sugges-tions as to their underlying cause shortly after a multitude of these observations werepublished[22][23][24] . The essence of these models involves a binary star system in whicha neutron star and a main sequence or giant star revolve around each other, as in Figure2.3. A neutron star is an extremely dense body, mostly composed of neutrons, left behindfrom a massive star’s core-collapse explosion, known a type-II supernova. Main sequencestars synthesize helium from hydrogen in their cores, but are mostly hydrogen. Giantstars have evolved off the main sequence, having burned through most of their corehydrogen, and have an outer envelope made mostly of hydrogen and helium. All starsbegin as main sequence stars and evolve into giant stars. Those that are roughly 8 timesthe mass of the sun (8M⊙ ) and above eventually become type-II supernova. The mainpaths taken in stellar evolution are shown in Figure 2.2[25] . For a typical x-ray burstingsystem the neutron star is a roughly 1.4M⊙ supernova remnant and its companion is agiant star of order 1M⊙ or less. In an x-ray binary system giant star is transferring gas to the neutron star in a processcalled “accretion”. Mass transfer is possible because the giant star has expanded so that 10
  25. 25. Figure 2.2: Stellar evolution possibilities.its gas fills its Roche lobe while overlapping the neutron star’s Roche lobe. The Rochelobe is essentially sphere in which a star’s mass is gravitationally bound [26] . Once masstransfer is initiated gas flows freely from the surface of the giant star to the surface of theneutron star, as shown in Figure 2.3[27] . As a result of accretion, gas rich in hydrogenand helium builds up on the crust of the neutron star. This results in the emission ofx-rays due to the gravitational energy released during accretion in all of these systemsand nearly half also undergo in type-I x-ray bursts [28] . Due to the system’s steady emission of light which peaks in the x-ray portion ofthe spectrum, astrophysicists can infer the temperature of the environment via the wellknown relations hc E= ∼ kT λ (4.1 × 10−21 M eV ∗ s)(3. × 108 m/s) T ∼ −9 −11 ∼ 1. × 108 K, (0.1 × 10 m)(8.6 × 10 M eV /K)where k is Boltzmann’s constant, h is Planck’s constant, and c is the speed of light. A 6 6more realistic approach utilizes Wien’s displacement law, T = 2.9×10λnm∗K = 2.9×10 nm∗K = 0.1nm2.9 × 107 K. While this allows us to calculate the temperature at the surface of the burst-ing site, this temperature must be related to the temperature of the bursting zone viamodels. In general models infer the thickness of a burning layer by calculating how manynuclei, each releasing roughly 5MeV of energy in a given fusion reaction, it would taketo create the observed energy of ∼1038 erg . Observational indications that the site is a sec 11
  26. 26. Figure 2.3: Artist’s conception of an accreting binary system.neutron star, which are beyond the scope of this paper, can be included to arrive at thegeneral conditions for an x-ray burst that can be included in simulations. Why study x-ray bursts? From a statistical point of view x-ray bursts are uniqueastronomical objects in that over 1,000 have been observed from over 40 separate sites[29] . We are thus able to see how bursts vary between binary systems and how the burstsvary within a single system’s recorded bursting history. This allows for the identificationof common features and dependencies of the bursts on things such as the giant star’smass, the giant star’s composition, and the rate of accretion. In astronomy such a robustdata set is very rare, meaning that x-ray bursts are invaluable sources of information. X-ray bursts have the potential to be a wealth of physics information, though muchwork must still be put into understanding them before that wealth can be exploited. Ofparticular interest is the nuclear physics of x-ray bursts that provides input regardingthe neutron star’s radius and its crustal composition. Each of these allows us to learnabout the neutron star structure, which provides information about the equation of stateof dense nuclear matter and consequently about the strong nuclear force [30] . Observingthe effects gravitational redshift has on the thermal emission spectrum of matter beingaccreted onto the neutron star provides information on its mass to radius ratio andstudying the final abundances of nuclei produced by the rp-process indicates what thecrustal composition neutron star would be[19] . However, we will not be able to extractthese parameters with the necessary level of confidence until we have improved our modelsof x-ray bursts[31] , which are very sensitive to nuclear physics data [32] . Currently oneof the main ways to determine which nuclear physics data is of particular importance inx-ray bursts is to determine which data are important in the rp-process. 12
  27. 27. 2.2 RP-Process and Its Waiting PointsThe rp-process is a mechanism of nucleosynthesis in which protons are captured on nucleito create successively heavier proton-rich nuclei. Proton capture can be stalled when anucleus is reached whose proton capture rate is prohibitively small so that it must undergoβ + -decay for the process to continue[33] . The nuclei that cause this occasional stallingare especially interesting because differences in the time the rp-process waits there cancause a large difference in the final abundance of nuclei produced [19] . These nucleiare called “waiting points”. Nuclear physics data combined with nuclear astrophysicalmodels allow us to determine which nuclei are waiting points. Before the rp-process is initiated, the x-ray burst begins due to thermonuclear run-away, a process in which a reaction that is highly sensitive to temperature releases energy,increasing the temperature, thereby increasing the reaction rate and providing positivefeedback [26] . Here runaway is triggered due to the highly temperature sensitive triple-alpha reaction, which ultimately synthesizes 12 C from three 4 He (a.k.a. α). Temperaturesthen rise to initiate α-capture which then provides the energy and seed nuclei necessaryto initiate hydrogen burning for the rp-process [34] . The exact path of the rp-processis highly dependent on temperature and density, particularly regarding capture on lightnuclei due to competition with α-capture induced reactions, but above calcium the rp-process is only determined by proton captures and β-decays[33] . For nuclei in this regionalong the proton drip line, the rp-process is dominated by β-decay lifetime of waitingpoint nuclei [33] . Thus if the process were able to bypass a waiting point nucleus via aproton capture, the path of the rp-process, and consequently the light curve and finalcomposition of the x-ray burst, could be significantly altered[35] . Of the high A nuclei on the rp-process, one that has been identified as a waitingpoint, from β-decay measurements, is 68 Se. However, uncertainties remain in calculatingthe proton capture reaction rate, so it is possible that successive capture of two protonscould allow the rp-process to bypass 68 Se [19] . The issue then is to determine these protoncapture rates on earth. When studying nuclei that are proton-rich we have seen that are short-lived. Beingthat they do not maintain their current proton-rich state for very long, it is apparent thatadding a proton to one of these nuclei is not a simple task. So, to circumvent this issue,we instead study the opposite process. Here this means we study the proton emission of69 Be instead of the proton capture by 68 Se. Though the rates for these processes are farfrom equivalent, the nuclear structure is the same. As the mass difference, given fromnuclear structure, between 69 Br and 68 Se is the most important variable in determiningthe proton-capture Q-value, we attempt to determine 69 Br’s ground state mass. We de-termine this mass by detecting the energy of protons resulting from 69 Br proton emission,which we study by necessity via the β-delayed proton emission of 69 Kr. The method ofdetermining this structure is detailed in Chapter 5. 13
