A W thesis old - Revision history

Wellali3 at 17:37, 5 May 2015

2015-05-05T17:37:40Z

Wellali3: /* Background contribution to the SNR error */

2015-03-30T19:18:45Z

Background contribution to the SNR error

Wellali3: /* Background contribution to the SNR error */

2015-03-30T19:08:35Z

Background contribution to the SNR error

Wellali3: /* Old Analysis Section */

2015-03-30T19:07:33Z

Old Analysis Section

Wellali3: /* Old Analysis Section */

2015-03-30T19:04:03Z

Old Analysis Section

Show changes

Wellali3: /* Fit method */

2015-03-30T19:03:30Z

Fit method

Wellali3: /* =other */

2014-11-18T19:03:11Z

=other

Wellali3: /* Apparatus */

2014-10-27T16:36:42Z

Apparatus

Wellali3: /* 898 keV signal table */

2014-10-27T16:35:03Z

898 keV signal table

Wellali3: /* Efficiency on 2/28/2014 */

2014-10-13T14:44:51Z

Efficiency on 2/28/2014

← Older revision		Revision as of 17:37, 5 May 2015
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		+	=Results and Conclusion=
		+	This thesis set out to measure the detection limit improvement of coincidence photon activation analysis over the more common photon activation analysis method. By requiring detected photons to be in coincidence, it is thought that the detection limit can be improved over standard PAA. The following sections contain the results obtain performing singles and coincidence counting for PAA.
		+
		+
		+	==Detection Limit of PAA for a Yt-89 foil==
		+
		+
		+
		+	The detection limit represents a quantitative measurement of the lowest number of nuclei that may be observed. This quantity may be expressed in units of parts-per-million (PPM) or in the equivalent units of (<math>\mu g/g</math>).
		+
		+	The concept of photon activation analysis relies on activating a nucleus by using a high energy photon to eject one or more nucleons (protons or neutrons). The nuclei that have had one or more nucleons removed are typically unstable and decay. One can determine this rate of decay in terms of the probability of decay , <math>\lambda.</math>. If I let N(t) represent the number of radioactive nuclei at time t I can estimate the change in this number by
		+
		+	===Radioactive decay===
		+
		+	:<math>N(t) -N(t + \Delta t) = N(t) (\lambda \Delta t)</math>
		+
		+	dividing by <math>\Delta t</math> and taking the limit of <math>\Delta t \rightarrow 0</math>
		+	:<math>\Rightarrow \lim_{\Delta t \rightarrow 0} \frac{N(t+\Delta t) - N(t) }{\Delta t} = \frac{dN}{dt} = - \lambda N(t)</math>
		+
		+	The solution to the above differential is
		+
		+	:<math>N(t) = N_0 e^{\lambda t}</math>
		+
		+	If I want to know the time required until the original number of activated nuclei (<math>N_0</math>) has been cut in half
		+
		+	:<math>\Rightarrow \frac{1}{2} = e^{\lambda t_{1/2}} \Rightarrow t_{1/2} = \frac{\ln 2}{\lambda}</math>
		+
		+	The half life of a decaying nucleus is inversely proportional to the probability of decay.
		+
		+	The activity<math> (A)</math> of a sample of radioactive nuclei is defined as the rate of the decay and is given by
		+
		+	:<math>A = \lambda N(t)</math>
		+
		+	The above has the units of decays per sec , or Bacquerel.
		+
		+	The nucleus Y-88 for example has a half life of 106.6 days. If I measure the activity of the sample at time <math>t</math> then the number of radioactive nuclei at time <math>t</math> is given by
		+
		+
		+	: <math>N= A \frac{t_{1/2}}{\ln 2} = \left ( 1.33 \times 10^7 \mbox {s} \right ) A</math>
		+
		+	where <math>A</math> is the number of measured decays per sec.
		+
		+	The isotope Y-88 was produced by ejecting a neutron from the stable Y-89 nucleus using a photon having more energy enough energy to overcome the binding energy.
		+
		+	Neutron Separation Energy=<math>S_n = B({A \atop Z} X_{N})-B({{A-1} \atop Z} X_{N-1})</math>
		+
		+	<math>B({89 \atop39} Y_{50}) = 775538.048 keV</math>
		+	<math>B({88 \atop39} Y_{49}) = 764061.688 keV</math>
		+	:<math>S_n = B({89 \atop 39} X_{50})-B({{88} \atop 39} Y_{49})=775538.048-764061.688=11.47636</math> MeV
