Geant4 Simulations for the Radon Electric Dipole Moment Search at

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Counts 1400 1300 1200 1100 1000 2 χ red = 1.04 f = 1.9999(2) Hz Counts 24000 23000 22000 21000 0 5 10 15 20 25 30 Seconds (500ms Time Bins) 900 800 700 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Seconds (20ms Time Bins) Figure 4.8: The fit to the 416 keV γ-ray time projection presented in Figure 4.5 for two anti-parallel GRIFFIN detectors. The resulting reduced chi-squared indicates a good fit and the precession frequency agrees with the simulated value of 2 Hz. 4.2.2 Fitting Process Precession frequencies were extracted through fitting the data to a representative function and using a χ 2 minimization method [56]. This method utilized a maximum likelihood approach tailored for counting experiments based on Poisson statistics. The function used to fit the data was y = A 2 e −ln(2)x A 1 +A 3 e −x A 4 + { A 7 sin(1A 5 (2πx)+A 6 ) +A 8 sin(3A 5 (2πx)+A 6 )+A 9 sin(5A 5 (2πx)+A 6 )+···}e −x A 4 , (4.2) where A i are the fit parameters. The first term (A 2 e −ln(2)x A 1 ) describes the radioactive decay of the radonnuclei, where A 1 isthe half-lifein seconds andA 2 is theintensity in counts per second. The second term (A 3 e −x A 4 ) describes the average intensity (A 3 ) as a function of the depolarization time (A 4 ). Depending on the shape of γ ray angular 70
distribution, this average intensity can increase or decrease over the depolarization time. The 416 keV M1 transition shown in Figure 4.5(b) clearly illustrates this effect. Even though the number of nuclei inside the cell, and hence the total activity is decreasing, the observed average count rate increases over the depolarization time scale (which is short compared to the 223 Rn half-life of 24.3 minutes). This change in the average count rate occurs because the “donut shaped” distribution depolarizes into an isotropic distribution that has a larger average γ-ray intensity in the plane of the eight GRIFFIN detectors. This effect is further studied in Figures 4.6 and 4.7. The remaining terms describe the precession, where A 5 is the frequency, A 6 is the phase and A 7 , A 8 , A 9 , ··· are the intensities of odd-sine oscillations. A maximum of 14 odd-sine terms were included into the fitting program (up to A 20 ), however, often only the first few odd-sine terms were non-zero. In this case all other sine terms fixed to zero and removed from the fit. Figure 4.8 illustrates the fit to the 416 keV time projection data given in Figure 4.5(b). In the fit the half-life was “fixed” to its simulated value of 1458 seconds and the remaining parameters were left “free” to be fitted by the program. The fit resulted in a good reduced χ 2 of 1.04 and a precession frequency which agrees with the simulated value of 2 Hz. The input precession frequency was 1 Hz, but due to the symmetric nature of the γ-ray angular distribution the observed frequency is twice the input value. The fitted parameters are summarized in Table 4.1. It should be noted that the analyzing power A in Equation 4.1, which that detects a change of counts ∆N = AN, was estimated as A = 0.2 in the calculated statistical limits for the RnEDM experiment [32]. Figure 4.8 validates that estimate as the ratio of the signal amplitude to the background is approximately 0.2. From this single measurement we can calculate the resulting sensitivity in the 71
Page 1 and 2:
GEANT4 SIMULATIONS FOR THE RADON EL
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Dictated but not read. i
Page 5 and 6:
Contents Acknowledgements ii 1 Intr
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4 Results 60 4.1 γ-Ray Spectroscop
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List of Figures 1.1 An illustration
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Chapter 1 Introduction Thesearchfor
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ˆP ր ˆT ց Figure 1.1: An illust
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1.1.1 CP Violation Following the ob
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Figure 1.2: Experimental upper limi
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Figure 1.3: Illustration of the dou
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Chapter 2 RnEDM Experiment at TRIUM
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Figure 2.1: A schematic of the ISAC
Page 25 and 26:
a measurement cell. The RnEDM exper
Page 27 and 28:
NMR techniques, and supplementing s
Page 29 and 30: Occupied Orbitals Fine Structure Hy
Page 31 and 32: energy levels are separated accordi
Page 33 and 34: (σ + ) along the axis of the B fie
Page 35 and 36: atom and absorbed by another. Radia
Page 37 and 38: anaverageof120kHzphotopeakcountrate
Page 39 and 40: Figure 2.7: One GRIFFIN/TIGRESS HPG
Page 41 and 42: (a) One GRIFFIN detector in the HPG
Page 43 and 44: 3.1 Introduction 3.1.1 Previous Wor
Page 45 and 46: energies, branching ratios, emissio
Page 47 and 48: used around the measurement cell in
Page 49 and 50: 3.2.5 Simulated Data Thecodewaswrit
Page 51 and 52: lower its total energy. Internal co
Page 53 and 54: 10000 1000 2 χ red = 1.21 t 1/2 =
Page 55 and 56: as [47] I(E) = G 2π 3 7 c 6 | M i
Page 57 and 58: was to use an average X-ray energy
Page 59 and 60: 1.5 1.4 1.3 1.2 P = 100% P = 75% P
Page 61 and 62: where (a b c d | e f) are Clebsch-G
Page 63 and 64: 2 2 1.5 J i = 5/2, J f = 5/2 J i =
Page 65 and 66: of radius 10 cm, allowing the GRIFF
Page 67 and 68: (a) Screenshot showing the detector
Page 69 and 70: 3.6.2 Output Data and Sort Codes Th
Page 71 and 72: (user-defined option), secondly toa
Page 73 and 74: 30 Absolute Efficiency (%) 25 20 15
Page 75 and 76: 11 10 9 8 7 6 5 4 3 2 1 0 1e+06 Cou
Page 77 and 78: 4.2.1 Multipolarity Effects The sha
Page 79: Figure 4.7: The time projections an
Page 83 and 84: Table 4.1: The fit results for the
Page 85 and 86: 12 10 linear regression: y = 0.2243
Page 87 and 88: 15 Linear Counts (e+04) 10 5 0 1e+0
Page 89 and 90: Chapter 5 Conclusions and Future Di
Page 91 and 92: simulated given sufficient parent a
Page 93 and 94: Appendix A Figure A.1: Simulated de
Page 95 and 96: Figure A.3: Simulated decay scheme
Page 97 and 98: Figure A.5: Simulated decay scheme
Page 99 and 100: 6 out = (1/(1+∆ˆ2))*(f(k,jf,L1,L
Page 101 and 102: 44 return; 45 end 46 if abs(m) > j
Page 103 and 104: 1 % LegendreP.m 2 function P = Lege
Page 105 and 106: 39 xx(i+1,j+1) = r(i+1,1)*sin((i*re
Page 107 and 108: 11 %warning('m1 + m2 + m3 must equa
Page 109 and 110: 23 end 24 % ////////// 25 j1 = J1;
Page 111 and 112: 33 if L1 == L2 && ∆ == 0 34 title
Page 113 and 114: Bibliography [1] J. M. Pendlebury a
Page 115 and 116: [25] P. G. Bricault, M. Dombsky, Je
Page 117: [47] RichardA.Dunlap. An introducti
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