  28. 28. 14
  29. 29. Chapter 3Simulation PackagesThe physics of charged particle interactions in detector systems involves many processesthat are highly sensitive to incident energies, occur on small timescales, and involve smallspatial scales. As a result, modeling this physics requires a simulation code that is ableto take into account large and varied data and implement this data with the smallestpossible spatial and temporal resolution. While creating a personal simulation packagefor such physics is not out of the question, the process would require years of effort toensure a properly working code. Thus, to avoid reinventing the wheel, it is often morepractical to employ previously tested and developed simulation packages. The simulation packages used here were Monte Carlo N-Particle X (MCNPX)[36] ,Geometry and Tracking 4 (GEANT)[37] , and Monte Carlo Simulation of Electron Tra-jectory in Solids (CASINO)[38] . Each of these packages is the result of over a decade ofdevelopment and testing. Also, each is relatively easy to acquire, though MCNPX takessome extra effort. GEANT4 was the primary simulation package used and MCNPX andCASINO were used to verify its results. The following sections will attempt to brieflyexplain the uses and methods of simulation for each package.3.1 MCNPXMCNPX is a simulation package developed by Los Alamos National Laboratory whichhas major updates roughly every 3 years [36] . The version used in this study was MCNPX2.6.0 (package ID:C00740MNYCP02), originally released in April 2008. A copy of thissoftware can be obtained by contacting the Radiation Safety Information ComputationalCenter (RSICC)[39] . However, as MCNPX is a product of the United States Departmentof Energy, it requires paperwork to be submitted and it is advisable that contact withRSICC is initiated by a laboratory or university software representative. The entireprocess can take anywhere between two weeks and one month before the software is inhand. 15
  30. 30. Figure 3.1: A minimalistic MCNPX simulation input file. Additionally, it must be noted that once the MCNPX package has been approvedfor use, the source code is likely to be unavailable for viewing. A user’s manual thatdescribes every aspect of the physics and algorithms employed in the code is provided inaddition to the simulation package. It is generally sufficient in describing what the codecan do and how one can make the code perform specific tasks. It is important to notethat this manual cannot be shown to anyone who does not also have permission to useMCNPX from RSICC under penalty of imprisonment. However, input and output of thesimulations are free to share amongst research colleagues. Regarding input, the simulations in MCNPX are coded in a unique, single-documentenvironment separated by an empty line into three sections: cell, surface, and data. Theinput in each section generally devotes one line of code to specify a given aspect of thesimulation, where each line is referred to as a “card”. Thus a simulation is coded cardby card, where the simplest of simulations could contain as few as 10 cards (A verysimple example is shown in Figure 3.1). In the author’s opinion, a marked advantagehere is simplicity, however the accompanying disadvantage is a general obfuscation of thesimulation’s inner workings. 16
  31. 31. As it is easiest to describe the input cards with an example, Figure 3.1 will be de-scribed beginning at the first line and continuing to the bottom, with some mention ofcards and options for cards that are not shown. While this example fills only 26 lines,including comments, some simulations in this study were over four times this length, un-derlining the importance of ample comments (See Appendix). The example shown firesa neutron 1 × 105 times with an initial direction selected from an isotropic distributioninside the center of a sphere of Oxygen located near a sphere of Iron, all inside a cube ofCarbon, which itself is located inside an infinite vacuum. Data is only recorded regardingthe flux of the neutrons and distance traveled by neutrons within the iron sphere. A given cell card, of which there are four, lists the assigned cell number, numberassigned to a desired material that is defined below, the density of said material, and thevolume of the cell as defined by the surface cards. Negative signs for density indicate units gof cm3 and negative signs for cell surfaces indicate a cell is located within that surface. gThus cell one is Oxygen with a density of 0.0014 cm3 bounded within the spherical surface gnumber seven. Similarly cell two is Iron of density 7.86 cm3 bounded by the spherical gsurface eight. Cell three is Carbon of density 1.6 cm3 bounded within the cube definedby planar surfaces one through six. Finally, cell four is the vacuum that surrounds cellthree. Much more complicated cell volumes could be defined, however these will notbe described here as this work consisted solely of rectangular, spherical, and cylindricalcells. Surface cards, as is evident in the preceding paragraph, describe surfaces that canbe used to construct cells. Unused surfaces will register a warning upon running thesimulation. Surface cards list the assigned surface number, the area type with a labeldefined in the MCNPX user manual, and a sequence of numbers describing coordinateswithin the entire volume required to fully define said surface, also detailed in the usermanual. Surface one is a plane with its normal oriented along the z-axis, as indicatedby “PZ”, at z = −5cm. Here one may be bothered by the introduction of arbitraryaxes, but it is necessary that one make a choice of orientation with the beginning surfacecards and stick to that convention to assure consistency in defining cell cards. Surfacestwo through six are defined in a similar manner to surface one. As a general note, onecould instead define the surfaces of a rectangular prism in one card. Surface seven is asphere, as indicated by “S” with a centroid located at (x,y,z)=(,−4.0cm,−2.5cm)and a radius r = 0.5cm. Surface eight is similarly defined but with centroid coordinates(,,4.5cm). As with the cell cards, much more complicated surfaces are possible,where many examples of these are given in the MCNPX user manual. Whereas the previous cards describe the geometry of the simulation, the data cardsprimarily describe the physics input and output. The importance card, denoted by “IMP”specifies what particle type, here “N” for neutron, to track in which cells. By defaultMCNPX includes all known physical processes relevant to the tracked particle. Physicsrelevant to other particle types could be additionally specified by using the “PHY:” card 17