		+	A photon needs to have at least 11.5 MeV of energy to eject one neutron from Y-89.
		+
		+	To determine the number of Y-89 atoms that were converted you need to know the efficiency of the detector (<math>\epsilon</math>), the branching ratio of the photons measured (Br), and the probability of creating Y-88 from Y-89. The detector efficiency for measuring a 898 keV photon using an HpGe detector was (0.7830 +/- 0.0471) % and ( 0.3119 +/- 0.0310) % for 1836.1 keV photons. The Y-88 activity was extrapolated to be 300 Hz using the known half life and the observed efficiency corrected count rate in a HpGe detector. The branching ratio for the 898 keV line is almost unity (95 %) indicating that after irradiation there were 300 Y-88 nuclei decaying per second or
		+	:: <math>N= A \frac{t_{1/2}}{\ln 2} = \left ( 1.33 \times 10^7 \mbox {s} \right ) 300 Hz = 4 \times 10^{9}</math> activated Nuclei.
		+
		+	To determine how many Y-89 atoms had a neutron removed we would need to know what fraction of all the photon induced reaction are single neutron knockout.
		+
		+	The number of atoms in a Yt foil having a mass of <math>0.0496 \pm 0.002</math> g is
		+
		+	: <math>n_{Y-89} = (0.0496 \pm 0.002 g) \times \left ( \frac {1 \mbox{mole}}{88.90585 \mbox{g}}\right ) \times \left ( \frac {6 \times 10^{23} \mbox{atoms}}{ \mbox{mole}}\right ) = 3.35 \times 10^{20}</math> atoms
		+
		+	==Activation efficiency for Y-88==
		+
		+	It is well understood that radioactive materials decay as an exponential function of time. We can therefore use the measured signals of the Y-88 sample fitted to an exponential curve to find the initial number of atoms in the foil. The exponential fit was extrapolated back to the initial time t=0 when the foil was activated. We want to convert this initial rate (Hz) into units of Curie. The half-life of Y-88 is well know, 106.63 days, and was used to calculate the decay constant <math>\lambda</math>. Using the relationship between activity and the number density <math>A=\lambda N</math> we can find <math>N_0</math> for t=0.
		+
		+	The yttrium foil's mass was weighted at the IAC and found to be 0.0288 +/- 0.0002 g. Using Avogadro's number, <math>N_a</math>, and the isotopic mass of Y-89, <math>m_i=88.905848 \frac{g}{mol}</math>, we can plug into the following equation: <math>Number of atoms = \frac{mN_a}{m_i}</math>. The foil is predicted to contain <math>1.95\times 10^{20} \pm 1.35\times 10^{18}</math> atoms of Y-89.
		+
		+	Taking to ratio of <math>N_0</math> and the number of atoms will measure the accelerator beam's efficiency at activating the sample. Using the above number of atoms and using the average <math>N_0</math> found previously, we get a ratio of <math> (19.7 \pm 2.72) \times 10^{-12}</math>.
		+
		+
		+	----------------
		+
		+	During activation of the Y-90 sample, a neutron can be knocked out of the Y-90 nucleus leaving behind the Y-88 nucleus in an excited state. The Y-88 nucleus has a decay half life of 106.63 days. During the irradiation you have two competing processes, the knocking out of a neutron to make Y-88 and the decay of Y-88 while you are activating it.
		+
		+	==Determining the lowest measurable activity==
		+
		+	The lowest activity of Y-88 that the apparatus could measure is predicted by extrapolating the measured signal to noise ratio forward in time until it is zero. The signal to noise ratio fits shown in figureXX.YY were used for this extrapolation. Beyond this point in time, we will not be able to distinguish the signal from the background noise and measurements will no longer be possible with this apparatus. This time for the SNR to be zero was used in the exponential decay function <math>N(t)=N_0e^{-\lambda t}</math> to find the lowest measurable activity, <math> N(t_{final}) </math>. This activity is reported in Table XX.III for singles and coincidence measurements of both photon energies.
		+
		+
	=Apparatus=		=Apparatus=

← Older revision		Revision as of 19:18, 30 March 2015
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	\|}		\|}

		+
		+	=== Singles Efficiency on 2/28/2014 ===
		+
		+	A measurement of the HpGe detectors geometric efficiency for detecting the Y-88 energy lines at 898 keV and 1836.1 keV was performed in order to determine the absolute activity of the sample. The count rate for several sources of known activity was measured by the data acquisition system. Since each sample has decayed since the original calibration by the source vendor, column 4 of tableXX.YY. reports the expected rates from each calibrated sample that were calculated using the half life and the known activity of the standard sources. The characteristic energy peaks from each source was fit to a gaussian distribution. The variance from that fit was used to determine the range of integration for the count rate measurement. The integration energy range was selected to include counts over the energy interval from <math>\bar{E} - (2\sigma+\Delta \sigma)</math> to <math>\bar{E} + (2\sigma+\Delta \sigma)</math>. The measured rates for each calibrated source using the HpGe detector are listed in column 5. The efficiency given by the ratio of the rates in column 5 to the expected rates in column 4 are shown in column 6 of the same table. The percent efficiency of the standard sources was fit to a exponential curve shown in figureXX.YY. The singles efficiency for 898 keV and 1836.1 keV were extrapolated from the exponential equation and are recorded in tableXX.YY. This process was repeated for the NaI detector and the results can be seen in figureXX.YY and tablesXX.YY and XX.YY.
		+
		+
		+	==== HpGe Detector ====
		+
		+	{\| border="1" \|cellpadding="20" cellspacing="0
		+	\|-
		+	\| Run \|\| Source \|\| Energy \|\| Expected rate (Hz) \|\|HpGe Det B Rate (ADC 7) (Hz) \|\| HpGe Eff (%)
		+	\|-
		+	\| 7027 \|\| Na-22 \|\|511 \|\| 1589.218 +/- 49.425 \|\| 18.07 +/- 0.111 \|\| 1.137 +/- 0.0317
		+	\|-
		+	\| 7025 \|\| Cs-137 \|\|661.657 \|\| 2548.03 +/- 80.008 \|\| 25.468+/- 0.172 \|\| 0.9995 +/- 0.0321
		+	\|-
		+	\| 7029 \|\| Mn-54\|\| 834.848 \|\| 41.405 +/- 1.300 \|\| 0.485 +/- 0.014 \|\| 1.171 +/- 0.0427
		+	\|-
		+	\| 7026 \|\| Co-60 \|\| 1173.228\|\| 1876.619 +/- 58.926 \|\| 11.03 +/- 0.106\|\| 0.588 +/- 0.0328
		+	\|-
		+	\| 7027 \|\| Na-22 \|\| 1274.537\|\| 888.264 +/- 27.625 \|\| 4.857 +/- 0.034 \|\| 0.5468 +/- 0.0319
		+	\|-
		+	\| 7026 \|\| Co-60 \|\| 1332.492 \|\| 1878.167 +/- 58.974 \|\| 9.584 +/- 0.023 \|\| 0.510 +/- 0.0315
		+	\|-
		+	\|}
		+
		+
		+	1 Constant 6.36491e-01 4.70444e-02 1.00271e-05 -3.28621e-03
		+	2 Slope -9.81232e-04 5.68236e-05 1.21109e-08 -1.59453e+00
		+
		+
		+
		+	[[File:SingEff_NoMn.png \| 400 px]]
		+
		+
		+
		+	'''Extrapolated Efficiency'''
		+	{\| border="1" \|cellpadding="20" cellspacing="0
		+	\|-
		+	\| Source \|\| Energy \|\| HpGe Eff (%)
		+	\|-
		+	\| Y-88 \|\| 898 \|\| 0.7830 +/- 0.0471
		+	\|-
		+	\| Y-88 \|\| 1836.1 \|\| 0.3119 +/- 0.0310
		+	\|-
		+	\|}
		+
		+	==== NaI Detector ====
		+
		+
		+	{\| border="1" \|cellpadding="20" cellspacing="0
		+	\|-
		+	\| Run \|\| Source \|\| Energy \|\| Expected rate (Hz) \|\| NaI Det B Rate (ADC 7) (Hz) \|\| NaI Eff (%)
		+	\|-
		+	\| 7027 \|\| Na-22 \|\|511 \|\| 1589.218 +/- 49.425 \|\| 14.393 +/- 0.715 \|\| 0.9057 +/- 0.0586
		+	\|-
		+	\| 7025 \|\| Cs-137 \|\|661.657 \|\| 2548.03 +/- 80.008 \|\| 22.8 +/- 0.9154 \|\| 0.8948 +/- 0.0510
		+	\|-
		+	\| 7026 \|\| Co-60 \|\| 1173.228\|\| 1876.619 +/- 58.926 \|\| 7.529 +/- 0.5503 \|\| 0.4012 +/- 0.0796
		+	\|-
		+	\| 7027 \|\| Na-22 \|\| 1274.537\|\| 888.264 +/- 27.625 \|\| 3.654 +/- 0.5266 \|\| 0.4114 +/- 0.1474
		+	\|-
		+	\| 7026 \|\| Co-60 \|\| 1332.492 \|\| 1878.167 +/- 58.974 \|\| 6.784 +/- 0.5345 \|\| 0.3612 +/- 0.0848
		+	\|-
		+	\|}
		+
		+
		+	[[File:SingEffNaI_corrected.png \| 400 px]]
		+
		+
		+	{\| border="1" \|cellpadding="20" cellspacing="0
		+	\|-
		+	\| Source \|\| Energy \|\| NaI Eff (%)
		+	\|-
		+	\| Y-88 \|\| 898 \|\| 0.6262 +/- 0.0246
		+	\|-
		+	\| Y-88 \|\| 1836.1 \|\| 0.2158 +/- 0.0466
		+	\|-
		+	\|}
		+
		+	=== Coincidence Efficiency ===
		+
		+	Unlike the singles efficiency found above, the efficiency for a coincidence measurement relies on the combined efficiency of both detectors. A known Y-88 source was not available to measure the coincidence activity directly. Instead, the HpGe's geometric efficiency for detecting the Y-88 energy lines at 898 keV and 1836.1 keV was combined with the NaI detectors efficiency for the 1836.1 and 898 keV lines respectively. For example, to obtain the 898 keV coincidence efficiency, the HpGe singles efficiency at this energy line is multiplied by the NaI singles efficiency at the 1836.1 keV line. The uncertainties of the singles efficiency are added in quadrature and the resulting values recorded in column 4 of tableXX.YY. The reverse case was applied to find the coincidence efficiency at the 1836.1 keV line and the values are listed in column 4 of tableXX.YY.
		+
		+
		+	{\| border="1" \|cellpadding="20" cellspacing="0
		+	\|-
		+	\| Source \|\| HpGe Singles 898 keV Eff (%) \|\| NaI Singles 1836.1 keV Eff (%) \|\| HpGe Coincidence Eff (%)
		+	\|-
		+	\| Y-88 \|\| 0.7830 +/- 0.0471 \|\| 0.2158 +/- 0.0466 \|\| 0.1690 +/- 0.0663
		+	\|-
		+	\|}
		+
		+
		+	{\| border="1" \|cellpadding="20" cellspacing="0
		+	\|-
		+	\| Source \|\| HpGe Singles 1836.1 keV Eff (%) \|\| NaI Singles 898 keV Eff (%) \|\| HpGe Coincidence Eff (%)
		+	\|-
		+	\| Y-88 \|\| 0.3119 +/- 0.0310 \|\| 0.6262 +/- 0.0246 \|\| 0.1953 +/- 0.0396
		+	\|-
		+	\|}