  32. 32. and its respective options, followed by the symbol for the desired particle, on the linebeneath the “IMP” card. Cell importances are assigned in the order they are definedwith a 1 indicating important and a 0 indicating not important. Note that if the particleof interest must traverse a cell that may be of no interest in order to get to one that isof interest, the traversed cell must still be assigned a 1 so that the particle “makes it” tothe interesting cell. “SDEF” is the source definition card that specifies all of the characteristics of thesimulated source. The source shown here is as simple as it could possible be. In generalthis card will be used with many more options which additionally specify things such asinitial direction, initial energy, and particle type. Directions and energies can be selectedfrom self-defined or predefined functional or discrete distributions. The source here istaken to b a neutron by default since it is the only particle assigned any importanceby the “IMP” card, located at the coordinate (,−4.0cm,−2.5cm). As an additionalcheck, one can specify the cell of the origin to ensure the chosen position is correct, ornearly so. If left undefined, the default directional distribution is isotropic and the defaultinitial energy is particle specific and defined in the MCNPX user manual. The following sets of cards, beginning with “F” and “E” always appear in conjunctionand are referred to as “tallies”. The cards with “F” followed by some number specify thephysics of the source particle to be recorded for output. The letter-number combinationsthat correspond to given data are listed in the MCNPX user manual. Following “F#:” isthe particle type and the cell(s) for which to record this data, as is evident in Figure 3.1.The “E” card indicates how to bin the data that is specified to record, with the numberfollowing “E” denoting which type of recorded data it is binning and the units of saidbinning (usually energy in MeV) being defined for each data type in the MCNPX usermanual. If a given data type as already been binned, the number listed is increased byan increment of ten from the previous “E” card that pertains to this data type (e.g. forF2 one could have cards E2, E12, E22, etc). If one wishes to use the same binning forall “F” cards then the “E0” card is used. The “M” cards specify the materials used to fill various cells in the simulation. If amaterial is specified, but not used a warning will be issued upon running the simulation.The card contains “M” followed by an assigned material number, then the isotope(s)the material is composed, followed by the relative amount of that isotope in the givenmaterial. The elements are specified with six or less numbers were the first three denotethe element and the last three the atomic mass A. If the numbers for A are all zero, theaverage mass of a particular element on earth is used. The total amount of isotopes in agiven material should add up to some multiple of 10, so as to mimic percentages, howeverif they do not the simulation will normalize the total fractional amount to one and issuea warning. Thus material one is fully 16 O, two is mostly 56 Fe with some 54,57,58 Fe, andthree is mostly 12 C with some 13 C. Finally the “NPS” card indicates how many timesthe Monte Carlo simulation will run. Recall that much more complex data cards are 18
  33. 33. possible, however one should consult the MCNPX user manual for such cards. To produce output, one must first source the MCNPX package software with thecommand “source /filepath/”. The simulation is then run with the command “mcnpxi=InputFilename o=OutputFilename. Additional commands can be appended to thisline for a more customized output. Of particular use in the debugging phases is theoption “PRINT”, however this should not be used for long (> 1e4) simulations as itcreates a large output and consequently slows runtime. Visual output, also invaluable indebugging, can be created by loading input files into the VISED[40] software, howeverthis too must be obtained from RSICC. The output of the MCNPX simulation contains many pieces of information, mostare of little interest here, so an attempt will be made to briefly highlight importantoutput quantities. The basic structure of the output is as follows: restate the input,describe the input geometry, describe the specified source, list physical characteristicsof initial group of Monte Carlo simulations, list results of “F” tallies as binned by “E”tallies, list statistical qualities of recorded tallies, and list the total simulation time inhuman units (e.g. actual minutes). A sample output is not pictured here due to itsexcessive length, e.g. 300 lines for the simple input shown. As was stated,a more verboseoutput can be printed, and should be during debugging phases, using the “PRINT”option. Additionally, warnings will be listed after the listed physics input or output thatMCNPX developers think generally require special attention. In practice the outputinitially requires a close reading with the MCNPX manual in hand, so no effort will bemade to describe it any further. Output from simulations performed in this study is notlisted in the appendix due to size, however the author can be contacted if one wishes toconsult a full output file of a simulation presented.3.2 GEANT4GEANT4 is a simulation package developed by users of the CERN facility[41],[42] and ismaintained by the its user community. The installation used here was version 9.1.0, whichwas released in January 2008. GEANT4 software is freely available online, provided oneis able to download a roughly 0.5Gigabyte file. As the code is open source, one is freelyavailable to inspect and alter source code with the caution that the software has beendeveloped and inspected by hundreds of professionals. GEANT4 simulations are coded modularly in a C++ style language, where hundredsof pre-made classes contained in the original software are available for use. Generalknowledge of C++ syntax is not required to create GEANT4 simulations, but it is highlyrecommended. An attempt will be made here to describe the general make-up of a simpleGEANT4 simulation, however due to the modularity of the code the following descriptionwill certainly lack the clarity of that given in the section on MCNPX. All codes described 19
  34. 34. will be located in the appendix. Regarding general modules of the simulation, a main code is run that contains ref-erences to the header files of the primary components of the simulation. These primarycomponents are main geometry, materials used, physics processes included, method inwhich a single simulation iteration is generated, and method in which desired data isrecorded. Each header file contains definitions of included classes as well as references tominor components of the simulation that specify things such as an individual detector’sgeometry or a special method of tracking data in a particular component of the simu-lation. Header files have a corresponding source file which contains instances of classesdefined in the headers. Generally the main code exists in a directory above two sepa-rate directories, include which has the header files and src which has the source files.Throughout the code references are often made to predefined classes that contain infor-mation such as a method of specifying a given geometry or an algorithm to sample aGaussian distribution. Other than this, no pieces of physics, input, or output are pro-vided for the user. As such, the author advises that one begin by working by inspectingand imitating working examples, using references such as the GEANT4 User Support[43] and the doxygen GEANT4 documentation [44] . The main code is the driver for all other codes. It initializes the conditions of thesimulation by calling the main modules of the simulation. The driver constructs thesimulation volume, initializes the method of outputting the results, initializes the physicsto be included, initialize the visualization method, initialize the method of generatinga given simulation event, and finally the simulation event is run. The simulation iscompiled such that it handles a single event. The compiled code is iterated over for auser-specified number of events by a compact macro that will be described after maincode components. Construction of the volumes within the simulation is generally done by a code calledDetectorConstruction, or something similar to this. Within this code each physical com-ponent of the desired simulation is constructed and oriented within an arbitrarily defined“world volume”. It is generally more convenient to reference the components of the sys-tem via separate modules so that one could swap, say, a cylinder made of aluminumwith a rectangle made of lead, by changing a few lines of code. For each componentconstructed, a material is specified to fill the volume, the volume itself is specified viasome shape and central coordinates, and an associated “messenger” class is called. Amessenger class is necessary for any volume through which the particle of interest mightpass on its way to a volume of interest, much like the “IMP” card in MCNPX. Ad-ditionally, for volumes that are detectors which will ultimately “detect” your particle,as the double-sided silicon strip detector in this study, the volume must be specified as“sensitive”. Sensitive volumes require an additional code that specifies what and how totrack in said volume. The method of recording and outputting of results is varied and very loosely defined in 20
  35. 35. GEANT4 documentation. The results code must interface with the code that generatesthe initial source particles as well as the code for the sensitive detector. (The code usedhere, Results, was based on work by Ron Fox.) In this code a hexadecimal value isassigned to variables that indicate the type and initial energy of source particles and thetype and energy of particles that impact a sensitive detector. Prior to printing the stringof assigned variables for an event to an output file, a variable is written indicating thebeginning of an event and, after the string of variables, a variable is written indicatingthe end of an event. This data is sorted into a ROOT readable format by a code that willbe described after the description of the macro that runs the simulation. Note that onedoes not necessarily need to output results in the same manner as described here, butsome method must be employed if one is to go beyond simply visualizing the simulationresults. The physical processes to be included in a simulation are contained in the code calledsomething like PhysicsList. Here the processes in which a source particle can interactwith a detector system are individually listed for each potential particle of interest. Forcertain particle types, like the electron, special “low energy” (< 1MeV) processes can beemployed. The processes are assigned an order to be evaluated and some are executedonly once a particle has dropped below a given kinetic energy. For example, when simu-lating a positron in this study, included are scattering, ionization, bremsstrahlung, and,only once the positron is “at rest”, annihilation. During a single event of a simulation theparticle will move along in steps with the direction of motion being decided in a proba-bilistic (but physical) manner and whose length are specified in GEANT4 documentation(but are changeable). Certain types of processes, e.g. scattering and ionization, can hap-pen at substeps of a given step, while others, e.g. bremsstrahlung, only occur after astep. Additionally, one can specify here at what energy to effectively stop a given par-ticle or simply choose to accept default values. (Here default values were used becausea positron is stopped at 1keV, however the detector thresholds in the actual experimentare no lower than 70keV.) As with simulation results, the method of visualization varies widely amongst GEANT4codes. Here the package VRMLview[45] version 1.0 was used. This package is not nec-essarily recommended, particularly as it is from 1997, however it was used in this studybecause it was available. Regardless of the package employed, a code generally namedVisManager initializes the graphics system and allows it to communicate with the simu-lation as it runs. Creation of a visualization can be turned on or off in the compact macrothat runs the simulation. It is advisable to not create visualizations for simulations ofmore than 1,000 events unless a computer with considerable processor power is employed. Source particles are emitted (“fired”) by a code generally named something like Pri-maryGeneratorAction. This code specifies all of the characteristics of the source. Here asource can be as simple as a monoenergetic electron fired in a single direction, or it canbe made to fully replicate an actual radiation source. If the latter is chosen, one must 21