	[[A_W_thesis]]		[[A_W_thesis]]

← Older revision		Revision as of 19:08, 30 March 2015
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	\|}		\|}

		+
		+	==Systematic error in the SNR==
		+
		+	The singles measurement of the 898 keV peak had an initial high background that decays quickly and was more or less constant for singles measurements take 159 days after irradiation. We assumed that this reflected the presence of activated material with half lives longer that 245 days. As a result the background for the last three measurements was averaged and used in the denominator for the SNR. The first singles measurement has a large background due to activated nuclei with short half lives. This background decreased substantially after about 51 days when the next measurement was taken (the half-life of Y-88 is 106.6 days). The singles background near the 1836 keV line was measured to be around 0.5 Hz and fluctuated less over the experiment compared to the background around the 898 peak. The coincidence measurements had such little background, due to the nature of the apparatus, that the background was averaged over the first three measurements for both the 898 and the 1836 peaks separately. The background for the final coincidence measurements was ignored because of the increased noise produced when the detectors nitrogen dewar was filled during the 5 day background measurement.
		+
		+	[[File:Background_Update.png \| 400 px]]
		+
		+	The systematic uncertainty of the background was not analysed and propagated into the final SNR uncertainty. The signal's total systematic error, described above, was used for the final uncertainty.
		+
		+
		+
		+	'''Signal to Noise Ratio'''
		+	{\| border="1" \|cellpadding="20" cellspacing="0
		+	\|-
		+	\| Energy (keV) \|\| Trig \|\|Variance of Averaged Background
		+	\|-
		+	\| rowspan="2" \| 898 \|\| sing \|\| <math>\pm 39.16%</math>
		+	\|-
		+	\| coin \|\| <math>\pm 50.48%</math>
		+	\|-
		+	\| rowspan="2" \| 1836.1 \|\| sing \|\| N/A
		+	\|-
		+	\| coin \|\| <math>\pm 153.50%</math>
		+	\|-
		+	\|}
		+
		+	The background's systematic error is being ignored.