  36. 36. code all source particles, energies, and their respective probabilities of emission. Whenchoosing this option it is wise to consult the National Nuclear Data Center (NNDC)[46]and to be sure to include only decay branches that have a statistically significant proba-bility of occurring during the total number of simulations run. Regardless of the sourcechosen, one can specify the initial position of the source as well as the direction in whichto fire the source particle, where each could be chosen probabilistically. To compile the code, one must first source the GEANT4 library with the command“source”. and env.csh are two files which exist in the same directoryas the driver. These files contain information on how to compile the GEANT4 code.Before the code is executed one must ensure that their .bashrc file contains the command“export G4WORKDIR=/filepath.” One then runs “make clean”, “make”, and finally“./ExecutableName”. At this point a compact code for a single simulation as been createdwhich typically shares the name of the executable file, but lacks the file extension. The full simulation is finally run using a compact macro, here my vis.mac. This isa short code, typically 10s of lines long, in which it is specified how verbose the outputof the simulation should be, whether or not to create a visualization, and how manysimulation events to perform. The full Monte Carlo simulation is then run with thecommand “./ExecutableName CompactMacro OutputFile”. The contents of the outputfile are specified by the results code. For analysis it is desirable to convert the output into a ROOT[47] -readable format.(There are likely many ways to do this, however the author simply followed an examplecreated by Ron Fox.) This code, generically called something like Sort2Root, initializesa ROOT Tree, its Branches, and their Leafs to bin the data from the OutputFile intohistograms that can be used in analysis. Additionally, this code can be used to applydetector-like resolution by effectively smearing out data bins with some desired distribu-tion. Here this was done by taking each event energy as the centroid of a Gaussian andusing the weighted probability of the Gaussian to select a new energy, finally putting theevent into the corresponding new energy bin. Prior to writing such a code it is advisablethat one gain some familiarity with the ROOT software. Examples of all of the previouslydescribed code will be included in the appendix as they looked for the final performedsimulations. Source code for simpler versions are also available if one wishes to contactthe author.3.3 CASINOCASINO is software created to model the trajectory of electrons in solids, particularly forsituations involving Scanning Electron Microscopoes (SEM)[48] . The code was developedby the research teams at the Universit´ de Sherbrooke[38] and is freely available for edownload online, provided one register for permission on their website. The full source 22
  37. 37. code is available for download, however only the executable graphical user interface (GUI)was used in this study. A simulation in CASINO consists of firing an electron given some initial positionaldistribution with some initial angular distribution directly into a volume of specified sizeand composition. Results from the simulation are given in graphical form and includeinformation such as the energy of backscattered electrons, depth to which electrons pen-etrated, paths electrons followed, and x-rays emitted due to electron interactions. Instudies such as the one performed, CASINO is useful for verifying simulation results bychecking quantities such as the required thickness of a given material to stop an electronof a given energy. One begins creating a simulation by specifying the material composition and thicknessthrough which the electron is to be fired. Multiple layers can be created, however here asingle layer of Silicon was used. The range of electron energies, the positional and angulardistributions of fired electrons, as well as the total number of electron firing events tosimulate are then specified. One then chooses which data to output in graphical form.Next the physics models for different electron energy loss processes and random numbergenerator are chosen. Finally one chooses how many electron trajectories to display andthe simulation is started. The entire process is quite simple to learn and, in the author’sopinion, this simplicity justifies CASINO’s use though its output is limited. 23
  38. 38. 24
  39. 39. Chapter 4Verification and Validation ofSimulationsIn order to properly interpret the results of any experiment in nuclear physics, it is oftennecessary to have an accompanying simulation. Simulations provide insight into theinvolved physical processes and they provide a laboratory in which one can freely changeexperimental conditions and visualized their impact on the results. Here the simulationis required to correct the observed particle energy for β-summing to extract the correctproton energy. However, before a simulation can be used it must be extensively tested toensure it provides results that replicate the system of interest. The processes of testinga simulation are known as verification and validation. Verification is ensuring that a code accurately reproduces the desired theoreticalmodel being used to describe a physical situation. Validation is ensuring that the cho-sen physical model accurately represents the physics of the situation of interest[49] . Inverifying a code one uses methods such as plausibility checks, back of the envelope calcu-lations, rigorous examination of output for known cases, echoing of input upon output,and comparison with codes made for a similar purpose. In validating a code one per-forms a controlled, usually simple, experiment whose results are robust and compares theexperimental results to those of a simulation replicating that experiment. The actionstaken to verify and validate the simulations presented in this study are given below.4.1 VerificationVerification has two main classes: internal verification and external verification. Internalverification checks the output of a given code against its input to ensure the desiredmodel was properly simulated. External verification, or benchmarking, compares theresults of simulations performed with separate codes that have identical, or as identicalas possible, conditions. Internal verification was performed here for the MCNPX and 25
  40. 40. GEANT4 simulators and benchmarking was performed for GEANT4 using MCNPX andCASINO. MCNPX prints a multitude of information in its output files that can be used inverifying a simulation. The first set of information described aids in determining ifthe simulation setup is correct. The input file used to generate a given output file isincluded at the beginning of the output so that it is very clear which simulation led towhich results. Warnings are sometimes listed here when errors are made in constructingthe geometry, though errors that elicit these warnings often stop the simulation fromrunning. The volume, material, and importance of each cell is listed in Print Table 60so that one can be sure their geometry is as intended. Print Table 126 provides theuser with information on the total number of particle interactions occurring in a givencell. While this information doesn’t necessarily indicate the simulation was correct, itcan provide a quick confirmation that something is very wrong, e.g. if a given cell has ananomalously high relative number of interactions. Arguably the most important checkon the simulation setup is the visualization, where the general orientation of objects inthe simulation can be quickly confirmed. A second set of MCNPX output information that can be used for verification indicatesthat statistical validity of the entire Monte Carlo simulation as a whole. While thesechecks do not guarantee statistical validity, they do provide supporting evidence thatan ample amount of events have been run to ensure convergence. The tally information √given includes a statistical error assigned to each bin as N , where N is the numberof counts in a bin. The MCNPX manual suggests that no bin have an error greaterthan 10% and provides near assurance of convergence if no bin has an error greater than1%. These errors are used to provide information following the tallies on the validityof the simulation using 10 statistical checks, which are described in the MCNPX usermanual. In practice final simulations should be run to satisfy all suggested statisticalconditions, however such simulations are computationally expensive. Thus a practicalsolution during development is to reduce the number of events by a factor of 10 forthe initially working simulation until the results no loner agree. Subsequent simulationsrun during development should be run with a much smaller number of events, thoughoccasional checks should be made to ensure these results are convergent with a longersimulation. For example, simulations performed in this study often satisfied all statisticalchecks for 1 × 107 events, but they provided the same results for 1 × 105 events. So manyof the simulations during development were run with the shorter number of events, butthose for final results were run with the greater number of events. While equally thorough verification output is possible with GEANT4, it was notimplemented in this study in order to simplify coding of the output. Internal verificationconsisted mainly of checks with the visualization as well as ensuring the output wasreasonable. An example of reasonable output being roughly even total energy depositionsfor all detector strips in a given hemisphere when the source is isotropic. Another more 26
  41. 41. (a) MCNPX Verification Setup (b) GEANT4 Verification Setup Figure 4.1: Near identical initial conditions used for verification simulations.rigid check is ensuring the energy deposited in a detector is never greater than the initialenergy of the source particle. Once MCNPX and GEANT4 were separately internally verified, GEANT4 was bench-marked with MCNPX. With as identical conditions as possible, several simulations wereperformed. The physical setup of the simulations consisted of an Aluminum cylinder sur-rounding a double-sided Silicon strip detector (DSSD), with a vacuum in the open space.The cylinder has a length l = 16.32cm, inner radius RI = 7.5cm and outer radius RO =7.62cm and the DSSD has dimensions length × width × height = 4cm×4cm×0.05cm,where the long axis of the cylinder and the height of the DSSD are oriented along thez-direction. The plane of the closest cylinder end is 8.27cm from the closest DSSD surfaceand the centroid of the DSSD is at (x,y)=(0,0) with respect to the cylinder’s coordinates.The source is located at the center, (x,y,z)=(0,0,0), of the cylinder emitting monoener-getic electrons isotropically. (See Figure 4.1.) Each verification simulation was carried out with a single electron energy. Energieschosen were 0.481, 0.553, 0.565, 0.975, 1.000, 1.047, 1.059,and 1.682MeV. 1.000MeV waschosen arbitrarily, while the other energies were chosen because they are each includedin the source for the validation experiment. No detector resolution was included in thesimulations. For all energies the simulations had excellent agreement, except for themarked divergence below 0.17MeV, where MCNPX generally had twice the counts ofGEANT4. As an example the counts vs deposited energy are shown for the low, middle,and high initial source energies simulated in Figure 4.2, where each simulation had 1×106initial source events with an overall isotropic distribution. GEANT4 was verified in a very general way with CASINO. As identical simulationconditions could not be reproduced, instead CASINO was used to check if it was plausible 27
  42. 42. (a) 0.481MeV e− (b) 1.000MeV e− (c) 1.682MeV e−Figure 4.2: General agreement between MCNPX and GEANT4 verification simulations.that electrons of a given energy could be stopped in Silicon of a given thickness. Tomimic the DSSD, the material chosen in the CASINO verification simulation was 500µmof Silicon. The initial electron energy was chosen to be 975keV, as this is the energy ofprimary importance in the validation experiment, and the initial angle was chosen to be50◦ , admittedly an extreme case. This simulation confirms that some of these electronscan and are stopped in the Silicon, as is shown by the energy deposited by depth inFigure 4.3. Here it is shown that 90% of the electron’s energy are deposited within thered contour when an electron enters the Silicon at an angle of 50◦ , well within a depthof 500µm, the thickness of the DSSD. (A useful paper for interpreting CASINO plots is[50].)4.2 Validation 2074.2.1 Validation Experiment: Bi Calibration SourceValidation was performed using an experiment whose basic setup was identical to thatdescribed for the verification simulations. The source used was 207 Bi which predominantlyemits electrons with energies 0.481, 0.553, 0.565, 0.976, 1.048, 1.059, and 1.682MeV withprobabilities 13.1, 3.8, 1.3, 60.9, 16.0, 4.7, and 0.2%, respectively[46] , where probabilitiesare normalized to only include these electrons. Electron energies which 207 Bi also emitswere not included due to their small probability of emission. For example, the mostfrequent electron energy that was not simulated is MeV, which is emitted once in every2 × 103 times the 976keV electron is emitted. (See [46] for a full characterization of thesource). The DSSD, a type “BB1” purchased from MicronSemiconductor[51] , was heldup by four aluminum rods which extended from one of the cylinder end caps. The datacollected was relative energy deposited by electrons in the DSSD, which was recorded 28
  43. 43. Figure 4.3: Evidence 976MeV e− can be stopped in 500µm of collecting electron-hole pairs created as the electron passed through the Silicon. Avoltage of 50V was applied across the detector so that charges from all parts of thedetector could be collected. An engineering drawing of the actual setup, without thesurrounding cylinder, is shown in Figure Replication via SimulationIn the simulation many simplifications were made, however it seems they are justified.Source energies mentioned in the previous subsection are not all of the electron energiesemitted by 207 Bi, however other physical energies are emitted with a relatively low proba-bility. Additionally 207 Bi emits photons, but it was found these do not significantly affectthe energy spectra. A full characterization of 207 Bi can be found at [46]. As is apparentfrom comparing Figure 4.4 and 4.1, numerous approximations were made in creating thesimulation geometry. Ultimately only the Aluminum cylinder and the DSSD were in-cluded because it was found that backscattering of electrons off the Aluminum chamberhad little impact on simulation results. So it was then assumed that the aluminum rodssupporting the DSSD would have an even smaller effect. 29