	==Background contribution to the SNR error==		==Background contribution to the SNR error==

@@ Line 1,098: / Line 1,098: @@
 |-
 |}
 [[A_W_thesis]]

← Older revision		Revision as of 19:03, 30 March 2015
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		+	=Old Analysis Section=

	[[A_W_thesis]]		[[A_W_thesis]]

@@ Line 317: / Line 317: @@
 ==other=
 [[File:Run7204_Y88_898_signalnoise.png | 400 px]]
 [[File:Run7204_Y88_898_signal.png | 400 px]]

← Older revision		Revision as of 16:36, 27 October 2014
Line 1:		Line 1:
	=Apparatus=		=Apparatus=

		+	The coincidence counting set-up and modules path are as follows. A source is set atop a base constructed of hydrogen dense blocks. These were chosen to reduce the number of background energy spikes detected. The source is placed an equal distance from decorator A and detector B.
		+	Detector A is positioned directly above the source. A high-purity germanium detector is being utilized for this set-up. The one outgoing signal enters a ORTEC 673 Spectroscopy Amplifier and the outgoing signal then passes through a CANBERRA CFD 2035A. The signal can then enter an optional CAEN CFD to produce a time delay, or can pass directly into a channel (1) of the Level Translator. The second outgoing signal from the Spec Amp goes to a peak sensing CAEN V785N. The output from this module goes to the DAQ.
		+	Perpendicular from detector A and placed an equal distance from the source is detector B. This detector can either be a NaI-3 or a germanium detector depending on the source being counted. Detector B’s signal goes to a Post Amplifier and one outgoing signal goes to the above mentioned CAEN V785N and also to the DAQ. The second signal enters a CANBERRA CFD 2035A. The outgoing signal goes to a different channel (4) of the same Level Translator. A ribbon cable on the Level Translator module goes to a Time-to-Digital Converter (TDC) CAEN V775 that is operating in common start mode.
		+	Both channels (1 and 4) of the Level Translator outgoing signal pass to a 3-fold Logic Unit which is used in both OR mode and AND mode to see coincidence lines. This data is collected in the Trig DAQ.

	=898 keV signal table=		=898 keV signal table=

@@ Line 1: / Line 1: @@
 =898 keV signal table=
@@ Line 75: / Line 78: @@
 [[File:SNR_898_both2.png | 400 px]]
 =1836 keV signal table=

← Older revision		Revision as of 14:44, 13 October 2014
Line 363:		Line 363:


		+
		+	==== HpGe Detector ====
		+
		+	{\| border="1" \|cellpadding="20" cellspacing="0
		+	\|-
		+	\| Run \|\| Source \|\| Energy \|\| Expected rate (Hz) \|\|HpGe Det B Rate (ADC 7) (Hz) \|\| HpGe Eff (%)
		+	\|-
		+	\| 7027 \|\| Na-22 \|\|511 \|\| 1589.218 +/- 49.425 \|\| 18.07 +/- 0.111 \|\| 1.137 +/- 0.0317
		+	\|-
		+	\| 7025 \|\| Cs-137 \|\|661.657 \|\| 2548.03 +/- 80.008 \|\| 25.468+/- 0.172 \|\| 0.9995 +/- 0.0321
		+	\|-
		+	\| 7029 \|\| Mn-54\|\| 834.848 \|\| 41.405 +/- 1.300 \|\| 0.485 +/- 0.014 \|\| 1.171 +/- 0.0427
		+	\|-
		+	\| 7026 \|\| Co-60 \|\| 1173.228\|\| 1876.619 +/- 58.926 \|\| 11.03 +/- 0.106\|\| 0.588 +/- 0.0328
		+	\|-
		+	\| 7027 \|\| Na-22 \|\| 1274.537\|\| 888.264 +/- 27.625 \|\| 4.857 +/- 0.034 \|\| 0.5468 +/- 0.0319
		+	\|-
		+	\| 7026 \|\| Co-60 \|\| 1332.492 \|\| 1878.167 +/- 58.974 \|\| 9.584 +/- 0.023 \|\| 0.510 +/- 0.0315
		+	\|-
		+	\|}
		+
		+
		+
		+	[[File:SingEff_corrected.png \| 400 px]]
		+
		+
		+	'''Extrapolated Efficiency'''
		+	{\| border="1" \|cellpadding="20" cellspacing="0
		+	\|-
		+	\| Source \|\| Energy \|\| HpGe Eff (%)
		+	\|-
		+	\| Y-88 \|\| 898 \|\| 1.036 +/- 0.0226
		+	\|-
		+	\| Y-88 \|\| 1836.1 \|\| 0.1983 +/- 0.0178
		+	\|-
		+	\|}
		+
		+
		+	=====Exp Fit including Cs-137=====
		+	1 Constant 7.96246e-01 6.78458e-02 6.83891e-05 -2.33206e-03
		+	2 Slope -1.07699e-03 7.10063e-05 7.15739e-08 -2.09517e+00
		+
		+	f(x) = exp(p0+p1*x).
		+
		+	'''Extrapolated Efficiency'''
		+	{\| border="1" \|cellpadding="20" cellspacing="0
		+	\|-
		+	\| Source \|\| Energy \|\| HpGe Eff (%)
		+	\|-
		+	\| Y-88 \|\| 898 \|\| 0.8429 +/- 0.0034
		+	\|-
		+	\| Y-88 \|\| 1836.1 \|\| 0.3069 +/- 0.0192
		+	\|-
		+	\|}
		+
		+
		+	[[File:SingEff_ExpoFit.png \| 400 px]]
		+
		+
		+	{\| border="1" \|cellpadding="20" cellspacing="0
		+	\|-
		+	\| Energy \|\| Trig \|\| <math>N_0</math> (before efficiency)
		+	\|-
		+	\| rowspan="2" \| 898 \|\| sing \|\|1.281e-8 +/- 2.254e-9
		+	\|-
		+	\| coin \|\|6.411e-11 +/- 3.572e-12
		+	\|-
		+	\| rowspan="2" \| 1836.1 \|\| sing \|\|9.634e-9 +/- 1.102e-9
		+	\|-
		+	\| coin \|\|8.147e-11 +/- 2.987e-12
		+	\|-
		+	\|}
		+
		+	=====Exp Fit including all Na-22 points and excluding Mn-54=====
		+
		+	1 Constant 6.36491e-01 4.70444e-02 1.00271e-05 -3.28621e-03
		+	2 Slope -9.81232e-04 5.68236e-05 1.21109e-08 -1.59453e+00
		+
		+
		+	'''Extrapolated Efficiency'''
		+	{\| border="1" \|cellpadding="20" cellspacing="0
		+	\|-
		+	\| Source \|\| Energy \|\| HpGe Eff (%)
		+	\|-
		+	\| Y-88 \|\| 898 \|\| 0.7830 +/- 0.0471
		+	\|-
		+	\| Y-88 \|\| 1836.1 \|\| 0.3119 +/- 0.0310
		+	\|-
		+	\|}
		+
		+
		+	[[File:SingEff_NoMn.png \| 400 px]]
		+
		+	{\| border="1" \|cellpadding="20" cellspacing="0
		+	\|-
		+	\| Energy \|\| Trig \|\| <math>N_0</math> (before efficiency)
		+	\|-
		+	\| rowspan="2" \| 898 \|\| sing \|\|1.281e-8 +/- 2.254e-9
		+	\|-
		+	\| coin \|\|6.411e-11 +/- 3.572e-12
		+	\|-
		+	\| rowspan="2" \| 1836.1 \|\| sing \|\|9.634e-9 +/- 1.102e-9
		+	\|-
		+	\| coin \|\|8.147e-11 +/- 2.987e-12
		+	\|-
		+	\|}

	=== Efficiency on 2/28/2014 ===		=== Efficiency on 2/28/2014 ===