  44. 44. Figure 4.4: Engineering drawing of Beta Counting Station[52] .4.2.3 Comparison Between Simulation and ExperimentIn order to compare data from the validation experiment and simulations of that ex-periment, a calibration had to be performed to the DSSD. This was necessary becausethe energy that is recorded is relative and is binned into “channels”. Channel to energycalibration was performed by M. del Santo by recording the channels the recorded energydeposition for several sources of known energy. M. del Santo additionally performed acalibration using Compton scattering. Here photons from a source that mainly emits aphoton of a given energy is allowed to pass through the DSSD and is detected afterwardby a germanium detector. The change in the photon’s angle and energy is sufficient toobtain the energy imparted to the detector, as is shown schematically in Figure 4.5. The channel to energy calibration ultimately resulted in a 4th order polynomial func-tion that could be applied to the data. Adjustments were also made to the gain appliedto the data and the total number of simulation events was designed such that the totalnumber of recorded events would match the data. The resulting calibration functionapplied to the data in the presented results was Energy(x = Channel) = G ∗ (p0 + p1 ∗ x + p2 ∗ x2 + p3 ∗ x3 + p4 ∗ x4 ), (4.1)where, to two decimal places, G = 8.6 × 102 and p0,1,2,3,4 = 0.0, 4.90 × 10−3 , 2.02 ×10−4 , −6.94 × 10−7 , and 8.15 × 10−10 , respectively. The GEANT4 simulation used forcomparison had 1 × 105 source events, but the resulting data bins were multiplied by afactor of 25 to have the same overall counts. The resulting comparison is shown in Figure4.6. 30
  45. 45. Figure 4.5: Formula and schematic for Compton scattering. Note the general agreement between the GEANT4 simulation and the experimentaldata. Relative count peak heights are reproduced very well as are their profiles. It isapparent that the relative spacing between the two most prominent peaks is not consistentbetween simulation and experiment. This suggests that perhaps adjustments need to bemade to the calibration function or maybe more calibration data is required in the energyrange of interest.4.3 Potential Further Verification and ValidationIdeally more verification and validation checks will be performed to ensure the accuracyof the code. Regarding additional verification of the GEANT4 simulations, there are many options.The first, and perhaps most obvious, would be to upgrade the output so that it includesinformation on the volume and coordinates of simulation components. It would alsobe beneficial to add statistical errors to the output, as it is done in MCNPX, so thatthe statistical validity of a simulation will be more apparent. Arguably the most usefuladditional verification would be benchmarking for more situations and with other codes. Ideally benchmarking would have been performed for a dual positron and protonemission as well, as for β-delayed proton emission, which is the focus of this study.However, it was found that non-physical behaviour occurs for MCNPX when positrons areemitted within a detector of small volume. As an example of nonphysical behavior, notethe double-peaked mean energy deposition for a 1MeV isotropic electron emitting source 31
  46. 46. Figure 4.6: Experimental data and GEANT4 simulation comparison for validation.centrally located within in a DSSD shown in Figure 4.7. These simulations could notbe performed with CASINO as it only simulates the trajectory of electrons in materials.For benchmarking this type of physics, the author has recently become aware of theFLUKA[55],[56] simulation package, which seems well suited due to its versatility andwell developed user support. Regarding additional validation, any number of experiments could be performed. Themost useful experiments would use another discrete electron source or an alpha sourceor a proton beam. An alpha source was not simulated in this study. Being that theproton, for which the alpha calibrates, is generally fully stopped within the DSSD, it wasassumed here that the centroid of its energy distribution would be centered around itsfull energy with a full width half maximum of the detector’s resolution. As experimentalinformation provided this full width half maximum, it seemed unnecessary to performa simulation to confirm this result as the full width half maximum of detector responseis given to the simulation as input. A proton beam was not simulated because it seemsunlikely that the DSSD will be taken to a facility with a proton beam in the near future. 32
  47. 47. 1MeV e- centrally emitted from 0.5 X 1 X 40mm Si strip 600000 1e7 runs, perfect resolution 500000 400000 Counts (total: 1e7) 300000 200000 100000 0 0 0.2 0.4 0.6 0.8 1 Pulse Height (MeV), 10keV binsFigure 4.7: Unphysical behavior by MCNPX when simulating an e− in a single Si strip. 33
  48. 48. 34
  49. 49. Chapter 5Prediction of Experimental ResultsPrior to describing the experiment and simulation that were the focus of this study,the purpose will be briefly rehashed. Recall that the goal is to identify levels in 69 Br,particularly the ground state, that lay below its isobaric analogs state (IAS). The protonemitted from the ground state of 69 Br is of particular interest because it will allow usto determine a ground state mass for the nucleus, which can be used to experimentallyassign a proton capture Q-value to the rp-process waiting point nucleus 68 Se. The methodwhich will be used to measure the proton’s energy is the detection of β-delayed protonemission by 69 Kr, which will inherently sum the energy of the emitted positron with theenergy of the proton, upon detection. The experiment being described to accomplish thistask is scheduled to be performed by Marcelo del Santo, accompanied by the researchgroup of Hendrik Schatz, from May 10 to May 18 (roughly one week from this writing)as experiment 07025 at the National Superconducting Cyclotron Laboratory (NSCL). 695.1 Kr ExperimentAs 69 Kr has a half-life of t 1 = 32ms[46] , it must be produced on site at the NSCL. An ion 2source produces 78 Kr, which is accelerated by the coupled K500 and K1200 cyclotrons[57] ,schematically shown in Figure 1.3, to an energy of 150 Mu (MeV per Nucleon). At 25 eVparticle-nanoamps (pnA), the beam will be fragmented by a Beryllium target to produce69 Kr and along with some contaminants. Most of the contaminants will then be removedas the beam passes through the A1900 fragment separator[30] and the Radio FrequencyFragment Separator[58] (RF Kicker). Finally the beam will pass through three singlesided PIN Silicon detectors and one DSSD, implanting 69 Kr in a second DSSD which hasbehind it a third DSSD and a fourth PIN detector. Collectively these Silicon detectorsare the Beta Counting Station (BCS)[52] . This is shown schematically in Figure 5.1. Notshown is the Segmented Germanium Array (SeGA)[59] which will surround the BCS. 35
  50. 50. Figure 5.1: Experimental set up for experiment 07025 at the NSCL. The data of primary interest in the experiment is the energy deposited in the BCSand SeGA. The BCS will collect energy from positrons and protons resultant from 69 Krβ-delayed proton emission and SeGA will collect energy from photons emitted in thede-excitation of 69 Br. As each system will also detect radiation from background andcontaminants, gates have been devised so that events having decay signals in the BCSand SeGA in coincidence can be isolated so as to effectively remove the majority ofcontaminants and background for decay branches that pass through an excited stateof 69 Br. For the ground state decay branch one would not expect a photon. Workingfrom the assumption that said gating will be effective, the simulation in this study onlyexamines the effects of radiation from β-delayed proton emission in the BCS.5.2 Simulation and ResultsAs was the case for the validation experiment, simplifications were made to approximatethe system of interest. Indeed the setup simulated here is identical to that described insection 4.2.2 and shown in Figure 4.1, with the only difference being the source and itslocation. Here the source is located within the DSSD and emits a positron and then aproton, so as to replicate β-delayed proton emission of 69 Kr. A time delay between thepositron and proton emission is not included, as this time in reality will be undetectableusing the given experimental setup. Any number of decay branches could have been simulated, however here we onlyexamined the decay through the IAS and the lower limit for the ground state of 69 Br.The IAS branch was chosen because it has been previously observed[5] . The ground 36
  51. 51. state decay branch was simulated because extracting its energy is the main goal of theexperiment and the lower limit was chosen because it provides the lowest energy signature,closest to detector threshold, we expect to detect. The simulation goes through the IAS branch 83% of the time, as this was the branch-ing ratio assigned by [5]. Upon selecting the decay branch, the rejection method[53] isused to select the energy of the emitted positron according to its β-spectrum, which isdefined by the decay’s Q-value. Recall that the positrons can have different energies for adecay of a given Q-value because β-decay is a three-body reaction and thus the positronand electron neutrino may divide the total available kinetic energy differently each time(see Figure 5.2). The β-spectrum was calculated using the simple relation[4] dPE dp dE = ξ ∗ dP ∗ dE dp dPE dE = ξ ∗ p2 ∗ (Q − E)2 ∗ dE dp dPE 2 dE = ξ ∗ p ∗ (Q − E) ∗ (E + me )where PE is the probability of emitting a positron of a given kinetic energy, E is anenergy selected randomly from E = 0 to E = Q, Q is the Q-value of the decay, p isthe momentum, me is the mass of a positron, and ξ is a normalization constant[4] thatcontains cancelling units and brings the maximum probability to 1. If PE is greaterthan a random number selected from 0 to a number greater than Pmaximum then thepositron is fired with energy E. A Coulomb correction factor[54] could have been added,however this would require integration of the probability distribution each event and,upon comparison, the distribution was negligibly different for the purposes of this study. Following positron emission, a proton is emitted with an energy in accordance to thedecay branch chosen. Thus, roughly 83% of the time a positron will be emitted with withan energy defined by a 10.069MeV Q-value, followed by a 4.07MeV proton, and the restof the time a positron will be emitted with an energy defined by a 14.019MeV Q-value,followed by a 0.50MeV proton. The simulation result that was primarily investigated was the total energy depositedin the DSSD in a decay event compared to the energy deposited only by the event’sproton. More specifically, the comparison made was the difference between the centroidsof the peaks for these energy deposition distributions, as this is the information used tocorrect for the summing effect. For the results shown (see Figures 5.3 and 5.4) the energydeposited was segmented into 0.035MeV bins and a detector resolution of 0.175MeV,experimentally determined by M. del Santo, was applied at all energies. One can see that the shift in the centroid of the energy deposition distribution dueto β + summing is 0.215MeV for both decay branches. This result indicates that thisshift will apply to all detected protons. Consequently, it seems unnecessary to simulateadditional decay branches until the experiment is performed. Once peaks in energydeposition from β-delayed proton emission are identified in data analysis, subtracting 37
  52. 52. Figure 5.2: Characteristics of a 14MeV Q-value β + -decay.0.215MeV from the peak’s mean value should yield a more accurate proton energy and, inthe case of the ground state decay branch, a more accurate ground state mass of 69 Br thatcan be used to help determine 68 Se’s proton capture Q-value. Note the asymmetric shapeof the summed energy peak. This asymmetry will allow for the disentanglement of thesumming effect from detector resolution, which spreads the energy peak symmetrically,in the analysis of the experimental data.5.3 Future Use of Simulations for Data AnalysisMore simulations will be performed to ensure a swift and accurate data analysis. Regard-ing the 69 Kr simulations, it will be important to simulate various combinations of decaybranches with different energies and ratios until the experimental results are reproduced.Of primary importance is the reproduction of the IAS decay branch, as the energy ofthese protons is known. Additionally, simulations of 22 Si and 23 Si could be performed, asthese β-delayed proton emitters have recently been measured at the NSCL. Regardingall simulations, a significant improvement would be to make the simulation setup morerealistic with the addition of the surrounding DSSDs. It will then be possible to findcorrelations between the implantation location in the central DSSD and the location ofpositron detection in the surrounding DSSDs. Should the results find some group ofstrips in a surrounding DSSD detects a positron more often than others, this informationcan be used to gate on the more relevant strips and consequently speed the analysis 38
  53. 53. 69Figure 5.3: Summing effect for IAS and proposed ground state decay branch for Krβ-delayed proton emission (blue=proton, red=sum).process. Ultimately many more simulations may be performed, however this depends onthe needs of the team involved in data analysis. 39
  54. 54. (a) Ground state decay branch (b) IAS decay branchFigure 5.4: Closeup of the summing effect for simulated decay branches. 40
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  58. 58. [59] sld 2007.pdf This thesis was prepared using the L TEX typesetting language [60, 61]. A[60] L. Lamport, 1985 Addison-Wesley, Boston, “LTEX: A Document preparation Sys- A tem”[61] D. E. Knuth, 1985 Addison-Wesley, Boston, “The TEXbook” 44